part its amount of metal; and this you may know by weighing the clay
of each part of the mould to which the quantity in the furnace must
correspond. And this is done in order that the furnace for the legs
when filled may not have to furnish metal from the legs to help out
the head, which would be impossible. [Cast at the same casting as
the horse the little door]
[Footnote: The importance of the notes included under this number is
not diminished by the fact that they have been lightly crossed out
with red chalk. Possibly they were the first scheme for some fuller
observations which no longer exist; or perhaps they were crossed out
when Leonardo found himself obliged to give up the idea of casting
the equestrian statue. In the original the first two sketches are
above l. 1, and the third below l. 9.]
711.
THE MOULD FOR THE HORSE.
Make the horse on legs of iron, strong and well set on a good
foundation; then grease it and cover it with a coating, leaving each
coat to dry thoroughly layer by layer; and this will thicken it by
the breadth of three fingers. Now fix and bind it with iron as may
be necessary. Moreover take off the mould and then make the
thickness. Then fill the mould by degrees and make it good
throughout; encircle and bind it with its irons and bake it inside
where it has to touch the bronze.
OF MAKING THE MOULD IN PIECES.
Draw upon the horse, when finished, all the pieces of the mould with
which you wish to cover the horse, and in laying on the clay cut it
in every piece, so that when the mould is finished you can take it
off, and then recompose it in its former position with its joins, by
the countersigns.
The square blocks _a b_ will be between the cover and the core, that
is in the hollow where the melted bronze is to be; and these square
blocks of bronze will support the intervals between the mould and
the cover at an equal distance, and for this reason these squares
are of great importance.
The clay should be mixed with sand.
Take wax, to return [what is not used] and to pay for what is used.
Dry it in layers.
Make the outside mould of plaster, to save time in drying and the
expense in wood; and with this plaster enclose the irons [props]
both outside and inside to a thickness of two fingers; make terra
cotta. And this mould can be made in one day; half a boat load of
plaster will serve you.
Good.
Dam it up again with glue and clay, or white of egg, and bricks and
rubbish.
[Footnote: See Pl. LXXV. The figure "40," close to the sketch in the
middle of the page between lines 16 and 17 has been added by a
collector's hand.
In the original, below line 21, a square piece of the page has been
cut out about 9 centimetres by 7 and a blank piece has been gummed
into the place.
Lines 22-24 are written on the margin. l. 27 and 28 are close to the
second marginal sketch. l. 42 is a note written above the third
marginal sketch and on the back of this sheet is the text given as
No. 642. Compare also No. 802.]
712.
All the heads of the large nails.
[Footnote: See Pl. LXXVI, No. i. This drawing has already been
published in the "_Saggio delle Opere di L. da Vinci_." Milano 1872,
Pl. XXIV, No. i. But, for various reasons I cannot regard the
editor's suggestions as satisfactory. He says: "_Veggonsi le
armature di legname colle quali forse venne sostenuto il modello,
quando per le nozze di Bianca Maria Sforza con Massimiliano
imperatore, esso fu collocato sotto un arco trionfale davanti al
Castello_."
713.
These bindings go inside.
714.
Salt may be made from human excrements, burnt and calcined, made
into lees and dried slowly at a fire, and all the excrements produce
salt in a similar way and these salts when distilled, are very
strong.
[Footnote: VASARI repeatedly states, in the fourth chapter of his
_Introduzione della Scultura_, that in preparing to cast bronze
statues horse-dung was frequently used by sculptors. If,
notwithstanding this, it remains doubtful whether I am justified in
having introduced here this text of but little interest, no such
doubt can be attached to the sketch which accompanies it.]
715.
METHOD OF FOUNDING AGAIN.
This may be done when the furnace is made [Footnote: this note is
written below the sketches.] strong and bruised.
Models for the horse of the Sforza monument (716-718).
7l6.
Messer Galeazzo's big genet
717.
Messer Galeazzo's Sicilian horse.
[Footnote: These notes are by the side of a drawing of a horse with
figured measurements.]
718.
Measurement of the Sicilian horse the leg from behind, seen in
front, lifted and extended.
[Footnote: There is no sketch belonging to this passage. Galeazze
here probably means Galeazze di San Severino, the famous captain who
married Bianca the daughter of Ludovico il Moro.]
Occasional references to the Sforza monument (719-724).
719.
Again, the bronze horse may be taken in hand, which is to be to the
immortal glory and eternal honour of the happy memory of the prince
your father, and of the illustrious house of Sforza.
[Footnote: The letter from which this passage is here extracted will
be found complete in section XXI. (see the explanation of it, on
page 2).]
720.
On the 23rd of April 1490 I began this book, and recommenced the
horse.
721.
There is to be seen, in the mountains of Parma and Piacenza, a
multitude of shells and corals full of holes, still sticking to the
rocks, and when I was at work on the great horse for Milan, a large
sackful of them, which were found thereabout, was brought to me into
my workshop, by certain peasants.
722.
Believe me, Leonardo the Florentine, who has to do the equestrian
bronze statue of the Duke Francesco that he does not need to care
about it, because he has work for all his life time, and, being so
great a work, I doubt whether he can ever finish it. [Footnote: This
passage is quoted from a letter to a committee at Piacenza for whom
Leonardo seems to have undertaken to execute some work. The letter
is given entire in section XXL; in it Leonardo remonstrates as to
some unreasonable demands.]
723.
Of the horse I will say nothing because I know the times. [Footnote:
This passage occurs in a rough copy of a letter to Ludovico il Moro,
without date (see below among the letters).]
724.
During ten years the works on the marbles have been going on I will
not wait for my payment beyond the time, when my works are finished.
[Footnote: This possibly refers to the works for the pedestal of the
equestrian statue concerning which we have no farther information in
the MSS. See p. 6.]
The project of the Trivulzio monument.
725.
THE MONUMENT TO MESSER GIOVANNI JACOMO DA TREVULZO.
[2] Cost of the making and materials for the horse [5].
[Footnote: In the original, lines 2-5, 12-14, 33-35, are written on
the margin. This passage has been recently published by G. Govi in
Vol. V, Ser. 3a, of _Transunti, Reale Accademia dei Linea, sed. del
5 Giugno, 1881,_ with the following introductory note: _"Desidero
intanto che siano stampati questi pochi frammenti perche so che sono
stati trascritti ultimamente, e verranno messi in luce tra poco
fuori d'Italia. Li ripubblichi pure chi vuole, ma si sappia almeno
che anche tra noi si conoscevano, e s'eran raccolti da anni per
comporne, quando che fosse, una edizione ordinata degli scritti di
Leonardo."_
The learned editor has left out line 22 and has written 3 _pie_ for
8 _piedi_ in line 25. There are other deviations of less importance
from the original.]
A courser, as large as life, with the rider requires for the cost of
the metal, duc. 500.
And for cost of the iron work which is inside the model, and
charcoal, and wood, and the pit to cast it in, and for binding the
mould, and including the furnace where it is to be cast ... duc.
200.
To make the model in clay and then in wax......... duc. 432.
To the labourers for polishing it when it is cast. ....... duc. 450.
in all. . duc. 1582.
[12] Cost of the marble of the monument [14].
Cost of the marble according to the drawing. The piece of marble
under the horse which is 4 braccia long, 2 braccia and 2 inches wide
and 9 inches thick 58 hundredweight, at 4 Lire and 10 Soldi per
hundredweight.. duc. 58.
And for 13 braccia and 6 inches of cornice, 7 in. wide and 4 in.
thick, 24 hundredweight....... duc. 24.
And for the frieze and architrave, which is 4 br. and 6 in. long, 2
br. wide and 6 in. thick, 29 hundredweight., duc. 20.
And for the capitals made of metal, which are 8, 5 inches in. square
and 2 in. thick, at the price of 15 ducats each, will come to......
duc. 122.
And for 8 columns of 2 br. 7 in., 4 1/2 in. thick, 20 hundredweight
duc. 20.
And for 8 bases which are 5 1/2 in. square and 2 in. high 5 hund'..
duc. 5.
And for the slab of the tombstone 4 br. io in. long, 2 br. 4 1/2 in.
wide 36 hundredweight....... duc. 36.
And for 8 pedestal feet each 8 br. long and 6 1/2 in. wide and 6 1/2
in. thick, 20 hundredweight come to... duc. 20.
And for the cornice below which is 4 br. and 10 in. long, and 2 br.
and 5 in. wide, and 4 in. thick, 32 hund'.. duc. 32.
And for the stone of which the figure of the deceased is to be made
which is 3 br. and 8 in. long, and 1 br. and 6 in. wide, and 9 in.
thick, 30 hund'.. duc. 30.
And for the stone on which the figure lies which is 3 br. and 4 in.
long and 1 br. and 2 in., wide and 4 1/2 in. thick duc. 16.
And for the squares of marble placed between the pedestals which are
8 and are 9 br. long and 9 in. wide, and 3 in. thick, 8
hundredweight . . . duc. 8. in all. . duc. 389.
[33]Cost of the work in marble[35].
Round the base on which the horse stands there are 8 figures at 25
ducats each ............ duc. 200.
And on the same base there are 8 festoons with some other ornaments,
and of these there are 4 at the price of 15 ducats each, and 4 at
the price of 8 ducats each ....... duc. 92.
And for squaring the stones duc. 6.
Again, for the large cornice which goes below the base on which the
horse stands, which is 13 br. and 6 in., at 2 due. per br. ......
duc. 27.
And for 12 br. of frieze at 5 due. per br. ........... duc. 60.
And for 12 br. of architrave at 1 1/2 duc. per br. ....... duc. 18.
And for 3 rosettes which will be the soffit of the monument, at 20
ducats each .......... duc. 60.
And for 8 fluted columns at 8 ducats each ......... duc. 64.
And for 8 bases at 1 ducat each, duc. 8.
And for 8 pedestals, of which 4 are at 10 duc. each, which go above
the angles; and 4 at 6 duc. each .. duc. 64.
And for squaring and carving the moulding of the pedestals at 2 duc.
each, and there are 8 .... duc. 16.
And for 6 square blocks with figures and trophies, at 25 duc. each
.. duc. 150.
And for carving the moulding of the stone under the figure of the
deceased .......... duc. 40.
For the statue of the deceased, to do it well .......... duc. 100.
For 6 harpies with candelabra, at 25 ducats each ......... duc. 150.
For squaring the stone on which the statue lies, and carving the
moulding ............ duc. 20.
in all .. duc. 1075.
The sum total of every thing added together amount to ...... duc.
3046.
726.
MINT AT ROME.
It can also be made without a spring. But the screw above must
always be joined to the part of the movable sheath: [Margin note:
The mint of Rome.] [Footnote: See Pl. LXXVI. This passage is taken
from a note book which can be proved to have been used in Rome.]
All coins which do not have the rim complete, are not to be accepted
as good; and to secure the perfection of their rim it is requisite
that, in the first place, all the coins should be a perfect circle;
and to do this a coin must before all be made perfect in weight, and
size, and thickness. Therefore have several plates of metal made of
the same size and thickness, all drawn through the same gauge so as
to come out in strips. And out of [24] these strips you will stamp
the coins, quite round, as sieves are made for sorting chestnuts
[27]; and these coins can then be stamped in the way indicated
above; &c.
[31] The hollow of the die must be uniformly wider than the lower,
but imperceptibly [35].
This cuts the coins perfectly round and of the exact thickness, and
weight; and saves the man who cuts and weighs, and the man who makes
the coins round. Hence it passes only through the hands of the
gauger and of the stamper, and the coins are very superior.
[Footnote: See Pl. LXXVI No. 2. The text of lines 31-35 stands
parallel 1. 24-27.
Farther evidence of Leonardo's occupations and engagements at Rome
under Pope Leo X. may be gathered from some rough copies of letters
which will be found in this volume. Hitherto nothing has been known
of his work in Rome beyond some doubtful, and perhaps mythical,
statements in Vasari.]
727.
POWDER FOR MEDALS.
The incombustible growth of soot on wicks reduced to powder, burnt
tin and all the metals, alum, isinglass, smoke from a brass forge,
each ingredient to be moistened, with aqua vitae or malmsey or
strong malt vinegar, white wine or distilled extract of turpentine,
or oil; but there should be little moisture, and cast in moulds.
[Margin note: On the coining of medals (727. 728).] [Footnote: The
meaning of _scagliuolo_ in this passage is doubtful.]
728.
OF TAKING CASTS OF MEDALS.
A paste of emery mixed with aqua vitae, or iron filings with
vinegar, or ashes of walnut leaves, or ashes of straw very finely
powdered.
[Footnote: The meaning of _scagliuolo_ in this passage is doubtful.]
The diameter is given in the lead enclosed; it is beaten with a
hammer and several times extended; the lead is folded and kept
wrapped up in parchment so that the powder may not be spilt; then
melt the lead, and the powder will be on the top of the melted lead,
which must then be rubbed between two plates of steel till it is
thoroughly pulverised; then wash it with aqua fortis, and the
blackness of the iron will be dissolved leaving the powder clean.
Emery in large grains may be broken by putting it on a cloth many
times doubled, and hit it sideways with the hammer, when it will
break up; then mix it little by little and it can be founded with
ease; but if you hold it on the anvil you will never break it, when
it is large.
Any one who grinds smalt should do it on plates of tempered steel
with a cone shaped grinder; then put it in aqua fortis, which melts
away the steel that may have been worked up and mixed with the
smalt, and which makes it black; it then remains purified and clean;
and if you grind it on porphyry the porphyry will work up and mix
with the smalt and spoil it, and aqua fortis will never remove it
because it cannot dissolve the porphyry.
If you want a fine blue colour dissolve the smalt made with tartar,
and then remove the salt.
Vitrified brass makes a fine red.
729.
STUCCO.
Place stucco over the prominence of the..... which may be composed
of Venus and Mercury, and lay it well over that prominence of the
thickness of the side of a knife, made with the ruler and cover this
with the bell of a still, and you will have again the moisture with
which you applied the paste. The rest you may dry [Margin note: On
stucco (729. 730).] [Footnote: In this passage a few words have been
written in a sort of cipher--that is to say backwards; as in l. 3
_erenev_ for _Venere_, l. 4 _oirucrem_ for Mercurio, l. 12 _il
orreve co ecarob_ for _il everro (?) co borace_. The meaning of the
word before _"di giesso"_ in l. 1 is unknown; and the sense, in
which _sagoma_ is used here and in other passages is obscure.--
_Venere_ and _Mercurio_ may mean 'marble' and 'lime', of which
stucco is composed.
12. The meaning of _orreve_ is unknown.]
well; afterwards fire it, and beat it or burnish it with a good
burnisher, and make it thick towards the side.
STUCCO.
Powder ... with borax and water to a paste, and make stucco of it,
and then heat it so that it may dry, and then varnish it, with fire,
so that it shines well.
730.
STUCCO FOR MOULDING.
Take of butter 6 parts, of wax 2 parts, and as much fine flour as
when put with these 2 things melted, will make them as firm as wax
or modelling clay.
GLUE.
Take mastic, distilled turpentine and white lead.
On bronze casting generally (731-740).
731.
TO CAST.
Tartar burnt and powdered with plaster and cast cause the plaster to
hold together when it is mixed up again; and then it will dissolve
in water.
732.
TO CAST BRONZE IN PLASTER.
Take to every 2 cups of plaster 1 of ox-horns burnt, mix them
together and make your cast with it.
733.
When you want to take a cast in wax, burn the scum with a candle,
and the cast will come out without bubbles.
734.
2 ounces of plaster to a pound of metal;-- walnut, which makes it
like the curve.
[Footnote: The second part of this is quite obscure.]
735.
[Dried earth 16 pounds, 100 pounds of metal wet clay 20,--of wet
100,-half,- which increases 4 Ibs. of water,--1 of wax, 1 Ib. of
metal, a little less,-the scrapings of linen with earth, measure for
measure.] [Footnote: The translation is given literally, but the
meaning is quite obscure.]
736.
Such as the mould is, so will the cast be.
737.
HOW CASTS OUGHT TO BE POLISHED.
Make a bunch of iron wire as thick as thread, and scrub them with
[this and] water; hold a bowl underneath that it may not make a mud
below.
HOW TO REMOVE THE ROUGH EDGES FROM BRONZE.
Make an iron rod, after the manner of a large chisel, and with this
rub over those seams on the bronze which remain on the casts of the
guns, and which are caused by the joins in the mould; but make the
tool heavy enough, and let the strokes be long and broad.
TO FACILITATE MELTING.
First alloy part of the metal in the crucible, then put it in the
furnace, and this being in a molten state will assist in beginning
to melt the copper.
TO PREVENT THE COPPER COOLING IN THE FURNACE.
When the copper cools in the furnace, be ready, as soon as you
perceive it, to cut it with a long stick while it is still in a
paste; or if it is quite cold cut it as lead is cut with broad and
large chisels.
IF YOU HAVE TO MAKE A LARGE CAST.
If you have to make a cast of a hundred thousand pounds do it with
two furnaces and with 2000 pounds in each, or as much as 3000 pounds
at most.
738.
HOW TO PROCEED TO BREAK A LARGE MASS OF BRONZE.
If you want to break up a large mass of bronze, first suspend it,
and then make round it a wall on the four sides, like a trough of
bricks, and make a great fire therein. When it is quite red hot give
it a blow with a heavy weight raised above it, and with great force.
739.
TO COMBINE LEAD WITH OTHER METAL.
If you wish for economy in combining lead with the metal in order to
lessen the amount of tin which is necessary in the metal, first
alloy the lead with the tin and then add the molten copper.
How TO MELT [METAL] IN A FURNACE.
The furnace should be between four well founded pillars.
OF THE THICKNESS OF THE COATING.
The coating should not be more than two fingers thick, it should be
laid on in four thicknesses over fine clay and then well fixed, and
it should be fired only on the inside and then carefully covered
with ashes and cow's dung.
OF THE THICKNESS OF THE GUN.
The gun being made to carry 600 Ibs. of ball and more, by this rule
you will take the measure of the diameter of the ball and divide it
into 6 parts and one of these parts will be its thickness at the
muzzle; but at the breech it must always be half. And if the ball is
to be 700 lbs., 1/7th of the diameter of the ball must be its
thickness in front; and if the ball is to be 800, the eighth of its
diameter in front; and if 900, 1/8th and 1/2 [3/16], and if 1000,
1/9th.
OF THE LENGTH OF THE BODY OF THE GUN.
If you want it to throw a ball of stone, make the length of the gun
to be 6, or as much as 7 diameters of the ball; and if the ball is
to be of iron make it as much as 12 balls, and if the ball is to be
of lead, make it as much as 18 balls. I mean when the gun is to have
the mouth fitted to receive 600 lbs. of stone ball, and more.
OF THE THICKNESS OF SMALL GUNS.
The thickness at the muzzle of small guns should be from a half to
one third of the diameter of the ball, and the length from 30 to 36
balls.
740.
OF LUTING THE FURNACE WITHIN.
The furnace must be luted before you put the metal in it, with earth
from Valenza, and over that with ashes.
[Footnote 1. 2.: _Terra di Valenza_.--Valenza is north of
Alessandria on the Po.]
OF RESTORING THE METAL WHEN IT IS BECOMING COOL.
When you see that the bronze is congealing take some willow-wood cut
in small chips and make up the fire with it.
THE CAUSE OF ITS CURDLING.
I say that the cause of this congealing often proceeds from too much
fire, or from ill-dried wood.
TO KNOW THE CONDITION OF THE FIRE.
You may know when the fire is good and fit for your purpose by a
clear flame, and if you see the tips of the flames dull and ending
in much smoke do not trust it, and particularly when the flux metal
is almost fluid.
OF ALLOYING THE METAL.
Metal for guns must invariably be made with 6 or even 8 per cent,
that is 6 of tin to one hundred of copper, for the less you put in,
the stronger will the gun be.
WHEN THE TIN SHOULD BE ADDED TO THE COPPER.
The tin should be put in with the copper when the copper is reduced
to a fluid.
HOW TO HASTEN THE MELTING.
You can hasten the melting when 2/3ds of the copper is fluid; you
can then, with a stick of chestnut-wood, repeatedly stir what of
copper remains entire amidst what is melted.
_Introductory Observations on the Architectural Designs (XII), and
Writings on Architecture (XIII)._
_Until now very little has been known regarding Leonardo's labours
in the domain of Architecture. No building is known to have been
planned and executed by him, though by some contemporary writers
incidental allusion is made to his occupying himself with
architecture, and his famous letter to Lodovico il Moro,--which has
long been a well-known document,--in which he offers his service as
an architect to that prince, tends to confirm the belief that he was
something more than an amateur of the art. This hypothesis has
lately been confirmed by the publication of certain documents,
preserved at Milan, showing that Leonardo was not only employed in
preparing plans but that he took an active part, with much credit,
as member of a commission on public buildings; his name remains
linked with the history of the building of the Cathedral at Pavia
and that of the Cathedral at Milan._
_Leonardo's writings on Architecture are dispersed among a large
number of MSS., and it would be scarcely possible to master their
contents without the opportunity of arranging, sorting and comparing
the whole mass of materials, so as to have some comprehensive idea
of the whole. The sketches, when isolated and considered by
themselves, might appear to be of but little value; it is not till
we understand their general purport, from comparing them with each
other, that we can form any just estimate of their true worth._
_Leonardo seems to have had a project for writing a complete and
separate treatise on Architecture, such as his predecessors and
contemporaries had composed--Leon Battista Alberti, Filarete,
Francesco di Giorgio and perhaps also Bramante. But, on the other
hand, it cannot be denied that possibly no such scheme was connected
with the isolated notes and researches, treating on special
questions, which are given in this work; that he was merely working
at problems in which, for some reason or other he took a special
interest._
_A great number of important buildings were constructed in Lombardy
during the period between 1472 and 1499, and among them there are
several by unknown architects, of so high an artistic merit, that it
is certainly not improbable that either Bramante or Leonardo da
Vinci may have been, directly or indirectly, concerned in their
erection._
_Having been engaged, for now nearly twenty years, in a thorough
study of Bramante's life and labours, I have taken a particular
interest in detecting the distinguishing marks of his style as
compared with Leonardo's. In 1869 I made researches about the
architectural drawings of the latter in the Codex Atlanticus at
Milan, for the purpose of finding out, if possible the original
plans and sketches of the churches of Santa Maria delle Grazie at
Milan, and of the Cathedral at Pavia, which buildings have been
supposed to be the work both of Bramante and of Leonardo. Since 1876
I have repeatedly examined Leonardo's architectural studies in the
collection of his manuscripts in the Institut de France, and some of
these I have already given to the public in my work on_ "Les Projets
Primitifs pour la Basilique de St. Pierre de Rome", _P1. 43. In 1879
I had the opportunity of examining the manuscript in the Palazzo
Trivulzio at Milan, and in 1880 Dr Richter showed me in London the
manuscripts in the possession of Lord Ashburnham, and those in the
British Museum. I have thus had opportunities of seeing most of
Leonardo's architectural drawings in the original, but of the
manuscripts tliemselves I have deciphered only the notes which
accompany the sketches. It is to Dr Richter's exertions that we owe
the collected texts on Architecture which are now published, and
while he has undertaken to be responsible for the correct reading of
the original texts, he has also made it his task to extract the
whole of the materials from the various MSS. It has been my task to
arrange and elucidate the texts under the heads which have been
adopted in this work. MS. B. at Paris and the Codex Atlanticus at
Milan are the chief sources of our knowledge of Leonardo as an
architect, and I have recently subjected these to a thorough
re-investigation expressly with a view to this work._
_A complete reproduction of all Leonardo's architectural sketches
has not, indeed, been possible, but as far as the necessarily
restricted limits of the work have allowed, the utmost completeness
has been aimed at, and no efforts have been spared to include every
thing that can contribute to a knowledge of Leonardo's style. It
would have been very interesting, if it had been possible, to give
some general account at least of Leonardo's work and studies in
engineering, fortification, canal-making and the like, and it is
only on mature reflection that we have reluctantly abandoned this
idea. Leonardo's occupations in these departments have by no means
so close a relation to literary work, in the strict sense of the
word as we are fairly justified in attributing to his numerous notes
on Architecture._
_Leonardo's architectural studies fall naturally under two heads:_
_I. Those drawings and sketches, often accompanied by short remarks
and explanations, which may be regarded as designs for buildings or
monuments intended to be built. With these there are occasionally
explanatory texts._
_II. Theoretical investigations and treatises. A special interest
attaches to these because they discuss a variety of questions which
are of practical importance to this day. Leonardo's theory as to the
origin and progress of cracks in buildings is perhaps to be
considered as unique in its way in the literature of Architecture._
_HENRY DE GEYMULLER_
_XII._
_Architectural Designs._
_I. Plans for towns._
_A. Sketches for laying out a new town with a double system of high-
level and low-level road-ways._
_Pl. LXXVII, No. 1 (MS. B, 15b). A general view of a town, with the
roads outside it sloping up to the high-level ways within._
_Pl. LXXVII, No. 3 (MS. B, 16b. see No. 741; and MS. B. 15b, see No.
742) gives a partial view of the town, with its streets and houses,
with explanatory references._
_Pl. LXXVII, No. 2 (MS. B, 15b; see No. 743). View of a double
staircaise with two opposite flights of steps._
_Pl. LXXVIII, Nos. 2 and 3 (MS. B, 37a). Sketches illustrating the
connection of the two levels of roads by means of steps. The lower
galleries are lighted by openings in the upper roadway._
_B. Notes on removing houses (MS. Br. M., 270b, see No. 744)._
741.
The roads _m_ are 6 braccia higher than the roads _p s_, and each
road must be 20 braccia wide and have 1/2 braccio slope from the
sides towards the middle; and in the middle let there be at every
braccio an opening, one braccio long and one finger wide, where the
rain water may run off into hollows made on the same level as _p s_.
And on each side at the extremity of the width of the said road let
there be an arcade, 6 braccia broad, on columns; and understand that
he who would go through the whole place by the high level streets
can use them for this purpose, and he who would go by the low level
can do the same. By the high streets no vehicles and similar objects
should circulate, but they are exclusively for the use of gentlemen.
The carts and burdens for the use and convenience of the inhabitants
have to go by the low ones. One house must turn its back to the
other, leaving the lower streets between them. Provisions, such as
wood, wine and such things are carried in by the doors _n_, and
privies, stables and other fetid matter must be emptied away
underground. From one arch to the next
742.
must be 300 braccia, each street receiving its light through the
openings of the upper streets, and at each arch must be a winding
stair on a circular plan because the corners of square ones are
always fouled; they must be wide, and at the first vault there must
be a door entering into public privies and the said stairs lead from
the upper to the lower streets and the high level streets begin
outside the city gates and slope up till at these gates they have
attained the height of 6 braccia. Let such a city be built near the
sea or a large river in order that the dirt of the city may be
carried off by the water.
743.
The construction of the stairs: The stairs _c d_ go down to _f g_,
and in the same way _f g_ goes down to _h k_.
744.
ON MOVING HOUSES.
Let the houses be moved and arranged in order; and this will be done
with facility because such houses are at first made in pieces on the
open places, and can then be fitted together with their timbers in
the site where they are to be permanent.
[9] Let the men of the country [or the village] partly inhabit the
new houses when the court is absent [12].
[Footnote: On the same page we find notes referring to Romolontino
and Villafranca with a sketch-map of the course of the "Sodro" and
the "(Lo)cra" (both are given in the text farther on). There can
hardly be a doubt that the last sentence of the passage given above,
refers to the court of Francis I. King of France.--L.9-13 are
written inside the larger sketch, which, in the original, is on the
right hand side of the page by the side of lines 1-8. The three
smaller sketches are below. J. P. R.]
_II. Plans for canals and streets in a town.
Pl. LXXIX, 1. and 2, (MS. B, 37b, see No. 745, and MS. B. 36a, see
No. 746). A Plan for streets and canals inside a town, by which the
cellars of the houses are made accessible in boats.
The third text given under No. 747 refers to works executed by
Leonardo in France._
745.
The front _a m_ will give light to the rooms; _a e_ will be 6
braccia--_a b_ 8 braccia --_b e_ 30 braccia, in order that the rooms
under the porticoes may be lighted; _c d f_ is the place where the
boats come to the houses to be unloaded. In order to render this
arrangement practicable, and in order that the inundation of the
rivers may not penetrate into the cellars, it is necessary to chose
an appropriate situation, such as a spot near a river which can be
diverted into canals in which the level of the water will not vary
either by inundations or drought. The construction is shown below;
and make choice of a fine river, which the rains do not render
muddy, such as the Ticino, the Adda and many others. [Footnote 12:
_Tesino, Adda e molti altri, i.e._ rivers coming from the mountains
and flowing through lakes.] The construction to oblige the waters to
keep constantly at the same level will be a sort of dock, as shown
below, situated at the entrance of the town; or better still, some
way within, in order that the enemy may not destroy it [14].
[Footnote: L. 1-4 are on the left hand side and within the sketch
given on Pl. LXXIX, No. I. Then follows after line 14, the drawing
of a sluicegate--_conca_--of which the use is explained in the text
below it. On the page 38a, which comes next in the original MS. is
the sketch of an oval plan of a town over which is written "_modo di
canali per la citta_" and through the longer axis of it "_canale
magior_" is written with "_Tesino_" on the prolongation of the
canal. J. P. R.]
746.
Let the width of the streets be equal to the average height of the
houses.
747.
The main underground channel does not receive turbid water, but that
water runs in the ditches outside the town with four mills at the
entrance and four at the outlet; and this may be done by damming the
water above Romorantin.
[11]There should be fountains made in each piazza[13].
[Footnote: In the original this text comes immediately after the
passage given as No. 744. The remainder of the writing on the same
page refers to the construction of canals and is given later, in the
"Topographical Notes".
Lines 1-11 are written to the right of the plan lines 11-13
underneath it. J. P. R.]
[Footnote 10: _Romolontino_ is Romorantin, South of Orleans in
France.]
_III. Castles and Villas.
A. Castles.
Pl. LXXX, No. 1 (P. V. fol. 39b; No. d'ordre 2282). The fortified
place here represented is said by Vallardi to be the_ "castello" _at
Milan, but without any satisfactory reason. The high tower behind
the_ "rivellino" _ravelin--seems to be intended as a watch-tower.
Pl. LXXX, No. 2 (MS. B, 23b). A similarly constructed tower probably
intended for the same use.
Pl. LXXX, No. 3 (MS. B). Sketches for corner towers with steps for a
citadel.
Pl. LXXX, No. 4 (W. XVI). A cupola crowning a corner tower; an
interesting example of decorative fortification. In this
reproduction of the original pen and ink drawing it appears
reversed.
B. Projects for Palaces.
Pl. LXXXI, No. 2 (MS. C. A, 75b; 221a, see No. 748). Project for a
royal residence at Amboise in France.
Pl. LXXXII, No. 1 (C. A 308a; 939a). A plan for a somewhat extensive
residence, and various details; but there is no text to elucidate
it; in courts are written the three names:
Sam cosi giova
_(St. Mark)_ _(Cosmo)_ _(John)_,
arch mo nino
C. Plans for small castles or Villas.
The three following sketches greatly resemble each other. Pl.
LXXXII, No. 2 (MS. K3 36b; see No. 749)._
_Pl. LXXXII, No. 3 (MS. B 60a; See No. 750).
Pl. LXXXIII (W. XVII). The text on this sheet refers to Cyprus (see
Topographical Notes No. 1103), but seems to have no direct
connection with the sketches inserted between.
Pl. LXXXVIII, Nos. 6 and 7 (MS. B, 12a; see No. 751). A section of a
circular pavilion with the plan of a similar building by the side of
it. These two drawings have a special historical interest because
the text written below mentions the Duke and Duchess of Milan.
The sketch of a villa on a terrace at the end of a garden occurs in
C. A. 150; and in C. A. 77b; 225b is another sketch of a villa
somewhat resembling the_ Belvedere _of Pope Innocent VIII, at Rome.
In C. A. 62b; 193b there is a Loggia.
Pl. LXXXII, No. 4 (C. A. 387a; 1198a) is a tower-shaped_ Loggia
_above a fountain. The machinery is very ingeniously screened from
view._
748.
The Palace of the prince must have a piazza in front of it.
Houses intended for dancing or any kind of jumping or any other
movements with a multitude of people, must be on the ground- floor;
for I have already witnessed the destruction of some, causing death
to many persons, and above all let every wall, be it ever so thin,
rest on the ground or on arches with a good foundation.
Let the mezzanines of the dwellings be divided by walls made of very
thin bricks, and without wood on account of fire.
Let all the privies have ventilation [by shafts] in the thickness of
the walls, so as to exhale by the roofs.
The mezzanines should be vaulted, and the vaults will be stronger in
proportion as they are of small size.
The ties of oak must be enclosed in the walls in order to be
protected from fire.
[Footnote: The remarks accompanying the plan reproduced on Pl.
LXXXI, No. 2 are as follows: Above, to the left: "_in_ a _angholo
stia la guardia de la sstalla_" (in the angle _a_ may be the keeper
of the stable). Below are the words "_strada dabosa_" (road to
Amboise), parallel with this "_fossa br 40_" (the moat 40 braccia)
fixing the width of the moat. In the large court surrounded by a
portico "_in terre No.--Largha br.80 e lugha br 120_." To the right
of the castle is a large basin for aquatic sports with the words
"_Giostre colle nave cioe li giostra li stieno sopra le na_"
(Jousting in boats that is the men are to be in boats). J. P. R.]
The privies must be numerous and going one into the other in order
that the stench may not penetrate into the dwellings., and all their
doors must shut off themselves with counterpoises.
The main division of the facade of this palace is into two portions;
that is to say the width of the court-yard must be half the whole
facade; the 2nd ...
749.
30 braccia wide on each side; the lower entrance leads into a hall
10 braccia wide and 30 braccia long with 4 recesses each with a
chimney.
[Footnote: On each side of the castle, Pl. LXXXII. No. 2 there are
drawings of details, to the left "_Camino_" a chimney, to the right
the central lantern, sketched in red "_8 lati_" _i.e._ an octagon.]
750.
The firststorey [or terrace] must be entirely solid.
751.
The pavilion in the garden of the Duchess of Milan.
The plan of the pavilion which is in the middle of the labyrinth of
the Duke of Milan.
[Footnote: This passage was first published by AMORETTI in _Memorie
Storiche_ Cap. X: Una sua opera da riportarsi a quest' anno fu il
bagno fatto per la duchessa Beatrice nel parco o giardino del
Castello. Lionardo non solo ne disegno il piccolo edifizio a foggia
di padiglione, nel cod. segnato Q. 3, dandone anche separatamente la
pianta; ma sotto vi scrisse: Padiglione del giardino della duchessa;
e sotto la pianta: Fondamento del padiglione ch'e nel mezzo del
labirinto del duca di Milano; nessuna data e presso il padiglione,
disegnato nella pagina 12, ma poco sopra fra molti circoli
intrecciati vedesi = 10 Luglio 1492 = e nella pagina 2 presso ad
alcuni disegni di legumi qualcheduno ha letto Settembre 1482 in vece
di 1492, come dovea scriverevi, e probabilmente scrisse Lionardo.
The original text however hardly bears the interpretation put upon
it by AMORETTI. He is mistaken as to the mark on the MS. as well as
in his statements as to the date, for the MS. in question has no
date; the date he gives occurs, on the contrary, in another
note-book. Finally, it appears to me quite an open question whether
Leonardo was the architect who carried out the construction of the
dome-like Pavilion here shown in section, or of the ground plan of
the Pavilion drawn by the side of it. Must we, in fact, suppose that
"_il duca di Milano_" here mentioned was, as has been generally
assumed, Ludovico il Moro? He did not hold this title from the
Emperor before 1494; till that date he was only called _Governatore_
and Leonardo in speaking of him, mentions him generally as "_il
Moro_" even after 1494. On January 18, 1491, he married Beatrice
d'Este the daughter of Ercole I, Duke of Ferrara. She died on the
2nd January 1497, and for the reasons I have given it seems
improbable that it should be this princess who is here spoken of as
the "_Duchessa di Milano_". From the style of the handwriting it
appears to me to be beyond all doubt that the MS. B, from which this
passage is taken, is older than the dated MSS. of 1492 and 1493. In
that case the Duke of Milan here mentioned would be Gian Galeazzo
(1469-1494) and the Duchess would be his wife Isabella of Aragon, to
whom he was married on the second February 1489. J. P. R.]
752.
The earth that is dug out from the cellars must be raised on one
side so high as to make a terrace garden as high as the level of the
hall; but between the earth of the terrace and the wall of the
house, leave an interval in order that the damp may not spoil the
principal walls.
_IV. Ecclesiastical Architecture.
A. General Observations._
753.
A building should always be detached on all sides so that its form
may be seen.
[Footnote: The original text is reproduced on Pl. XCII, No. 1 to the
left hand at the bottom.]
754.
Here there cannot and ought not to be any _campanile_; on the
contrary it must stand apart like that of the Cathedral and of San
Giovanni at Florence, and of the Cathedral at Pisa, where the
campanile is quite detached as well as the dome. Thus each can
display its own perfection. If however you wish to join it to the
church, make the lantern serve for the campanile as in the church at
Chiaravalle.
[Footnote: This text is written by the side of the plan given on Pl.
XCI. No. 2.]
[Footnote 12: The Abbey of Chiaravalle, a few miles from Milan, has
a central tower on the intersection of the cross in the style of
that of the Certosa of Pavia, but the style is mediaeval (A. D.
1330). Leonardo seems here to mean, that in a building, in which the
circular form is strongly conspicuous, the campanile must either be
separated, or rise from the centre of the building and therefore
take the form of a lantern.]
755.
It never looks well to see the roofs of a church; they should rather
be flat and the water should run off by gutters made in the frieze.
[Footnote: This text is to the left of the domed church reproduced
on Pl. LXXXVII, No. 2.]
_B. The theory of Dome Architecture.
This subject has been more extensively treated by Leonardo in
drawings than in writing. Still we may fairly assume that it was his
purpose, ultimately to embody the results of his investigation in a_
"Trattato delle Cupole." _The amount of materials is remarkably
extensive. MS. B is particularly rich in plans and elevations of
churches with one or more domes--from the simplest form to the most
complicated that can be imagined. Considering the evident connexion
between a great number of these sketches, as well as the
impossibility of seeing in them designs or preparatory sketches for
any building intended to be erected, the conclusion is obvious that
they were not designed for any particular monument, but were
theoretical and ideal researches, made in order to obtain a clear
understanding of the laws which must govern the construction of a
great central dome, with smaller ones grouped round it; and with or
without the addition of spires, so that each of these parts by
itself and in its juxtaposition to the other parts should produce
the grandest possible effect.
In these sketches Leonardo seems to have exhausted every imaginable
combination. [Footnote 1: In MS. B, 32b (see Pl. C III, No. 2) we
find eight geometrical patterns, each drawn in a square; and in MS.
C.A., fol. 87 to 98 form a whole series of patterns done with the
same intention.] The results of some of these problems are perhaps
not quite satisfactory; still they cannot be considered to give
evidence of a want of taste or of any other defect in Leonardo s
architectural capacity. They were no doubt intended exclusively for
his own instruction, and, before all, as it seems, to illustrate the
features or consequences resulting from a given principle._
_I have already, in another place,_ [Footnote 1: Les Projets
Primitifs pour la Basilique de St. Pierre de Rome, par Bramante,
Raphael etc.,Vol. I, p. 2.] _pointed out the law of construction for
buildings crowned by a large dome: namely, that such a dome, to
produce the greatest effect possible, should rise either from the
centre of a Greek cross, or from the centre of a structure of which
the plan has some symmetrical affinity to a circle, this circle
being at the same time the centre of the whole plan of the building.
Leonardo's sketches show that he was fully aware, as was to be
expected, of this truth. Few of them exhibit the form of a Latin
cross, and when this is met with, it generally gives evidence of the
determination to assign as prominent a part as possible to the dome
in the general effect of the building.
While it is evident, on the one hand, that the greater number of
these domes had no particular purpose, not being designed for
execution, on the other hand several reasons may be found for
Leonardo's perseverance in his studies of the subject.
Besides the theoretical interest of the question for Leonardo and
his_ Trattato _and besides the taste for domes prevailing at that
time, it seems likely that the intended erection of some building of
the first importance like the Duomos of Pavia and Como, the church
of Sta. Maria delle Grazie at Milan, and the construction of a Dome
or central Tower_ (Tiburio) _on the cathedral of Milan, may have
stimulated Leonardo to undertake a general and thorough
investigation of the subject; whilst Leonardo's intercourse with
Bramante for ten years or more, can hardly have remained without
influence in this matter. In fact now that some of this great
Architect's studies for S. Peter's at Rome have at last become
known, he must be considered henceforth as the greatest master of
Dome-Architecture that ever existed. His influence, direct or
indirect even on a genius like Leonardo seems the more likely, since
Leonardo's sketches reveal a style most similar to that of Bramante,
whose name indeed, occurs twice in Leonardo's manuscript notes. It
must not be forgotten that Leonardo was a Florentine; the
characteristic form of the two principal domes of Florence, Sta.
Maria del Fiore and the Battisterio, constantly appear as leading
features in his sketches.
The church of San Lorenzo at Milan, was at that time still intact.
The dome is to this day one of the most wonderful cupolas ever
constructed, and with its two smaller domes might well attract the
attention and study of a never resting genius such as Leonardo. A
whole class of these sketches betray in fact the direct influence of
the church of S. Lorenzo, and this also seems to have suggested the
plan of Bramante's dome of St. Peter's at Rome.
In the following pages the various sketches for the construction of
domes have been classified and discussed from a general point of
view. On two sheets: Pl. LXXXIV (C.A. 354b; 118a) and Pl. LXXXV,
Nos. 1-11 (Ash. II, 6b) we see various dissimilar types, grouped
together; thus these two sheets may be regarded as a sort of
nomenclature of the different types, on which we shall now have to
treat._
_1. Churches formed on the plan of a Greek cross.
Group I.
Domes rising from a circular base.
The simplest type of central building is a circular edifice.
Pl. LXXXIV, No. 9. Plan of a circular building surrounded by a
colonnade.
Pl. LXXXIV, No. 8. Elevation of the former, with a conical roof.
Pl. XC. No. 5. A dodecagon, as most nearly approaching the circle.
Pl. LXXXVI, No. 1, 2, 3. Four round chapels are added at the
extremities of the two principal axes;--compare this plan with fig.
1 on p. 44 and fig. 3 on p. 47 (W. P. 5b) where the outer wall is
octagonal.
Group II.
Domes rising from a square base.
The plan is a square surrounded by a colonnade, and the dome seems
to be octagonal.
Pl. LXXXIV. The square plan below the circular building No. 8, and
its elevation to the left, above the plan: here the ground-plan is
square, the upper storey octagonal. A further development of this
type is shown in two sketches C. A. 3a (not reproduced here), and in
Pl. LXXXVI, No. 5 (which possibly belongs to No. 7 on Pl. LXXXIV).
Pl, LXXXV, No. 4, and p. 45, Fig. 3, a Greek cross, repeated p. 45,
Fig. 3, is another development of the square central plan.
The remainder of these studies show two different systems; in the
first the dome rises from a square plan,--in the second from an
octagonal base._
_Group III.
Domes rising from a square base and four pillars. [Footnote 1: The
ancient chapel San Satiro, via del Falcone, Milan, is a specimen of
this type.]_
a) First type. _A Dome resting on four pillars in the centre of a
square edifice, with an apse in the middle, of each of the four
sides. We have eleven variations of this type.
aa) Pl. LXXXVIII, No. 3.
bb) Pl. LXXX, No. 5.
cc) Pl. LXXXV, Nos. 2, 3, 5.
dd) Pl. LXXXIV, No. 1 and 4 beneath.
ee) Pl. LXXXV, Nos. 1, 7, 10, 11._
b) Second type. _This consists in adding aisles to the whole plan of
the first type; columns are placed between the apses and the aisles;
the plan thus obtained is very nearly identical with that of S.
Lorenzo at Milan.
Fig. 1 on p. 56. (MS. B, 75a) shows the result of this treatment
adapted to a peculiar purpose about which we shall have to say a few
words later on.
Pl. XCV, No. 1, shows the same plan but with the addition of a short
nave. This plan seems to have been suggested by the general
arrangement of S. Sepolcro at Milan.
MS. B. 57b (see the sketch reproduced on p.51). By adding towers in
the four outer angles to the last named plan, we obtain a plan which
bears the general features of Bramante's plans for S. Peter's at
Rome. [Footnote 2: See_ Les projets primitifs _etc., Pl. 9-12.] (See
p. 51 Fig. 1.)
Group IV.
Domes rising from an octagonal base.
This system, developed according to two different schemes, has given
rise to two classes with many varieties.
In a) On each side of the octagon chapels of equal form are added.
In b) The chapels are dissimilar; those which terminate the
principal axes being different in form from those which are added on
the diagonal sides of the octagon.
a. First Class.
The Chapel_ "degli Angeli," _at Florence, built only to a height of
about 20 feet by Brunellesco, may be considered as the prototype of
this group; and, indeed it probably suggested it. The fact that we
see in MS. B. 11b (Pl. XCIV, No. 3) by the side of Brunellesco's
plan for the Basilica of Sto. Spirito at Florence, a plan almost
identical with that of the_ Capella degli Angeli, _confirms this
supposition. Only two small differences, or we may say improvements,
have been introduced by Leonardo. Firstly the back of the chapels
contains a third niche, and each angle of the Octagon a folded
pilaster like those in Bramante's_ Sagrestia di S. M. presso San
Satiro _at Milan, instead of an interval between the two pilasters
as seen in the Battistero at Florence and in the Sacristy of Sto.
Spirito in the same town and also in the above named chapel by
Brunellesco.
The first set of sketches which come under consideration have at
first sight the appearance of mere geometrical studies. They seem to
have been suggested by the plan given on page 44 Fig. 2 (MS. B, 55a)
in the centre of which is written_ "Santa Maria in perticha da
Pavia", _at the place marked A on the reproduction.
a) (MS. B, 34b, page 44 Fig. 3). In the middle of each side a column
is added, and in the axes of the intercolumnar spaces a second row
of columns forms an aisle round the octagon. These are placed at the
intersection of a system of semicircles, of which the sixteen
columns on the sides of the octagon are the centres.
b) The preceding diagram is completed and becomes more monumental in
style in the sketch next to it (MS. B, 35a, see p. 45 Fig. 1). An
outer aisle is added by circles, having for radius the distance
between the columns in the middle sides of the octagon.
c) (MS. B. 96b, see p. 45 Fig. 2). Octagon with an aisle round it;
the angles of both are formed by columns. The outer sides are formed
by 8 niches forming chapels. The exterior is likewise octagonal,
with the angles corresponding to the centre of each of the interior
chapels.
Pl. XCII, No. 2 (MS. B. 96b). Detail and modification of the
preceding plan--half columns against piers--an arrangement by which
the chapels of the aisle have the same width of opening as the inner
arches between the half columns. Underneath this sketch the
following note occurs:_ questo vole - avere 12 facce - co 12
tabernaculi - come - _a_ - _b_. _(This will have twelve sides with
twelve tabernacles as_ a b._) In the remaining sketches of this
class the octagon is not formed by columns at the angles.
The simplest type shows a niche in the middle of each side and is
repeated on several sheets, viz: MS. B 3; MS. C.A. 354b (see Pl.
LXXXIV, No. 11) and MS. Ash II 6b; (see Pl. LXXXV, No. 9 and the
elevations No. 8; Pl. XCII, No. 3; MS. B. 4b [not reproduced here]
and Pl. LXXXIV, No. 2)._
_Pl. XCII, 3 (MS. B, 56b) corresponds to a plan like the one in MS.
B 35a, in which the niches would be visible outside or, as in the
following sketch, with the addition of a niche in the middle of each
chapel.
Pl. XC, No. 6. The niches themselves are surrounded by smaller
niches (see also No. 1 on the same plate).
Octagon expanded on each side.
A. by a square chapel:
MS. B. 34b (not reproduced here).
B. by a square with 3 niches:
MS. B. 11b (see Pl. XCIV, No. 3).
C. by octagonal chapels:
a) MS. B, 21a; Pl. LXXXVIII, No. 4.
b) No. 2 on the same plate. Underneath there is the remark:_
"quest'e come le 8 cappele ano a essere facte" _(this is how the
eight chapels are to be executed).
c) Pl. LXXXVIII, No. 5. Elevation to the plans on the same sheet, it
is accompanied by the note:_ "ciasscuno de' 9 tiburi no'uole -
passare l'alteza - di - 2 - quadri" _(neither of the 9 domes must
exceed the height of two squares).
d) Pl. LXXXVIII, No. 1. Inside of the same octagon. MS. B, 30a, and
34b; these are three repetitions of parts of the same plan with very
slight variations.
D. by a circular chapel:
MS. B, 18a (see Fig. 1 on page 47) gives the plan of this
arrangement in which the exterior is square on the ground floor with
only four of the chapels projecting, as is explained in the next
sketch.
Pl. LXXXIX, MS. B, 17b. Elevation to the preceding plan sketched on
the opposite side of the sheet, and also marked A. It is accompanied
by the following remark, indicating the theoretical character of
these studies:_ questo - edifitio - anchora - starebbe - bene
affarlo dalla linja - _a_ - _b_ - _c_ - _d_ - insu. _("This edifice
would also produce a good effect if only the part above the lines_ a
b, c d, _were executed").
Pl. LXXXIV, No. 11. The exterior has the form of an octagon, but the
chapels project partly beyond it. On the left side of the sketch
they appear larger than on the right side.
Pl. XC, No. 1, (MS. B, 25b); Repetition of Pl. LXXXIV, No. 11.
Pl. XC, No. 2. Elevation to the plan No. 1, and also to No. 6 of the
same sheet._
_E. By chapels formed by four niches:
Pl. LXXXIV, No. 7 (the circular plan on the left below) shows this
arrangement in which the central dome has become circular inside and
might therefore be classed after this group. [Footnote 1: This plan
and some others of this class remind us of the plan of the Mausoleum
of Augustus as it is represented for instance by Durand. See_ Cab.
des Estampes, Bibliotheque Nationale, Paris, Topographie de Rome, V,
6, 82._]
The sketch on the right hand side gives most likely the elevation
for the last named plan.
F. By chapels of still richer combinations, which necessitate an
octagon of larger dimensions:
Pl. XCI, No. 2 (MS. Ash. 11. 8b) [Footnote 2: The note accompanying
this plan is given under No. 754.]; on this plan the chapels
themselves appear to be central buildings formed like the first type
of the third group. Pl. LXXXVIII, No. 3.
Pl. XCI, No. 2 above; the exterior of the preceding figure,
particularly interesting on account of the alternation of apses and
niches, the latter containing statues of a gigantic size, in
proportion to the dimension of the niches.
b. Second Class.
Composite plans of this class are generally obtained by combining
two types of the first class--the one worked out on the principal
axes, the other on the diagonal ones.
MS. B. 22 shows an elementary combination, without any additions on
the diagonal axes, but with the dimensions of the squares on the two
principal axes exceeding those of the sides of the octagon.
In the drawing W. P. 5b (see page 44 Fig. 1) the exterior only of
the edifice is octagonal, the interior being formed by a circular
colonnade; round chapels are placed against the four sides of the
principal axes.
The elevation, drawn on the same sheet (see page 47 Fig. 3), shows
the whole arrangement which is closely related with the one on Pl.
LXXXVI No. 1, 2.
MS. B. 21a shows:
a) four sides with rectangular chapels crowned by pediments Pl.
LXXXVII No. 3 (plan and elevation);
b) four sides with square chapels crowned by octagonal domes. Pl.
LXXXVII No. 4; the plan underneath.
MS. B. 18a shows a variation obtained by replacing the round chapels
in the principal axes of the sketch MS. B. l8a by square ones, with
an apse. Leonardo repeated both ideas for better comparison side by
side, see page 47. Fig. 2.
Pl. LXXXIX (MS. B. 17b). Elevation for the preceding figure. The
comparison of the drawing marked M with the plan on page 47 Fig. 2,
bearing the same mark, and of the elevation on Pl. LXXXIX below
(marked A) with the corresponding plan on page 47 is highly
instructive, as illustrating the spirit in which Leonardo pursued
these studies.
Pl. LXXXIV No. 12 shows the design Pl. LXXXVII No. 3 combined with
apses, with the addition of round chapels on the diagonal sides.
Pl. LXXXIV No. 13 is a variation of the preceding sketch.
Pl. XC No. 3. MS. B. 25b. The round chapels of the preceding sketch
are replaced by octagonal chapels, above which rise campaniles.
Pl. XC No. 4 is the elevation for the preceding plan.
Pl. XCII No. 1. (MS. B. 39b.); the plan below. On the principal as
well as on the diagonal axes are diagonal chapels, but the latter
are separated from the dome by semicircular recesses. The
communication between these eight chapels forms a square aisle round
the central dome.
Above this figure is the elevation, showing four campaniles on the
angles. [Footnote 1: The note accompanying this drawing is
reproduced under No. 753.]
Pl. LXXXIV No. 3. On the principal axes are square chapels with
three niches; on the diagonals octagonal chapels with niches. Cod.
Atl. 340b gives a somewhat similar arrangement.
MS. B. 30. The principal development is thrown on the diagonal axes
by square chapels with three niches; on the principal axes are inner
recesses communicating with outer ones.
The plan Pl. XCIII No. 2 (MS. B. 22) differs from this only in so
far as the outer semicircles have become circular chapels,
projecting from the external square as apses; one of them serves as
the entrance by a semicircular portico.
The elevation is drawn on the left side of the plan.
MS. B. 19. A further development of MS. B. 18, by employing for the
four principal chapels the type Pl. LXXXVIII No. 3, as we have
already seen in Pl. XCI No. 2; the exterior presents two varieties.
a) The outer contour follows the inner. [Footnote 2: These chapels
are here sketched in two different sizes; it is the smaller type
which is thus formed.]
b) It is semicircular.
Pl. LXXXVII No. 2 (MS. B. 18b) Elevation to the first variation MS.
B. 19. If we were not certain that this sketch was by Leonardo, we
might feel tempted to take it as a study by Bramante for St. Peter's
at Rome. [Footnote 3: See_ Les projets primitifs Pl. 43._]_
_MS. P. V. 39b. In the principal axes the chapels of MS. B. 19, and
semicircular niches on the diagonals. The exterior of the whole
edifice is also an octagon, concealing the form of the interior
chapels, but with its angles on their axes.
Group V.
Suggested by San Lorenzo at Milan.
In MS. C. A. 266 IIb, 8l2b there is a plan almost identical with
that of San Lorenzo. The diagonal sides of the irregular octagon are
not indicated.
If it could be proved that the arches which, in the actual church,
exist on these sides in the first story, were added in 1574 by
Martimo Bassi, then this plan and the following section would be
still nearer the original state of San Lorenzo than at present. A
reproduction of this slightly sketched plan has not been possible.
It may however be understood from Pl. LXXXVIII No. 3, by suppressing
the four pillars corresponding to the apses.
Pl. LXXXVII No. 1 shows the section in elevation corresponding with
the above-named plan. The recessed chapels are decorated with large
shells in the halfdomes like the arrangement in San Lorenzo, but
with proportions like those of Bramante's Sacristy of Santa Maria
presso S. Satiro.
MS. C. A. 266; a sheet containing three views of exteriors of Domes.
On the same sheet there is a plan similar to the one above-named but
with uninterrupted aisles and with the addition of round chapels in
the axes (compare Pl. XCVII No. 3 and page 44 Fig. 1), perhaps a
reminiscence of the two chapels annexed to San Lorenzo.--Leonardo
has here sketched the way of transforming this plan into a Latin
cross by means of a nave with side aisles.
Pl. XCI No. 1. Plan showing a type deprived of aisles and comprised
in a square building which is surrounded by a portico. It is
accompanied by the following text:_
756.
This edifice is inhabited [accessible] below and above, like San
Sepolcro, and it is the same above as below, except that the upper
story has the dome _c d_; and the [Footnote: The church of San
Sepolcro at Milan, founded in 1030 and repeatedly rebuilt after the
middle of the XVIth century, still stands over the crypt of the
original structure.] lower has the dome _a b_, and when you enter
into the crypt, you descend 10 steps, and when you mount into the
upper you ascend 20 steps, which, with 1/3 braccio for each, make 10
braccia, and this is the height between one floor of the church and
the other.
_Above the plan on the same sheet is a view of the exterior. By the
aid of these two figures and the description, sections of the
edifice may easily be reconstructed. But the section drawn on the
left side of the building seems not to be in keeping with the same
plan, notwithstanding the explanatory note written underneath it:
"dentro il difitio di sopra" (interior of the edifice
above)[Footnote 1: _The small inner dome corresponds to_ a b _on the
plan--it rises from the lower church into the upper-- above, and
larger, rises the dome_ c d. _The aisles above and below thus
correspond_ (e di sopra come di sotto, salvoche etc.). _The only
difference is, that in the section Leonardo has not taken the
trouble to make the form octagonal, but has merely sketched circular
lines in perspective._ J. P. R._].
_Before leaving this group, it is well to remark that the germ of it
seems already indicated by the diagonal lines in the plans Pl. LXXXV
No. 11 and No. 7. We shall find another application of the same type
to the Latin cross in Pl. XCVII No. 3.
_2. Churches formed on the plan of a Latin cross.
We find among Leonardo's studies several sketches for churches on
the plan of the Latin cross; we shall begin by describing them, and
shall add a few observations.
A. Studies after existing Monuments.
Pl. XCIV No. 2. (MS. B. 11b.) Plan of Santo Spirito at Florence, a
basilica built after the designs of Brunellesco.--Leonardo has added
the indication of a portico in front, either his own invention or
the reproduction of a now lost design.
Pl. XCV No. 2. Plan accompanied by the words: "A_ e santo sepolcro
di milano di sopra"(A _is the upper church of S. Sepolcro at Milan);
although since Leonardo's time considerably spoilt, it is still the
same in plan.
The second plan with its note: "B_ e la sua parte socto tera" (B _is
its subterranean part [the crypt]) still corresponds with the
present state of this part of the church as I have ascertained by
visiting the crypt with this plan. Excepting the addition of a few
insignificant walls, the state of this interesting part of the
church still conforms to Leonardo's sketch; but in the Vestibolo the
two columns near the entrance of the winding stairs are absent.
B. Designs or Studies.
PL. XCV No. 1. Plan of a church evidently suggested by that of San
Sepolcro at Milan. The central part has been added to on the
principle of the second type of Group III. Leonardo has placed the_
"coro" _(choir) in the centre._
_Pl. XCVI No. 2. In the plan the dome, as regards its interior,
belongs to the First Class of Group IV, and may be grouped with the
one in MS. B. 35a. The nave seems to be a development of the type
represented in Pl. XCV No. 2, B. by adding towers and two lateral
porticos[Footnote 1: Already published in Les projets primitifs Pl.
XLIII.].
On the left is a view of the exterior of the preceding plan. It is
accompanied by the following note:_
757.
This building is inhabited below and above; the way up is by the
campaniles, and in going up one has to use the platform, where the
drums of the four domes are, and this platform has a parapet in
front, and none of these domes communicate with the church, but they
are quite separate.
_Pl. XCVI No. 1 (MS. C. A. 16b; 65a). Perspective view of a church
seen from behind; this recalls the Duomo at Florence, but with two
campaniles[Footnote 2: Already published in the Saggio Pl. IX.].
Pl. XCVII No. 3 (MS. B. 52a). The central part is a development of
S. Lorenzo at Milan, such as was executed at the Duomo of Pavia.
There is sufficient analogy between the building actually executed
and this sketch to suggest a direct connection between them.
Leonardo accompanied Francesco di Giorgio[Footnote 3: See MALASPINA,
il Duomo di Pavia. Documents.] when the latter was consulted on June
21st, 1490 as to this church; the fact that the only word
accompanying the plan is:_ "sagrestia", _seems to confirm our
supposition, for the sacristies were added only in 1492, i. e. four
years after the beginning of the Cathedral, which at that time was
most likely still sufficiently unfinished to be capable of receiving
the form of the present sketch.
Pl. XCVII No. 2 shows the exterior of this design. Below is the
note:_ edifitio al proposito del fodameto figurato di socto
_(edifice proper for the ground plan figured below).
Here we may also mention the plan of a Latin cross drawn in MS. C.
A. fol. 266 (see p. 50).
Pl. XCIV No. 1 (MS. L. 15b). External side view of Brunellesco's
Florentine basilica San Lorenzo, seen from the North.
Pl. XCIV No. 4 (V. A. V, 1). Principal front of a nave, most likely
of a church on the plan of a Latin cross. We notice here not only
the principal features which were employed afterwards in Alberti's
front of S. Maria Novella, but even details of a more advanced
style, such as we are accustomed to meet with only after the year
1520.
In the background of Leonardo's unfinished picture of St. Jerome
(Vatican Gallery) a somewhat similar church front is indicated (see
the accompanying sketch).
[Illustration with caption: The view of the front of a temple,
apparently a dome in the centre of four corinthian porticos bearing
pediments (published by Amoretti Tav. II. B as being by Leonardo),
is taken from a drawing, now at the Ambrosian Gallery. We cannot
consider this to be by the hand of the master.]_
_C. Studies for a form of a Church most proper for preaching.
The problem as to what form of church might answer the requirements
of acoustics seems to have engaged Leonardo's very particular
attention. The designation of_ "teatro" _given to some of these
sketches, clearly shows which plan seemed to him most favourable for
hearing the preacher's voice.
Pl. XCVII, No. 1 (MS. B, 52). Rectangular edifice divided into three
naves with an apse on either side, terminated by a semicircular
theatre with rising seats, as in antique buildings. The pulpit is in
the centre. Leonardo has written on the left side of the sketch_:
"teatro da predicare" _(Theatre for preaching).
MS. B, 55a (see page 56, Fig. 1). A domed church after the type of
Pl. XCV, No. 1, shows four theatres occupying the apses and facing
the square_ "coro" _(choir), which is in the centre between the four
pillars of the dome.[Footnote 1: The note_ teatro de predicar, _on
the right side is, I believe, in the handwriting of Pompeo Leoni. J.
P. R.] The rising arrangement of the seats is shown in the sketch
above. At the place marked_ B _Leonardo wrote_ teatri per uldire
messa _(rows of seats to hear mass), at_ T teatri,_ and at_ C coro
_(choir).
In MS. C.A. 260, are slight sketches of two plans for rectangular
choirs and two elevations of the altar and pulpit which seem to be
in connection with these plans.
In MS. Ash II, 8a (see p. 56 and 57. Fig. 2 and 3)._ "Locho dove si
predica" _(Place for preaching). A most singular plan for a
building. The interior is a portion of a sphere, the centre of which
is the summit of a column destined to serve as the preacher's
pulpit. The inside is somewhat like a modern theatre, whilst the
exterior and the galleries and stairs recall the ancient
amphitheatres.
[Illustration with caption: Page 57, Fig. 4. A plan accompanying the
two preceding drawings. If this gives the complete form Leonardo
intended for the edifice, it would have comprised only about two
thirds of the circle. Leonardo wrote in the centre_ "fondamento", _a
word he often employed for plans, and on the left side of the view
of the exterior:_ locho dove si predicha _(a place for preaching
in)._]
_D. Design for a Mausoleum.
Pl. XCVIII (P. V., 182._ No. d'ordre 2386). In the midst of a hilly
landscape rises an artificial mountain in the form of a gigantic
cone, crowned by an imposing temple. At two thirds of the height a
terrace is cut out with six doorways forming entrances to galleries,
each leading to three sepulchral halls, so constructed as to contain
about five hundred funeral urns, disposed in the customary antique
style. From two opposite sides steps ascend to the terrace in a
single flight and beyond it to the temple above. A large circular
opening, like that in the Pantheon, is in the dome above what may be
the altar, or perhaps the central monument on the level of the
terrace below.
The section of a gallery given in the sketch to the right below
shows the roof to be constructed on the principle of superimposed
horizontal layers, projecting one beyond the other, and each
furnished with a sort of heel, which appears to be undercut, so as
to give the appearance of a beam from within. Granite alone would be
adequate to the dimensions here given to the key stone, as the
thickness of the layers can hardly be considered to be less than a
foot. In taking this as the basis of our calculation for the
dimensions of the whole construction, the width of the chamber would
be about 25 feet but, judging from the number of urns it
contains--and there is no reason to suppose that these urns were
larger than usual--it would seem to be no more than about 8 or 10
feet.
The construction of the vaults resembles those in the galleries of
some etruscan tumuli, for instance the Regulini Galeassi tomb at
Cervetri (lately discovered) and also that of the chamber and
passages of the pyramid of Cheops and of the treasury of Atreus at
Mycenae.
The upper cone displays not only analogies with the monuments
mentioned in the note, but also with Etruscan tumuli, such as the
Cocumella tomb at Vulci, and the Regulini Galeassi tomb_[Footnote 1:
_See_ FERSGUSON, _Handbook of Architecture, I,_ 291.]. _The whole
scheme is one of the most magnificent in the history of
Architecture.
It would be difficult to decide as to whether any monument he had
seen suggested this idea to Leonardo, but it is worth while to
enquire, if any monument, or group of monuments of an earlier date
may be supposed to have done so._[Footnote 2: _There are, in
Algiers, two Monuments, commonly called_ "Le Madracen" _and_ "Le
tombeau de la Chretienne," _which somewhat resemble Leonardo's
design. They are known to have served as the Mausolea of the Kings
of Mauritania. Pomponius Mela, the geographer of the time of the
Emperor Claudius, describes them as having been_ "Monumentum commune
regiae gentis." _See_ Le Madracen, Rapport fait par M. le Grand
Rabbin AB. CAHEN, Constantine 1873--Memoire sur les fouilles
executees au Madras'en .. par le Colonel BRUNON, Constantine
l873.--Deux Mausolees Africains, le Madracen et le tombeau de la
Chretienne par M. J. DE LAURIERE, Tours l874.--Le tombeau de la
Chretienne, Mausolee des rois Mauritaniens par M. BERBRUGGER, Alger
1867.--_I am indebted to M. LE BLANC, of the Institut, and M. LUD,
LALANNE, Bibliothecaire of the Institut for having first pointed out
to me the resemblance between these monuments; while M. ANT. HERON
DE VlLLEFOSSE of the Louvre was kind enough to place the
abovementioned rare works at my disposal. Leonardo's observations on
the coast of Africa are given later in this work. The Herodium near
Bethlehem in Palestine_ (Jebel el Fureidis, _the Frank Mountain)
was, according to the latest researches, constructed on a very
similar plan. See_ Der Frankenberg, von Baurath C. SCHICK in
Jerusalem, Zeitschrift des Deutschen Palastina-Vereins, _Leipzag_
1880, _Vol. III, pages_ 88-99 _and Plates IV and V._ J. P. R.]
_E. Studies for the Central Tower, or Tiburio of Milan Cathedral.
Towards the end of the fifteenth century the Fabbricceria del Duomo
had to settle on the choice of a model for the crowning and central
part of this vast building. We learn from a notice published by G.
L. Calvi [Footnote: G. L. CALVI, Notizie sulla vita e sulle opere
dei principali architetti scultori e pittori che fiorirono in
Milano, Part III, 20. See also: H. DE GEYMULLER, Les projets
primitifs etc. I, 37 and 116-119.--The Fabbricceria of the Duomo has
lately begun the publication of the archives, which may possibly
tell us more about the part taken by Leonardo, than has hitherto
been known.] that among the artists who presented models in the year
1488 were: Bramante, Pietro da Gorgonzola, Luca Paperio (Fancelli),
and Leonardo da Vinci.--
Several sketches by Leonardo refer to this important project:
Pl. XCIX, No. 2 (MS. S. K. III, No. 36a) a small plan of the whole
edifice.--The projecting chapels in the middle of the transept are
wanting here. The nave appears to be shortened and seems to be
approached by an inner "vestibolo".--
Pl. C, No. 2 (Tr. 21). Plan of the octagon tower, giving the
disposition of the buttresses; starting from the eight pillars
adjoining the four principal piers and intended to support the eight
angles of the Tiburio. These buttresses correspond exactly with
those described by Bramante as existing in the model presented by
Omodeo. [Footnote: Bramante's opinion was first published by G.
MONGERl, Arch. stor. Lomb. V, fasc. 3 and afterwards by me in the
publication mentioned in the preceding note.]
Pl. C, 3 (MS. Tr. 16). Two plans showing different arrangements of
the buttresses, which seem to be formed partly by the intersection
of a system of pointed arches such as that seen in **
Pl. C, No. 5 (MS. B, 27a) destined to give a broader base to the
drum. The text underneath is given under No. 788.
MS. B, 3--three slight sketches of plans in connexion with the
preceding ones._
_Pl. XCIX, No.1 (MS. Tr. 15) contains several small sketches of
sections and exterior views of the Dome; some of them show
buttress-walls shaped as inverted arches. Respecting these Leonardo
notes:_
758.
L'arco rivescio e migliore per fare spalla che l'ordinario, perche
il rovescio trova sotto se muro resistete alla sua debolezza, e
l'ordinario no trova nel suo debole se non aria
The inverted arch is better for giving a shoulder than the ordinary
one, because the former finds below it a wall resisting its
weakness, whilst the latter finds in its weak part nothing but air.
[Footnote: _Three slight sketches of sections on the same
leaf--above those reproduced here--are more closely connected with
the large drawing in the centre of Pl. C, No. 4 (M.S, Tr. 41) which
shows a section of a very elevated dome, with double vaults,
connected by ribs and buttresses ingeniously disposed, so as to
bring the weight of the lantern to bear on the base of the dome.
A sketch underneath it shows a round pillar on which is indicated
which part of its summit is to bear the weight: "il pilastro sara
charicho in . a . b." (The column will bear the weight at a b.)
Another note is above on the right side:_ Larcho regiera tanto sotto
asse chome di sopra se _(The arch supports as much below it [i. e. a
hanging weight] as above it).
Pl. C, No. 1 (C. A. 303a). Larger sketch of half section of the
Dome, with a very complicated system of arches, and a double vault.
Each stone is shaped so as to be knit or dovetailed to its
neighbours. Thus the inside of the Dome cannot be seen from below.
MS. C. A. 303b. A repetition of the preceding sketch with very
slight modifications._]
[Figs. 1. and Fig. 2. two sketeches of the dome]
MS. Tr. 9 (see Fig. 1 and 2). Section of the Dome with reverted
buttresses between the windows, above which iron anchors or chains
seem to be intended. Below is the sketch of the outside._
_PI. XCIX, No. 3 (C. A., 262a) four sketches of the exterior of the
Dome.
C. A. 12. Section, showing the points of rupture of a gothic vault,
in evident connection with the sketches described above.
It deserves to be noticed how easily and apparently without effort,
Leonardo manages to combine gothic details and structure with the
more modern shape of the Dome.
The following notes are on the same leaf,_ oni cosa poderosa, _and_
oni cosa poderosa desidera de(scendere); _farther below, several
multiplications most likely intended to calculate the weight of some
parts of the Dome, thus 16 x 47 = 720; 720 x 800 = 176000, next to
which is written:_ peso del pilastro di 9 teste _(weight of the
pillar 9 diameters high).
Below:_ 176000 x 8 = 1408000; _and below:_
Semjlio e se ce 80 (?) il peso del tiburio _(six millions six
hundred (?) 80 the weight of the Dome).
Bossi hazarded the theory that Leonardo might have been the
architect who built the church of Sta. Maria delle Grazie, but there
is no evidence to support this, either in documents or in the
materials supplied by Leonardos manuscripts and drawings. The sketch
given at the side shows the arrangement of the second and third
socle on the apses of the choir of that church; and it is remarkable
that those sketches, in MS. S. K. M. II2, 2a and Ib, occur with the
passage given in Volume I as No. 665 and 666 referring to the
composition of the Last Supper in the Refectory of that church._]
_F. The Project for lifting up the Battistero of Florence and
setting it on a basement._
_Among the very few details Vasari gives as to the architectural
studies of Leonardo, we read: "And among these models and designs
there was one by way of which he showed several times to many
ingenious citizens who then governed Florence, his readiness to lift
up without ruining it, the church of San Giovanni in Florence (the
Battistero, opposite the Duomo) in order to place under it the
missing basement with steps; he supported his assertions with
reasons so persuasive, that while he spoke the undertaking seemed
feasable, although every one of his hearers, when he had departed,
could see by himself the impossibility of so vast an undertaking."_
[Footnote: _This latter statement of Vasari's must be considered to
be exaggerated. I may refer here to some data given by_ LIBRI,
Histoire des sciences mathematiques en Italie (II, 216, 217): "On a
cru dans ces derniers temps faire un miracle en mecanique en
effectuant ce transport, et cependant des l'annee 1455, Gaspard Nadi
et Aristote de Fioravantio avaient transporte, a une distance
considerable, la tour de la Magione de Bologne, avec ses fondements,
qui avait presque quatre-vingts pieds de haut. Le continuateur de la
chronique de Pugliola dit que le trajet fut de 35 pieds et que
durant le transport auquel le chroniqueur affirme avoir assiste, il
arriva un accident grave qui fit pencher de trois pieds la tour
pendant qu'elle etait suspendue, mais que cet accident fut
promptement repare (Muratori, Scriptores rer. ital. Tom. XVIII, col.
717, 718). Alidosi a rapporte une note ou Nadi rend compte de ce
transport avec une rare simplicite. D'apres cette note, on voit que
les operations de ce genre n'etaient pas nouvelles. Celle-ci ne
couta que 150 livres (monnaie d'alors) y compris le cadeau que le
Legat fit aux deux mecaniciens. Dans la meme annee, Aristote
redressa le clocher de Cento, qui penchait de plus de cinq pieds
(Alidosi, instruttione p. 188-- Muratori, Scriptores rer. ital.,
tom. XXIII, col. 888.--Bossii, chronica Mediol., 1492, in-fol. ad
ann. 1455). On ne concoit pas comment les historiens des beaux-arts
ont pu negliger de tels hommes." J. P. R.]
_In the MS. C. A. fol. 293, there are two sketches which possibly
might have a bearing on this bold enterprise. We find there a plan
of a circular or polygonal edifice surrounded by semicircular arches
in an oblique position. These may be taken for the foundation of the
steps and of the new platform. In the perspective elevation the same
edifice, forming a polygon, is shown as lifted up and resting on a
circle of inverted arches which rest on an other circle of arches in
the ordinary position, but so placed that the inverted arches above
rest on the spandrels of the lower range._
_What seems to confirm the supposition that the lifting up of a
building is here in question, is the indication of engines for
winding up, such as jacks, and a rack and wheel. As the lifting
apparatus represented on this sheet does not seem particularly
applicable to an undertaking of such magnitude, we may consider it
to be a first sketch or scheme for the engines to be used._
_G. Description of an unknown Temple._
759.
Twelve flights of steps led up to the great temple, which was eight
hundred braccia in circumference and built on an octagonal plan. At
the eight corners were eight large plinths, one braccia and a half
high, and three wide, and six long at the bottom, with an angle in
the middle; on these were eight great pillars, standing on the
plinths as a foundation, and twenty four braccia high. And on the
top of these were eight capitals three braccia long and six wide,
above which were the architrave frieze and cornice, four braccia and
a half high, and this was carried on in a straight line from one
pillar to the next and so, continuing for eight hundred braccia,
surrounded the whole temple, from pillar to pillar. To support this
entablature there were ten large columns of the same height as the
pillars, three braccia thick above their bases which were one
braccia and a half high.
The ascent to this temple was by twelve flights of steps, and the
temple was on the twelfth, of an octagonal form, and at each angle
rose a large pillar; and between the pillars were placed ten columns
of the same height as the pillars, rising at once from the pavement
to a height of twenty eight braccia and a half; and at this height
the architrave, frieze and cornice were placed which surrounded the
temple having a length of eight hundred braccia. At the same height,
and within the temple at the same level, and all round the centre of
the temple at a distance of 24 braccia farther in, are pillars
corresponding to the eight pillars in the angles, and columns
corresponding to those placed in the outer spaces. These rise to the
same height as the former ones, and over these the continuous
architrave returns towards the outer row of pillars and columns.
[Footnote: Either this description is incomplete, or, as seems to me
highly probable, it refers to some ruin. The enormous dimensions
forbid our supposing this to be any temple in Italy or Greece. Syria
was the native land of colossal octagonal buildings, in the early
centuries A. D. The Temple of Baalbek, and others are even larger
than that here described. J. P. R.]
_V. Palace architecture.
But a small number of Leonardo's drawings refer to the architecture
of palaces, and our knowledge is small as to what style Leonardo
might have adopted for such buildings.
Pl. CII No. 1 (W. XVIII). A small portion of a facade of a palace
in two stories, somewhat resembling Alberti's Palazzo
Rucellai.--Compare with this Bramante's painted front of the Casa
Silvestri, and a painting by Montorfano in San Pietro in Gessate at
Milan, third chapel on the left hand side and also with Bramante's
palaces at Rome. The pilasters with arabesques, the rustica between
them, and the figures over the window may be painted or in
sgraffito. The original is drawn in red chalk.
Pl. LXXXI No. 1 (MS. Tr. 42). Sketch of a palace with battlements
and decorations, most likely graffiti; the details remind us of
those in the Castello at Vigevano._ [Footnote 1: _Count GIULIO
PORRO, in his valuable contribution to the_ Archivio Storico
Lombardo, Anno VIII, Fasc. IV (31 Dec. 1881): Leonardo da Vinci,
Libro di Annotazioni e Memorie, _refers to this in the following
note:_ "Alla pag. 41 vi e uno schizzo di volta ed accanto scrisse:
'il pilastro sara charicho in su 6' e potrebbe darsi che si
riferisse alla cupola della chiesa delle Grazie tanto piu che a
pag. 42 vi e un disegno che rassomiglia assai al basamento che oggi
si vede nella parte esterna del coro di quella chiesa." _This may
however be doubted. The drawing, here referred to, on page 41 of the
same manuscript, is reproduced on Pl. C No. 4 and described on page
61 as being a study for the cupola of the Duomo of Milan._ J. P. R.]
_MS. Mz. 0", contains a design for a palace or house with a loggia
in the middle of the first story, over which rises an attic with a
Pediment reproduced on page 67. The details drawn close by on the
left seem to indicate an arrangement of coupled columns against the
wall of a first story.
Pl. LXXXV No. 14 (MS. S. K. M. Ill 79a) contains a very slight
sketch in red chalk, which most probably is intended to represent
the facade of a palace. Inside is the short note 7 he 7 (7 and 7)._
_MS. J2 8a (see pages 68 Fig. 1 and 2) contains a view of an unknown
palace. Its plan is indicated at the side._
_In MS. Br. M. 126a(see Fig. 3 on page 68) there is a sketch of a
house, on which Leonardo notes; casa con tre terrazi (house with
three terraces)._
_Pl. CX, No. 4 (MS. L. 36b) represents the front of a fortified
building drawn at Cesena in 1502 (see No. 1040)._
_Here we may also mention the singular building in the allegorical
composition represented on Pl. LVIII in Vol. I. In front of it
appears the head of a sphinx or of a dragon which seems to be
carrying the palace away._
_The following texts refer to the construction of palaces and other
buildings destined for private use:_
760.
In the courtyard the walls must be half the height of its width,
that is if the court be 40 braccia, the house must be 20 high as
regards the walls of the said courtyard; and this courtyard must be
half as wide as the whole front.
[Footnote: See Pl. CI, no. 1, and compare the dimensions here given,
with No. 748 lines 26-29; and the drawing belonging to it Pl. LXXXI,
no. 2.]
On the dispositions of a stable.
761.
FOR MAKING A CLEAN STABLE.
The manner in which one must arrange a stable. You must first divide
its width in 3 parts, its depth matters not; and let these 3
divisions be equal and 6 braccia broad for each part and 10 high,
and the middle part shall be for the use of the stablemasters; the 2
side ones for the horses, each of which must be 6 braccia in width
and 6 in length, and be half a braccio higher at the head than
behind. Let the manger be at 2 braccia from the ground, to the
bottom of the rack, 3 braccia, and the top of it 4 braccia. Now, in
order to attain to what I promise, that is to make this place,
contrary to the general custom, clean and neat: as to the upper part
of the stable, i. e. where the hay is, that part must have at its
outer end a window 6 braccia high and 6 broad, through which by
simple means the hay is brought up to the loft, as is shown by the
machine _E_; and let this be erected in a place 6 braccia wide, and
as long as the stable, as seen at _k p_. The other two parts, which
are on either side of this, are again divided; those nearest to the
hay-loft are 4 braccia, _p s_, and only for the use and circulation
of the servants belonging to the stable; the other two which reach
to the outer walls are 2 braccia, as seen at _s k_, and these are
made for the purpose of giving hay to the mangers, by means of
funnels, narrow at the top and wide over the manger, in order that
the hay should not choke them. They must be well plastered and clean
and are represented at 4 _f s_. As to the giving the horses water,
the troughs must be of stone and above them [cisterns of] water. The
mangers may be opened as boxes are uncovered by raising the lids.
[Footnote: See Pl. LXXVIII, No.1.]
Decorations for feasts.
762.
THE WAY TO CONSTRUCT A FRAME-WORK FOR DECORATING BUILDINGS.
The way in which the poles ought to be placed for tying bunches of
juniper on to them. These poles must lie close to the framework of
the vaulting and tie the bunches on with osier withes, so as to clip
them even afterwards with shears.
Let the distance from one circle to another be half a braccia; and
the juniper [sprigs] must lie top downwards, beginning from below.
Round this column tie four poles to which willows about as thick as
a finger must be nailed and then begin from the bottom and work
upwards with bunches of juniper sprigs, the tops downwards, that is
upside down. [Footnote: See Pl. CII, No. 3. The words here given as
the title line, lines 1--4, are the last in the original MS.--Lines
5--16 are written under fig. 4.]
763.
The water should be allowed to fall from the whole circle _a b_.
[Footnote: Other drawings of fountains are given on Pl. CI (W. XX);
the original is a pen and ink drawing on blue paper; on Pl. CIII
(MS. B.) and Pl. LXXXII.]
_VI. Studies of architectural details._
_Several of Leonardo's drawings of architectural details prove that,
like other great masters of that period, he had devoted his
attention to the study of the proportion of such details. As every
organic being in nature has its law of construction and growth,
these masters endeavoured, each in his way, to discover and prove a
law of proportion in architecture. The following notes in Leonardo's
manuscripts refer to this subject._
_MS. S. K. M. Ill, 47b (see Fig. 1). A diagram, indicating the rules
as given by Vitruvius and by Leon Battista Alberti for the
proportions of the Attic base of a column._
_MS. S. K. M. Ill 55a (see Fig. 2). Diagram showing the same rules._
764.
B toro superiore . . . . . toro superiore
2B nestroli . . . . . . astragali quadre
3B orbiculo . . . . . . . . troclea
4B nestroli . . . . . . astragali quadre
5B toro iferiore . . . . . . toro iferiore
6B latastro . . . . . . . . plintho
[Footnote: No explanation can be offered of the meaning of the
letter B, which precedes each name. It may be meant for _basa_
(base). Perhaps it refers to some author on architecture or an
architect (Bramante?) who employed the designations, thus marked for
the mouldings. 3. _troclea._ Philander: _Trochlea sive trochalia aut
rechanum._ 6. _Laterculus_ or _latastrum_ is the Latin name for
_Plinthus_ (pi lambda Xiv) but Vitruvius adopted this Greek name
and "latastro" seems to have been little in use. It is to be found
besides the text given above, as far as I am aware, only two
drawings of the Uffizi Collection, where in one instance, it
indicates the _abacus_ of a Doric capital.]
765.
STEPS OF URRBINO.
The plinth must be as broad as the thickness of the wall against
which the plinth is built. [Footnote: See Pl. CX No. 3. The hasty
sketch on the right hand side illustrates the unsatisfactory effect
produced when the plinth is narrower than the wall.]
766.
The ancient architects ...... beginning with the Egyptians (?) who,
as Diodorus Siculus writes, were the first to build and construct
large cities and castles, public and private buildings of fine form,
large and well proportioned .....
The column, which has its thickness at the third part .... The one
which would be thinnest in the middle, would break ...; the one
which is of equal thickness and of equal strength, is better for the
edifice. The second best as to the usefulness will be the one whose
greatest thickness is where it joins with the base.
[Footnote: See Pl. CIII, No. 3, where the sketches belonging to
lines 10--16 are reproduced, but reversed. The sketch of columns,
here reproduced by a wood cut, stands in the original close to lines
5--8.]
The capital must be formed in this way. Divide its thickness at the
top into 8; at the foot make it 5/7, and let it be 5/7 high and you
will have a square; afterwards divide the height into 8 parts as you
did for the column, and then take 1/8 for the echinus and another
eighth for the thickness of the abacus on the top of the capital.
The horns of the abacus of the capital have to project beyond the
greatest width of the bell 2/7, i. e. sevenths of the top of the
bell, so 1/7 falls to the projection of each horn. The truncated
part of the horns must be as broad as it is high. I leave the rest,
that is the ornaments, to the taste of the sculptors. But to return
to the columns and in order to prove the reason of their strength or
weakness according to their shape, I say that when the lines
starting from the summit of the column and ending at its base and
their direction and length ..., their distance apart or width may be
equal; I say that this column ...
767.
The cylinder of a body columnar in shape and its two opposite ends
are two circles enclosed between parallel lines, and through the
centre of the cylinder is a straight line, ending at the centre of
these circles, and called by the ancients the axis.
[Footnote: Leonardo wrote these lines on the margin of a page of the
Trattato di Francesco di Giorgio, where there are several drawings
of columns, as well as a head drawn in profile inside an outline
sketch of a capital.]
768.
_a b_ is 1/3 of _n m_; _m o_ is 1/6 of _r o_. The ovolo projects 1/6
of _r o_; _s_ 7 1/5 of _r o_, _a b_ is divided into 9 1/2; the
abacus is 3/9 the ovolo 4/9, the bead-moulding and the fillet 2/9
and 1/2.
[Footnote: See Pl. LXXXV, No. 16. In the original the drawing and
writing are both in red chalk.]
_Pl. LXXXV No. 6 (MS. Ash. II 6b) contains a small sketch of a
capital with the following note, written in three lines:_ I chorni
del capitelo deono essere la quarta parte d'uno quadro _(The horns
of a capital must measure the fourth part of a square)._
_MS. S. K. M. III 72b contains two sketches of ornamentations of
windows._
_In MS. C. A. 308a; 938a (see Pl. LXXXII No. 1) there are several
sketches of columns. One of the two columns on the right is similar
to those employed by Bramante at the Canonica di S. Ambrogio. The
same columns appear in the sketch underneath the plan of a castle.
There they appear coupled, and in two stories one above the other.
The archivolls which seem to spring out of the columns, are shaped
like twisted cords, meant perhaps to be twisted branches. The walls
between the columns seem to be formed out of blocks of wood, the
pedestals are ornamented with a reticulated pattern. From all this
we may suppose that Leonardo here had in mind either some festive
decoration, or perhaps a pavilion for some hunting place or park.
The sketch of columns marked "35" gives an example of columns shaped
like candelabra, a form often employed at that time, particularly in
Milan, and the surrounding districts for instance in the Cortile di
Casa Castiglione now Silvestre, in the cathedral of Como, at Porta
della Rana &c._
769.
CONCERNING ARCHITRAVES OF ONE OR SEVERAL PIECES.
An architrave of several pieces is stronger than that of one single
piece, if those pieces are placed with their length in the direction
of the centre of the world. This is proved because stones have their
grain or fibre generated in the contrary direction i. e. in the
direction of the opposite horizons of the hemisphere, and this is
contrary to fibres of the plants which have ...
[Footnote: The text is incomplete in the original.]
_The Proportions of the stories of a building are indicated by a
sketch in MS. S. K. M. II2 11b (see Pl. LXXXV No. 15). The measures
are written on the left side, as follows: br 1 1/2--6 3/4--br
1/12--2 br--9 e 1/2--1 1/2--br 5--o 9--o 3 [br=braccia; o=oncie].
Pl. LXXXV No. 13 (MS. B. 62a) and Pl. XCIII No. 1. (MS. B. 15a) give
a few examples of arches supported on piers._
_XIII.
Theoretical writings on Architecture.
Leonardo's original writings on the theory of Architecture have come
down to us only in a fragmentary state; still, there seems to be no
doubt that he himself did not complete them. It would seem that
Leonardo entertained the idea of writing a large and connected book
on Architecture; and it is quite evident that the materials we
possess, which can be proved to have been written at different
periods, were noted down with a more or less definite aim and
purpose. They might all be collected under the one title: "Studies
on the Strength of Materials". Among them the investigations on the
subject of fissures in walls are particularly thorough, and very
fully reported; these passages are also especially interesting,
because Leonardo was certainly the first writer on architecture who
ever treated the subject at all. Here, as in all other cases
Leonardo carefully avoids all abstract argument. His data are not
derived from the principles of algebra, but from the laws of
mechanics, and his method throughout is strictly experimental.
Though the conclusions drawn from his investigations may not have
that precision which we are accustomed to find in Leonardo's
scientific labours, their interest is not lessened. They prove at
any rate his deep sagacity and wonderfully clear mind. No one
perhaps, who has studied these questions since Leonardo, has
combined with a scientific mind anything like the artistic delicacy
of perception which gives interest and lucidity to his observations.
I do not assert that the arrangement here adopted for the passages
in question is that originally intended by Leonardo; but their
distribution into five groups was suggested by the titles, or
headings, which Leonardo himself prefixed to most of these notes.
Some of the longer sections perhaps should not, to be in strict
agreement with this division, have been reproduced in their entirety
in the place where they occur. But the comparatively small amount of
the materials we possess will render them, even so, sufficiently
intelligible to the reader; it did not therefore seem necessary or
desirable to subdivide the passages merely for the sake of strict
classification._
_The small number of chapters given under the fifth class, treating
on the centre of gravity in roof-beams, bears no proportion to the
number of drawings and studies which refer to the same subject. Only
a small selection of these are reproduced in this work since the
majority have no explanatory text._
I.
ON FISSURES IN WALLS.
770.
First write the treatise on the causes of the giving way of walls
and then, separately, treat of the remedies.
Parallel fissures constantly occur in buildings which are erected on
a hill side, when the hill is composed of stratified rocks with an
oblique stratification, because water and other moisture often
penetrates these oblique seams carrying in greasy and slippery soil;
and as the strata are not continuous down to the bottom of the
valley, the rocks slide in the direction of the slope, and the
motion does not cease till they have reached the bottom of the
valley, carrying with them, as though in a boat, that portion of the
building which is separated by them from the rest. The remedy for
this is always to build thick piers under the wall which is
slipping, with arches from one to another, and with a good scarp and
let the piers have a firm foundation in the strata so that they may
not break away from them.
In order to find the solid part of these strata, it is necessary to
make a shaft at the foot of the wall of great depth through the
strata; and in this shaft, on the side from which the hill slopes,
smooth and flatten a space one palm wide from the top to the bottom;
and after some time this smooth portion made on the side of the
shaft, will show plainly which part of the hill is moving.
[Footnote: See Pl. CIV.]
771.
The cracks in walls will never be parallel unless the part of the
wall that separates from the remainder does not slip down.
WHAT IS THE LAW BY WHICH BUILDINGS HAVE STABILITY.
The stability of buildings is the result of the contrary law to the
two former cases. That is to say that the walls must be all built up
equally, and by degrees, to equal heights all round the building,
and the whole thickness at once, whatever kind of walls they may be.
And although a thin wall dries more quickly than a thick one it will
not necessarily give way under the added weight day by day and thus,
[16] although a thin wall dries more quickly than a thick one, it
will not give way under the weight which the latter may acquire from
day to day. Because if double the amount of it dries in one day, one
of double the thickness will dry in two days or thereabouts; thus
the small addition of weight will be balanced by the smaller
difference of time [18].
The adversary says that _a_ which projects, slips down.
And here the adversary says that _r_ slips and not _c_.
HOW TO PROGNOSTICATE THE CAUSES OF CRACKS IN ANY SORT OF WALL.
The part of the wall which does not slip is that in which the
obliquity projects and overhangs the portion which has parted from
it and slipped down.
ON THE SITUATION OF FOUNDATIONS AND IN WHAT PLACES THEY ARE A CAUSE
OF RUIN.
When the crevice in the wall is wider at the top than at the bottom,
it is a manifest sign, that the cause of the fissure in the wall is
remote from the perpendicular line through the crevice.
[Footnote: Lines 1-5 refer to Pl. CV, No. 2. Line 9 _alle due
anteciedete_, see on the same page.
Lines 16-18. The translation of this is doubtful, and the meaning in
any case very obscure.
Lines 19-23 are on the right hand margin close to the two sketches
on Pl. CII, No. 3.]
772.
OF CRACKS IN WALLS, WHICH ARE WIDE AT THE BOTTOM AND NARROW AT THE
TOP AND OF THEIR CAUSES.
That wall which does not dry uniformly in an equal time, always
cracks.
A wall though of equal thickness will not dry with equal quickness
if it is not everywhere in contact with the same medium. Thus, if
one side of a wall were in contact with a damp slope and the other
were in contact with the air, then this latter side would remain of
the same size as before; that side which dries in the air will
shrink or diminish and the side which is kept damp will not dry. And
the dry portion will break away readily from the damp portion
because the damp part not shrinking in the same proportion does not
cohere and follow the movement of the part which dries continuously.
OF ARCHED CRACKS, WIDE AT THE TOP, AND NARROW BELOW.
Arched cracks, wide at the top and narrow below are found in
walled-up doors, which shrink more in their height than in their
breadth, and in proportion as their height is greater than their
width, and as the joints of the mortar are more numerous in the
height than in the width.
The crack diminishes less in _r o_ than in _m n_, in proportion as
there is less material between _r_ and _o_ than between _n_ and _m_.
Any crack made in a concave wall is wide below and narrow at the
top; and this originates, as is here shown at _b c d_, in the side
figure.
1. That which gets wet increases in proportion to the moisture it
imbibes.
2. And a wet object shrinks, while drying, in proportion to the
amount of moisture which evaporates from it.
[Footnote: The text of this passage is reproduced in facsimile on
Pl. CVI to the left. L. 36-40 are written inside the sketch No. 2.
L. 41-46 are partly written over the sketch No. 3 to which they
refer.]
773.
OF THE CAUSES OF FISSURES IN [THE WALLS OF] PUBLIC AND PRIVATE
BUILDINGS.
The walls give way in cracks, some of which are more or less
vertical and others are oblique. The cracks which are in a vertical
direction are caused by the joining of new walls, with old walls,
whether straight or with indentations fitting on to those of the old
wall; for, as these indentations cannot bear the too great weight of
the wall added on to them, it is inevitable that they should break,
and give way to the settling of the new wall, which will shrink one
braccia in every ten, more or less, according to the greater or
smaller quantity of mortar used between the stones of the masonry,
and whether this mortar is more or less liquid. And observe, that
the walls should always be built first and then faced with the
stones intended to face them. For, if you do not proceed thus, since
the wall settles more than the stone facing, the projections left on
the sides of the wall must inevitably give way; because the stones
used for facing the wall being larger than those over which they are
laid, they will necessarily have less mortar laid between the
joints, and consequently they settle less; and this cannot happen if
the facing is added after the wall is dry.
_a b_ the new wall, _c_ the old wall, which has already settled; and
the part _a b_ settles afterwards, although _a_, being founded on
_c_, the old wall, cannot possibly break, having a stable foundation
on the old wall. But only the remainder _b_ of the new wall will
break away, because it is built from top to bottom of the building;
and the remainder of the new wall will overhang the gap above the
wall that has sunk.
774.
A new tower founded partly on old masonry.
775.
OF STONES WHICH DISJOIN THEMSELVES FROM THEIR MORTAR.
Stones laid in regular courses from bottom to top and built up with
an equal quantity of mortar settle equally throughout, when the
moisture that made the mortar soft evaporates.
By what is said above it is proved that the small extent of the new
wall between _A_ and _n_ will settle but little, in proportion to
the extent of the same wall between _c_ and _d_. The proportion will
in fact be that of the thinness of the mortar in relation to the
number of courses or to the quantity of mortar laid between the
stones above the different levels of the old wall.
[Footnote: See Pl. CV, No. 1. The top of the tower is wanting in
this reproduction, and with it the letter _n_ which, in the
original, stands above the letter _A_ over the top of the tower,
while _c_ stands perpendicularly over _d_.]
776.
This wall will break under the arch _e f_, because the seven whole
square bricks are not sufficient to sustain the spring of the arch
placed on them. And these seven bricks will give way in their middle
exactly as appears in _a b_. The reason is, that the brick _a_ has
above it only the weight _a k_, whilst the last brick under the arch
has above it the weight _c d x a_.
_c d_ seems to press on the arch towards the abutment at the point
_p_ but the weight _p o_ opposes resistence to it, whence the whole
pressure is transmitted to the root of the arch. Therefore the foot
of the arch acts like 7 6, which is more than double of _x z_.
II.
ON FISSURES IN NICHES.
777.
ON FISSURES IN NICHES.
An arch constructed on a semicircle and bearing weights on the two
opposite thirds of its curve will give way at five points of the
curve. To prove this let the weights be at _n m_ which will break
the arch _a_, _b_, _f_. I say that, by the foregoing, as the
extremities _c_ and _a_ are equally pressed upon by the thrust _n_,
it follows, by the 5th, that the arch will give way at the point
which is furthest from the two forces acting on them and that is the
middle _e_. The same is to be understood of the opposite curve, _d g
b_; hence the weights _n m_ must sink, but they cannot sink by the
7th, without coming closer together, and they cannot come together
unless the extremities of the arch between them come closer, and if
these draw together the crown of the arch must break; and thus the
arch will give way in two places as was at first said &c.
I ask, given a weight at _a_ what counteracts it in the direction
_n_ _f_ and by what weight must the weight at _f_ be counteracted.
778.
ON THE SHRINKING OF DAMP BODIES OF DIFFERENT THICKNESS AND WIDTH.
The window _a_ is the cause of the crack at _b_; and this crack is
increased by the pressure of _n_ and _m_ which sink or penetrate
into the soil in which foundations are built more than the lighter
portion at _b_. Besides, the old foundation under _b_ has already
settled, and this the piers _n_ and _m_ have not yet done. Hence the
part _b_ does not settle down perpendicularly; on the contrary, it
is thrown outwards obliquely, and it cannot on the contrary be
thrown inwards, because a portion like this, separated from the main
wall, is larger outside than inside and the main wall, where it is
broken, is of the same shape and is also larger outside than inside;
therefore, if this separate portion were to fall inwards the larger
would have to pass through the smaller--which is impossible. Hence
it is evident that the portion of the semicircular wall when
disunited from the main wall will be thrust outwards, and not
inwards as the adversary says.
When a dome or a half-dome is crushed from above by an excess of
weight the vault will give way, forming a crack which diminishes
towards the top and is wide below, narrow on the inner side and wide
outside; as is the case with the outer husk of a pomegranate,
divided into many parts lengthwise; for the more it is pressed in
the direction of its length, that part of the joints will open most,
which is most distant from the cause of the pressure; and for that
reason the arches of the vaults of any apse should never be more
loaded than the arches of the principal building. Because that which
weighs most, presses most on the parts below, and they sink into the
foundations; but this cannot happen to lighter structures like the
said apses.
[Footnote: The figure on Pl. CV, No. 4 belongs to the first
paragraph of this passage, lines 1-14; fig. 5 is sketched by the
side of lines l5--and following. The sketch below of a pomegranate
refers to line 22. The drawing fig. 6 is, in the original, over line
37 and fig. 7 over line 54.]
Which of these two cubes will shrink the more uniformly: the cube
_A_ resting on the pavement, or the cube _b_ suspended in the air,
when both cubes are equal in weight and bulk, and of clay mixed with
equal quantities of water?
The cube placed on the pavement diminishes more in height than in
breadth, which the cube above, hanging in the air, cannot do. Thus
it is proved. The cube shown above is better shown here below.
The final result of the two cylinders of damp clay that is _a_ and
_b_ will be the pyramidal figures below _c_ and _d_. This is proved
thus: The cylinder _a_ resting on block of stone being made of clay
mixed with a great deal of water will sink by its weight, which
presses on its base, and in proportion as it settles and spreads all
the parts will be somewhat nearer to the base because that is
charged with the whole weight.
III.
ON THE NATURE OF THE ARCH.
779.
WHAT IS AN ARCH?
The arch is nothing else than a force originated by two weaknesses,
for the arch in buildings is composed of two segments of a circle,
each of which being very weak in itself tends to fall; but as each
opposes this tendency in the other, the two weaknesses combine to
form one strength.
OF THE KIND OF PRESSURE IN ARCHES.
As the arch is a composite force it remains in equilibrium because
the thrust is equal from both sides; and if one of the segments
weighs more than the other the stability is lost, because the
greater pressure will outweigh the lesser.
OF DISTRIBUTING THE PRESSURE ABOVE AN ARCH.
Next to giving the segments of the circle equal weight it is
necessary to load them equally, or you will fall into the same
defect as before.
WHERE AN ARCH BREAKS.
An arch breaks at the part which lies below half way from the
centre.
SECOND RUPTURE OF THE ARCH.
If the excess of weight be placed in the middle of the arch at the
point _a_, that weight tends to fall towards _b_, and the arch
breaks at 2/3 of its height at _c e_; and _g e_ is as many times
stronger than _e a_, as _m o_ goes into _m n_.
ON ANOTHER CAUSE OF RUIN.
The arch will likewise give way under a transversal thrust, for when
the charge is not thrown directly on the foot of the arch, the arch
lasts but a short time.
780.
ON THE STRENGTH OF THE ARCH.
The way to give stability to the arch is to fill the spandrils with
good masonry up to the level of its summit.
ON THE LOADING OF ROUND ARCHES.
ON THE PROPER MANNER OF LOADING THE POINTED ARCH.
ON THE EVIL EFFECTS OF LOADING THE POINTED ARCH DIRECTLY ABOVE ITS
CROWN.
ON THE DAMAGE DONE TO THE POINTED ARCH BY THROWING THE PRESSURE ON
THE FLANKS.
An arch of small curve is safe in itself, but if it be heavily
charged, it is necessary to strengthen the flanks well. An arch of a
very large curve is weak in itself, and stronger if it be charged,
and will do little harm to its abutments, and its places of giving
way are _o p_.
[Footnote: Inside the large figure on the righi is the note: _Da
pesare la forza dell' archo_.]
781.
ON THE REMEDY FOR EARTHQUAKES.
The arch which throws its pressure perpendicularly on the abutments
will fulfil its function whatever be its direction, upside down,
sideways or upright.
The arch will not break if the chord of the outer arch does not
touch the inner arch. This is manifest by experience, because
whenever the chord _a o n_ of the outer arch _n r a_ approaches the
inner arch _x b y_ the arch will be weak, and it will be weaker in
proportion as the inner arch passes beyond that chord. When an arch
is loaded only on one side the thrust will press on the top of the
other side and be transmitted to the spring of the arch on that
side; and it will break at a point half way between its two
extremes, where it is farthest from the chord.
782.
A continuous body which has been forcibly bent into an arch, thrusts
in the direction of the straight line, which it tends to recover.
783.
In an arch judiciously weighted the thrust is oblique, so that the
triangle _c n b_ has no weight upon it.
784.
I here ask what weight will be needed to counterpoise and resist the
tendency of each of these arches to give way?
[Footnote: The two lower sketches are taken from the MS. S. K. M.
III, 10a; they have there no explanatory text.]
785.
ON THE STRENGTH OF THE ARCH IN ARCHITECTURE.
The stability of the arch built by an architect resides in the tie
and in the flanks.
ON THE POSITION OF THE TIE IN THE ABOVE NAMED ARCH.
The position of the tie is of the same importance at the beginning
of the arch and at the top of the perpendicular pier on which it
rests. This is proved by the 2nd "of supports" which says: that part
of a support has least resistance which is farthest from its solid
attachment; hence, as the top of the pier is farthest from the
middle of its true foundation and the same being the case at the
opposite extremities of the arch which are the points farthest from
the middle, which is really its [upper] attachment, we have
concluded that the tie _a b_ requires to be in such a position as
that its opposite ends are between the four above-mentioned
extremes.
The adversary says that this arch must be more than half a circle,
and that then it will not need a tie, because then the ends will not
thrust outwards but inwards, as is seen in the excess at _a c_, _b
d_. To this it must be answered that this would be a very poor
device, for three reasons. The first refers to the strength of the
arch, since it is proved that the circular parallel being composed
of two semicircles will only break where these semicircles cross
each other, as is seen in the figure _n m;_ besides this it follows
that there is a wider space between the extremes of the semicircle
than between the plane of the walls; the third reason is that the
weight placed to counterbalance the strength of the arch diminishes
in proportion as the piers of the arch are wider than the space
between the piers. Fourthly in proportion as the parts at _c a b d_
turn outwards, the piers are weaker to support the arch above them.
The 5th is that all the material and weight of the arch which are in
excess of the semicircle are useless and indeed mischievous; and
here it is to be noted that the weight placed above the arch will be
more likely to break the arch at _a b_, where the curve of the
excess begins that is added to the semicircle, than if the pier were
straight up to its junction with the semicircle [spring of the
arch].
AN ARCH LOADED OVER THE CROWN WILL GIVE WAY AT THE LEFT HAND AND
RIGHT HAND QUARTERS.
This is proved by the 7th of this which says: The opposite ends of
the support are equally pressed upon by the weight suspended to
them; hence the weight shown at _f_ is felt at _b c_, that is half
at each extremity; and by the third which says: in a support of
equal strength [throughout] that portion will give way soonest which
is farthest from its attachment; whence it follows that _d_ being
equally distant from _f, e_ .....
If the centering of the arch does not settle as the arch settles,
the mortar, as it dries, will shrink and detach itself from the
bricks between which it was laid to keep them together; and as it
thus leaves them disjoined the vault will remain loosely built, and
the rains will soon destroy it.
786.
ON THE STRENGTH AND NATURE OF ARCHES, AND WHERE THEY ARE STRONG OR
WEAK; AND THE SAME AS TO COLUMNS.
That part of the arch which is nearer to the horizontal offers least
resistance to the weight placed on it.
When the triangle _a z n_, by settling, drives backwards the 2/3 of
each 1/2 circle that is _a s_ and in the same way _z m_, the reason
is that _a_ is perpendicularly over _b_ and so likewise _z_ is above
_f_.
Either half of an arch, if overweighted, will break at 2/3 of its
height, the point which corresponds to the perpendicular line above
the middle of its bases, as is seen at _a b_; and this happens
because the weight tends to fall past the point _r_.--And if,
against its nature it should tend to fall towards the point _s_ the
arch _n s_ would break precisely in its middle. If the arch _n s_
were of a single piece of timber, if the weight placed at _n_ should
tend to fall in the line _n m_, the arch would break in the middle
of the arch _e m_, otherwise it will break at one third from the top
at the point a because from _a_ to _n_ the arch is nearer to the
horizontal than from _a_ to _o_ and from _o_ to _s_, in proportion
as _p t_ is greater than _t n_, _a o_ will be stronger than _a n_
and likewise in proportion as _s o_ is stronger than _o a_, _r p_
will be greater than _p t_.
The arch which is doubled to four times of its thickness will bear
four times the weight that the single arch could carry, and more in
proportion as the diameter of its thickness goes a smaller number of
times into its length. That is to say that if the thickness of the
single arch goes ten times into its length, the thickness of the
doubled arch will go five times into its length. Hence as the
thickness of the double arch goes only half as many times into its
length as that of the single arch does, it is reasonable that it
should carry half as much more weight as it would have to carry if
it were in direct proportion to the single arch. Hence as this
double arch has 4 times the thickness of the single arch, it would
seem that it ought to bear 4 times the weight; but by the above rule
it is shown that it will bear exactly 8 times as much.
THAT PIER, WHICH is CHARGED MOST UNEQUALLY, WILL SOONEST GIVE WAY.
The column _c b_, being charged with an equal weight, [on each side]
will be most durable, and the other two outward columns require on
the part outside of their centre as much pressure as there is inside
of their centre, that is, from the centre of the column, towards the
middle of the arch.
Arches which depend on chains for their support will not be very
durable.
THAT ARCH WILL BE OF LONGER DURATION WHICH HAS A GOOD ABUTMENT
OPPOSED TO ITS THRUST.
The arch itself tends to fall. If the arch be 30 braccia and the
interval between the walls which carry it be 20, we know that 30
cannot pass through the 20 unless 20 becomes likewise 30. Hence the
arch being crushed by the excess of weight, and the walls offering
insufficient resistance, part, and afford room between them, for the
fall of the arch.
But if you do not wish to strengthen the arch with an iron tie you
must give it such abutments as can resist the thrust; and you can do
this thus: fill up the spandrels _m n_ with stones, and direct the
lines of the joints between them to the centre of the circle of the
arch, and the reason why this makes the arch durable is this. We
know very well that if the arch is loaded with an excess of weight
above its quarter as _a b_, the wall _f g_ will be thrust outwards
because the arch would yield in that direction; if the other quarter
_b c_ were loaded, the wall _f g_ would be thrust inwards, if it
were not for the line of stones _x y_ which resists this.
787.
PLAN.
Here it is shown how the arches made in the side of the octagon
thrust the piers of the angles outwards, as is shown by the line _h
c_ and by the line _t d_ which thrust out the pier _m_; that is they
tend to force it away from the centre of such an octagon.
788.
An Experiment to show that a weight placed on an arch does not
discharge itself entirely on its columns; on the contrary the
greater the weight placed on the arches, the less the arch transmits
the weight to the columns. The experiment is the following. Let a
man be placed on a steel yard in the middle of the shaft of a well,
then let him spread out his hands and feet between the walls of the
well, and you will see him weigh much less on the steel yard; give
him a weight on the shoulders, you will see by experiment, that the
greater the weight you give him the greater effort he will make in
spreading his arms and legs, and in pressing against the wall and
the less weight will be thrown on the steel yard.
IV.
ON FOUNDATIONS, THE NATURE OF THE GROUND AND SUPPORTS.
789.
The first and most important thing is stability.
As to the foundations of the component parts of temples and other
public buildings, the depths of the foundations must bear the same
proportions to each other as the weight of material which is to be
placed upon them.
Every part of the depth of earth in a given space is composed of
layers, and each layer is composed of heavier or lighter materials,
the lowest being the heaviest. And this can be proved, because these
layers have been formed by the sediment from water carried down to
the sea, by the current of rivers which flow into it. The heaviest
part of this sediment was that which was first thrown down, and so
on by degrees; and this is the action of water when it becomes
stagnant, having first brought down the mud whence it first flowed.
And such layers of soil are seen in the banks of rivers, where their
constant flow has cut through them and divided one slope from the
other to a great depth; where in gravelly strata the waters have run
off, the materials have, in consequence, dried and been converted
into hard stone, and this happened most in what was the finest mud;
whence we conclude that every portion of the surface of the earth
was once at the centre of the earth, and _vice_versa_ &c.
790.
The heaviest part of the foundations of buildings settles most, and
leaves the lighter part above it separated from it.
And the soil which is most pressed, if it be porous yields most.
You should always make the foundations project equally beyond the
weight of the walls and piers, as shown at _m a b_. If you do as
many do, that is to say if you make a foundation of equal width from
the bottom up to the surface of the ground, and charge it above with
unequal weights, as shown at _b e_ and at _e o_, at the part of the
foundation at _b e_, the pier of the angle will weigh most and
thrust its foundation downwards, which the wall at _e o_ will not
do; since it does not cover the whole of its foundation, and
therefore thrusts less heavily and settles less. Hence, the pier _b
e_ in settling cracks and parts from the wall _e o_. This may be
seen in most buildings which are cracked round the piers.
791.
The window _a_ is well placed under the window _c_, and the window
_b_ is badly placed under the pier _d_, because this latter is
without support and foundation; mind therefore never to make a break
under the piers between the windows.
792.
OF THE SUPPORTS.
A pillar of which the thickness is increased will gain more than its
due strength, in direct proportion to what its loses in relative
height.
EXAMPLE.
If a pillar should be nine times as high as it is broad--that is to
say, if it is one braccio thick, according to rule it should be nine
braccia high--then, if you place 100 such pillars together in a mass
this will be ten braccia broad and 9 high; and if the first pillar
could carry 10000 pounds the second being only about as high as it
is wide, and thus lacking 8 parts of its proper length, it, that is
to say, each pillar thus united, will bear eight times more than
when disconnected; that is to say, that if at first it would carry
ten thousand pounds, it would now carry 90 thousand.
V.
ON THE RESISTANCE OF BEAMS.
793.
That angle will offer the greatest resistance which is most acute,
and the most obtuse will be the weakest.
[Footnote: The three smaller sketches accompany the text in the
original, but the larger one is not directly connected with it. It
is to be found on fol. 89a of the same Manuscript and there we read
in a note, written underneath, _coverchio della perdicha del
castello_ (roof of the flagstaff of the castle),--Compare also Pl.
XCIII, No. 1.]
794.
If the beams and the weight _o_ are 100 pounds, how much weight will
be wanted at _ae_ to resist such a weight, that it may not fall
down?
795.
ON THE LENGTH OF BEAMS.
That beam which is more than 20 times as long as its greatest
thickness will be of brief duration and will break in half; and
remember, that the part built into the wall should be steeped in hot
pitch and filleted with oak boards likewise so steeped. Each beam
must pass through its walls and be secured beyond the walls with
sufficient chaining, because in consequence of earthquakes the beams
are often seen to come out of the walls and bring down the walls and
floors; whilst if they are chained they will hold the walls strongly
together and the walls will hold the floors. Again I remind you
never to put plaster over timber. Since by expansion and shrinking
of the timber produced by damp and dryness such floors often crack,
and once cracked their divisions gradually produce dust and an ugly
effect. Again remember not to lay a floor on beams supported on
arches; for, in time the floor which is made on beams settles
somewhat in the middle while that part of the floor which rests on
the arches remains in its place; hence, floors laid over two kinds
of supports look, in time, as if they were made in hills [Footnote:
19 M. RAVAISSON, in his edition of MS. A gives a very different
rendering of this passage translating it thus: _Les planchers qui
sont soutenus par deux differentes natures de supports paraissent
avec le temps faits en voute a cholli_.]
Remarks on the style of Leonardo's architecture.
A few remarks may here be added on the style of Leonardo's
architectural studies. However incomplete, however small in scale,
they allow us to establish a certain number of facts and
probabilities, well worthy of consideration.
When Leonardo began his studies the great name of Brunellesco was
still the inspiration of all Florence, and we cannot doubt that
Leonardo was open to it, since we find among his sketches the plan
of the church of Santo Spirito[Footnote 1: See Pl. XCIV, No. 2. Then
only in course of erection after the designs of Brunellesco, though
he was already dead; finished in 1481.] and a lateral view of San
Lorenzo (Pl. XCIV No. 1), a plan almost identical with the chapel
Degli Angeli, only begun by him (Pl. XCIV, No. 3) while among
Leonardo's designs for domes several clearly betray the influence of
Brunellesco's Cupola and the lantern of Santa Maria del
Fiore[Footnote 2: A small sketch of the tower of the Palazzo della
Signoria (MS. C.A. 309) proves that he also studied mediaeval
monuments.]
The beginning of the second period of modern Italian architecture
falls during the first twenty years of Leonardo's life. However the
new impetus given by Leon Battista Alberti either was not generally
understood by his contemporaries, or those who appreciated it, had
no opportunity of showing that they did so. It was only when taken
up by Bramante and developed by him to the highest rank of modern
architecture that this new influence was generally felt. Now the
peculiar feature of Leonardo's sketches is that, like the works of
Bramante, they appear to be the development and continuation of
Alberti's.
_But a question here occurs which is difficult to answer. Did
Leonardo, till he quitted Florence, follow the direction given by
the dominant school of Brunellesco, which would then have given rise
to his "First manner", or had he, even before he left Florence, felt
Alberti's influence--either through his works (Palazzo Ruccellai,
and the front of Santa Maria Novella) or through personal
intercourse? Or was it not till he went to Milan that Alberti's work
began to impress him through Bramante, who probably had known
Alberti at Mantua about 1470 and who not only carried out Alberti's
views and ideas, but, by his designs for St. Peter's at Rome, proved
himself the greatest of modern architects. When Leonardo went to
Milan Bramante had already been living there for many years. One of
his earliest works in Milan was the church of Santa Maria presso San
Satiro, Via del Falcone[Footnote 1: Evidence of this I intend to
give later on in a Life of Bramante, which I have in preparation.].
Now we find among Leonardos studies of Cupolas on Plates LXXXIV and
LXXXV and in Pl. LXXX several sketches which seem to me to have been
suggested by Bramante's dome of this church.
The MSS. B and Ash. II contain the plans of S. Sepolcro, the
pavilion in the garden of the duke of Milan, and two churches,
evidently inspired by the church of San Lorenzo at Milan.
MS. B. contains besides two notes relating to Pavia, one of them a
design for the sacristy of the Cathedral at Pavia, which cannot be
supposed to be dated later than 1492, and it has probably some
relation to Leonardo's call to Pavia June 21, 1490[Footnote 2: The
sketch of the plan of Brunellesco's church of Santo Spirito at
Florence, which occurs in the same Manuscript, may have been done
from memory.]. These and other considerations justify us in
concluding, that Leonardo made his studies of cupolas at Milan,
probably between the years 1487 and 1492 in anticipation of the
erection of one of the grandest churches of Italy, the Cathedral of
Pavia. This may explain the decidedly Lombardo-Bramantesque tendency
in the style of these studies, among which only a few remind us of
the forms of the cupolas of S. Maria del Fiore and of the Baptistery
of Florence. Thus, although when compared with Bramante's work,
several of these sketches plainly reveal that master's influence, we
find, among the sketches of domes, some, which show already
Bramante's classic style, of which the Tempietto of San Pietro in
Montorio, his first building executed at Rome, is the foremost
example[Footnote 3: It may be mentioned here, that in 1494 Bramante
made a similar design for the lantern of the Cupola of the Church of
Santa Maria delle Grazie.].
On Plate LXXXIV is a sketch of the plan of a similar circular
building; and the Mausoleum on Pl. XCVIII, no less than one of the
pedestals for the statue of Francesco Sforza (Pl. LXV), is of the
same type.
The drawings Pl. LXXXIV No. 2, Pl. LXXXVI No. 1 and 2 and the ground
flour ("flour" sic but should be "floor" ?) of the building in the
drawing Pl. XCI No. 2, with the interesting decoration by gigantic
statues in large niches, are also, I believe, more in the style
Bramante adopted at Rome, than in the Lombard style. Are we to
conclude from this that Leonardo on his part influenced Bramante in
the sense of simplifying his style and rendering it more congenial
to antique art? The answer to this important question seems at first
difficult to give, for we are here in presence of Bramante, the
greatest of modern architects, and with Leonardo, the man comparable
with no other. We have no knowledge of any buildings erected by
Leonardo, and unless we admit personal intercourse--which seems
probable, but of which there is no proof--, it would be difficult to
understand how Leonardo could have affected Bramante's style. The
converse is more easily to be admitted, since Bramante, as we have
proved elsewhere, drew and built simultaneously in different
manners, and though in Lombardy there is no building by him in his
classic style, the use of brick for building, in that part of Italy,
may easily account for it._
_Bramante's name is incidentally mentioned in Leonardo's manuscripts
in two passages (Nos. 1414 and 1448). On each occasion it is only a
slight passing allusion, and the nature of the context gives us no
due information as to any close connection between the two artists._
_It might be supposed, on the ground of Leonardo's relations with
the East given in sections XVII and XXI of this volume, that some
evidence of oriental influence might be detected in his
architectural drawings. I do not however think that any such traces
can be pointed out with certainty unless perhaps the drawing for a
Mausoleum, Pl. XC VIII._
_Among several studies for the construction of cupolas above a Greek
cross there are some in which the forms are decidedly monotonous.
These, it is clear, were not designed as models of taste; they must
be regarded as the results of certain investigations into the laws
of proportion, harmony and contrast._
_The designs for churches, on the plan of a Latin cross are
evidently intended to depart as little as possible from the form of
a Greek cross; and they also show a preference for a nave surrounded
with outer porticos._
_The architectural forms preferred by Leonardo are pilasters coupled
(Pl. LXXXII No. 1; or grouped (Pl. LXXX No. 5 and XCIV No. 4), often
combined with niches. We often meet with orders superposed, one in
each story, or two small orders on one story, in combination with
one great order (Pl. XCVI No. 2)._
The drum (tamburo) of these cupolas is generally octagonal, as in
the cathedral of Florence, and with similar round windows in its
sides. In Pl. LXXXVII No. 2 it is circular like the model actually
carried out by Michael Angelo at St. Peter's.
The cupola itself is either hidden under a pyramidal roof, as in the
Baptistery of Florence, San Lorenzo of Milan and most of the Lombard
churches (Pl. XCI No. 1 and Pl. XCII No. 1); but it more generally
suggests the curve of Sta Maria del Fiore (Pl. LXXXVIII No. 5; Pl.
XC No. 2; Pl. LXXXIX, M; Pl XC No. 4, Pl. XCVI No. 2). In other
cases (Pl. LXXX No. 4; Pl. LXXXIX; Pl. XC No. 2) it shows the sides
of the octagon crowned by semicircular pediments, as in
Brunellesco's lantern of the Cathedral and in the model for the
Cathedral of Pavia.
Finally, in some sketches the cupola is either semicircular, or as
in Pl. LXXXVII No. 2, shows the beautiful line, adopted sixty years
later by Michael Angelo for the existing dome of St. Peter's.
It is worth noticing that for all these domes Leonardo is not
satisfied to decorate the exterior merely with ascending ribs or
mouldings, but employs also a system of horizontal parallels to
complete the architectural system. Not the least interesting are the
designs for the tiburio (cupola) of the Milan Cathedral. They show
some of the forms, just mentioned, adapted to the peculiar gothic
style of that monument.
The few examples of interiors of churches recall the style employed
in Lombardy by Bramante, for instance in S. Maria di Canepanuova at
Pavia, or by Dolcebuono in the Monastero Maggiore at Milan (see Pl.
CI No. 1 [C. A. 181b; 546b]; Pl. LXXXIV No. 10).
The few indications concerning palaces seem to prove that Leonardo
followed Alberti's example of decorating the walls with pilasters
and a flat rustica, either in stone or by graffitti (Pl. CII No. 1
and Pl. LXXXV No. 14).
By pointing out the analogies between Leonardo's architecture and
that of other masters we in no way pretend to depreciate his
individual and original inventive power. These are at all events
beyond dispute. The project for the Mausoleum (Pl. XCVIII) would
alone suffice to rank him among the greatest architects who ever
lived. The peculiar shape of the tower (Pl. LXXX), of the churches
for preaching (Pl. XCVII No. 1 and pages 56 and 57, Fig. 1-4), his
curious plan for a city with high and low level streets (Pl. LXXVII
and LXXVIII No. 2 and No. 3), his Loggia with fountains (Pl. LXXXII
No. 4) reveal an originality, a power and facility of invention for
almost any given problem, which are quite wonderful.
_In addition to all these qualities he propably stood alone in his
day in one department of architectural study,--his investigations,
namely, as to the resistance of vaults, foundations, walls and
arches._
_As an application of these studies the plan of a semicircular vault
(Pl. CIII No. 2) may be mentioned here, disposed so as to produce no
thrust on the columns on which it rests:_ volta i botte e non
ispignie ifori le colone. _Above the geometrical patterns on the
same sheet, close to a circle inscribed in a square is the note:_ la
ragio d'una volta cioe il terzo del diamitro della sua ... del
tedesco in domo.
_There are few data by which to judge of Leonardo's style in the
treatment of detail. On Pl. LXXXV No. 10 and Pl. CIII No. 3, we find
some details of pillars; on Pl. CI No. 3 slender pillars designed
for a fountain and on Pl. CIII No. 1 MS. B, is a pen and ink drawing
of a vase which also seems intended for a fountain. Three handles
seem to have been intended to connect the upper parts with the base.
There can be no doubt that Leonardo, like Bramante, but unlike
Michael Angelo, brought infinite delicacy of motive and execution to
bear on the details of his work._
_XIV._
_Anatomy, Zoology and Physiology._
_Leonardo's eminent place in the history of medicine, as a pioneer
in the sciences of Anatomy and Physiology, will never be appreciated
till it is possible to publish the mass of manuscripts in which he
largely treated of these two branches of learning. In the present
work I must necessarily limit myself to giving the reader a general
view of these labours, by publishing his introductory notes to the
various books on anatomical subjects. I have added some extracts,
and such observations as are scattered incidentally through these
treatises, as serving to throw a light on Leonardo's scientific
attitude, besides having an interest for a wider circle than that of
specialists only._
_VASARI expressly mentions Leonardo's anatomical studies, having had
occasion to examine the manuscript books which refer to them.
According to him Leonardo studied Anatomy in the companionship of
Marc Antonio della Torre_ "aiutato e scambievolmente
aiutando."_--This learned Anatomist taught the science in the
universities first of Padua and then of Pavia, and at Pavia he and
Leonardo may have worked and studied together. We have no clue to
any exact dates, but in the year 1506 Marc Antonio della Torre seems
to have not yet left Padua. He was scarcely thirty years old when he
died in 1512, and his writings on anatomy have not only never been
published, but no manuscript copy of them is known to exist._
_This is not the place to enlarge on the connection between Leonardo
and Marc Antonio della Torre. I may however observe that I have not
been able to discover in Leonardo's manuscripts on anatomy any
mention of his younger contemporary. The few quotations which occur
from writers on medicine--either of antiquity or of the middle ages
are printed in Section XXII. Here and there in the manuscripts
mention is made of an anonymous "adversary"_ (avversario) _whose
views are opposed and refuted by Leonardo, but there is no ground
for supposing that Marc Antonio della Torre should have been this
"adversary"._
_Only a very small selection from the mass of anatomical drawings
left by Leonardo have been published here in facsimile, but to form
any adequate idea of their scientific merit they should be compared
with the coarse and inadequate figures given in the published books
of the early part of the XVI. century.
William Hunter, the great surgeon--a competent judge--who had an
opportunity in the time of George III. of seeing the originals in
the King's Library, has thus recorded his opinion: "I expected to
see little more than such designs in Anatomy as might be useful to a
painter in his own profession. But I saw, and indeed with
astonishment, that Leonardo had been a general and deep student.
When I consider what pains he has taken upon every part of the body,
the superiority of his universal genius, his particular excellence
in mechanics and hydraulics, and the attention with which such a man
would examine and see objects which he has to draw, I am fully
persuaded that Leonardo was the best Anatomist, at that time, in the
world ... Leonardo was certainly the first man, we know of, who
introduced the practice of making anatomical drawings" (Two
introductory letters. London 1784, pages 37 and 39).
The illustrious German Naturalist Johan Friedrich Blumenback
esteemed them no less highly; he was one of the privileged few who,
after Hunter, had the chance of seeing these Manuscripts. He writes:
_Der Scharfblick dieses grossen Forschers und Darstellers der Natur
hat schon auf Dinge geachtet, die noch Jahrhunderte nachher
unbemerkt geblieben sind_" (see _Blumenbach's medicinische
Bibliothek_, Vol. 3, St. 4, 1795. page 728).
These opinions were founded on the drawings alone. Up to the present
day hardly anything has been made known of the text, and, for the
reasons I have given, it is my intention to reproduce here no more
than a selection of extracts which I have made from the originals at
Windsor Castle and elsewhere. In the Bibliography of the
Manuscripts, at the end of this volume a short review is given of
the valuable contents of these Anatomical note books which are at
present almost all in the possession of her Majesty the Queen of
England. It is, I believe, possible to assign the date with
approximate accuracy to almost all the fragments, and I am thus led
to conclude that the greater part of Leonardo's anatomical
investigations were carried out after the death of della Torre.
Merely in reading the introductory notes to his various books on
Anatomy which are here printed it is impossible to resist the
impression that the Master's anatomical studies bear to a very great
extent the stamp of originality and independent thought.
I.
ANATOMY.
796.
A general introduction
I wish to work miracles;--it may be that I shall possess less than
other men of more peaceful lives, or than those who want to grow
rich in a day. I may live for a long time in great poverty, as
always happens, and to all eternity will happen, to alchemists, the
would-be creators of gold and silver, and to engineers who would
have dead water stir itself into life and perpetual motion, and to
those supreme fools, the necromancer and the enchanter.
[Footnote 23: The following seems to be directed against students of
painting and young artists rather than against medical men and
anatomists.]
And you, who say that it would be better to watch an anatomist at
work than to see these drawings, you would be right, if it were
possible to observe all the things which are demonstrated in such
drawings in a single figure, in which you, with all your cleverness,
will not see nor obtain knowledge of more than some few veins, to
obtain a true and perfect knowledge of which I have dissected more
than ten human bodies, destroying all the other members, and
removing the very minutest particles of the flesh by which these
veins are surrounded, without causing them to bleed, excepting the
insensible bleeding of the capillary veins; and as one single body
would not last so long, since it was necessary to proceed with
several bodies by degrees, until I came to an end and had a complete
knowledge; this I repeated twice, to learn the differences [59].
[Footnote: Lines 1-59 and 60-89 are written in two parallel columns.
When we here find Leonardo putting himself in the same category as
the Alchemists and Necromancers, whom he elsewhere mocks at so
bitterly, it is evidently meant ironically. In the same way
Leonardo, in the introduction to the Books on Perspective sets
himself with transparent satire on a level with other writers on the
subject.]
And if you should have a love for such things you might be prevented
by loathing, and if that did not prevent you, you might be deterred
by the fear of living in the night hours in the company of those
corpses, quartered and flayed and horrible to see. And if this did
not prevent you, perhaps you might not be able to draw so well as is
necessary for such a demonstration; or, if you had the skill in
drawing, it might not be combined with knowledge of perspective; and
if it were so, you might not understand the methods of geometrical
demonstration and the method of the calculation of forces and of the
strength of the muscles; patience also may be wanting, so that you
lack perseverance. As to whether all these things were found in me
or not [Footnote 84: Leonardo frequently, and perhaps habitually,
wrote in note books of a very small size and only moderately thick;
in most of those which have been preserved undivided, each contains
less than fifty leaves. Thus a considerable number of such volumes
must have gone to make up a volume of the bulk of the '_Codex
Atlanticus_' which now contains nearly 1200 detached leaves. In the
passage under consideration, which was evidently written at a late
period of his life, Leonardo speaks of his Manuscript note-books as
numbering 12O; but we should hardly be justified in concluding from
this passage that the greater part of his Manuscripts were now
missing (see _Prolegomena_, Vol. I, pp. 5-7).], the hundred and
twenty books composed by me will give verdict Yes or No. In these I
have been hindered neither by avarice nor negligence, but simply by
want of time. Farewell [89].
Plans and suggestions for the arrangement of materials (797-802).
797.
OF THE ORDER OF THE BOOK.
This work must begin with the conception of man, and describe the
nature of the womb and how the foetus lives in it, up to what stage
it resides there, and in what way it quickens into life and feeds.
Also its growth and what interval there is between one stage of
growth and another. What it is that forces it out from the body of
the mother, and for what reasons it sometimes comes out of the
mother's womb before the due time.
Then I will describe which are the members, which, after the boy is
born, grow more than the others, and determine the proportions of a
boy of one year.
Then describe the fully grown man and woman, with their proportions,
and the nature of their complexions, colour, and physiognomy.
Then how they are composed of veins, tendons, muscles and bones.
This I shall do at the end of the book. Then, in four drawings,
represent four universal conditions of men. That is, Mirth, with
various acts of laughter, and describe the cause of laughter.
Weeping in various aspects with its causes. Contention, with various
acts of killing; flight, fear, ferocity, boldness, murder and every
thing pertaining to such cases. Then represent Labour, with pulling,
thrusting, carrying, stopping, supporting and such like things.
Further I would describe attitudes and movements. Then perspective,
concerning the functions and effects of the eye; and of
hearing--here I will speak of music--, and treat of the other
senses.
And then describe the nature of the senses.
This mechanism of man we will demonstrate in ... figures; of which
the three first will show the ramification of the bones; that is:
first one to show their height and position and shape: the second
will be seen in profile and will show the depth of the whole and of
the parts, and their position. The third figure will be a
demonstration of the bones of the backparts. Then I will make three
other figures from the same point of view, with the bones sawn
across, in which will be shown their thickness and hollowness. Three
other figures of the bones complete, and of the nerves which rise
from the nape of the neck, and in what limbs they ramify. And three
others of the bones and veins, and where they ramify. Then three
figures with the muscles and three with the skin, and their proper
proportions; and three of woman, to illustrate the womb and the
menstrual veins which go to the breasts.
[Footnote: The meaning of the word _nervo_ varies in different
passages, being sometimes used for _muscolo_ (muscle).]
798.
THE ORDER OF THE BOOK.
This depicting of mine of the human body will be as clear to you as
if you had the natural man before you; and the reason is that if you
wish thoroughly to know the parts of man, anatomically, you--or your
eye--require to see it from different aspects, considering it from
below and from above and from its sides, turning it about and
seeking the origin of each member; and in this way the natural
anatomy is sufficient for your comprehension. But you must
understand that this amount of knowledge will not continue to
satisfy you; seeing the very great confusion that must result from
the combination of tissues, with veins, arteries, nerves, sinews,
muscles, bones, and blood which, of itself, tinges every part the
same colour. And the veins, which discharge this blood, are not
discerned by reason of their smallness. Moreover integrity of the
tissues, in the process of the investigating the parts within them,
is inevitably destroyed, and their transparent substance being
tinged with blood does not allow you to recognise the parts covered
by them, from the similarity of their blood-stained hue; and you
cannot know everything of the one without confusing and destroying
the other. Hence, some further anatomy drawings become necessary. Of
which you want three to give full knowledge of the veins and
arteries, everything else being destroyed with the greatest care.
And three others to display the tissues; and three for the sinews
and muscles and ligaments; and three for the bones and cartilages;
and three for the anatomy of the bones, which have to be sawn to
show which are hollow and which are not, which have marrow and which
are spongy, and which are thick from the outside inwards, and which
are thin. And some are extremely thin in some parts and thick in
others, and in some parts hollow or filled up with bone, or full of
marrow, or spongy. And all these conditions are sometimes found in
one and the same bone, and in some bones none of them. And three you
must have for the woman, in which there is much that is mysterious
by reason of the womb and the foetus. Therefore by my drawings every
part will be known to you, and all by means of demonstrations from
three different points of view of each part; for when you have seen
a limb from the front, with any muscles, sinews, or veins which take
their rise from the opposite side, the same limb will be shown to
you in a side view or from behind, exactly as if you had that same
limb in your hand and were turning it from side to side until you
had acquired a full comprehension of all you wished to know. In the
same way there will be put before you three or four demonstrations
of each limb, from various points of view, so that you will be left
with a true and complete knowledge of all you wish to learn of the
human figure[Footnote 35: Compare Pl. CVII. The original drawing at
Windsor is 28 1/2 X 19 1/2 centimetres. The upper figures are
slightly washed with Indian ink. On the back of this drawing is the
text No. 1140.].
Thus, in twelve entire figures, you will have set before you the
cosmography of this lesser world on the same plan as, before me, was
adopted by Ptolemy in his cosmography; and so I will afterwards
divide them into limbs as he divided the whole world into provinces;
then I will speak of the function of each part in every direction,
putting before your eyes a description of the whole form and
substance of man, as regards his movements from place to place, by
means of his different parts. And thus, if it please our great
Author, I may demonstrate the nature of men, and their customs in
the way I describe his figure.
And remember that the anatomy of the nerves will not give the
position of their ramifications, nor show you which muscles they
branch into, by means of bodies dissected in running water or in
lime water; though indeed their origin and starting point may be
seen without such water as well as with it. But their ramifications,
when under running water, cling and unite--just like flat or hemp
carded for spinning--all into a skein, in a way which makes it
impossible to trace in which muscles or by what ramification the
nerves are distributed among those muscles.
799.
THE ARRANGEMENT OF ANATOMY
First draw the bones, let us say, of the arm, and put in the motor
muscle from the shoulder to the elbow with all its lines. Then
proceed in the same way from the elbow to the wrist. Then from the
wrist to the hand and from the hand to the fingers.
And in the arm you will put the motors of the fingers which open,
and these you will show separately in their demonstration. In the
second demonstration you will clothe these muscles with the
secondary motors of the fingers and so proceed by degrees to avoid
confusion. But first lay on the bones those muscles which lie close
to the said bones, without confusion of other muscles; and with
these you may put the nerves and veins which supply their
nourishment, after having first drawn the tree of veins and nerves
over the simple bones.
800.
Begin the anatomy at the head and finish at the sole of the foot.
801.
3 men complete, 3 with bones and nerves, 3 with the bones only. Here
we have 12 demonstrations of entire figures.
802.
When you have finished building up the man, you will make the statue
with all its superficial measurements.
[Footnote: _Cresciere l'omo_. The meaning of this expression appears
to be different here and in the passage C.A. 157a, 468a (see No.
526, Note 1. 2). Here it can hardly mean anything else than
modelling, since the sculptor forms the figure by degrees, by adding
wet clay and the figure consequently increases or grows. _Tu farai
la statua_ would then mean, you must work out the figure in marble.
If this interpretation is the correct one, this passage would have
no right to find a place in the series on anatomical studies. I may
say that it was originally inserted in this connection under the
impression that _di cresciere_ should be read _descrivere_.]
Plans for the representation of muscles by drawings (803-809).
803.
You must show all the motions of the bones with their joints to
follow the demonstration of the first three figures of the bones,
and this should be done in the first book.
804.
Remember that to be certain of the point of origin of any muscle,
you must pull the sinew from which the muscle springs in such a way
as to see that muscle move, and where it is attached to the
ligaments of the bones.
NOTE.
You will never get any thing but confusion in demonstrating the
muscles and their positions, origin, and termination, unless you
first make a demonstration of thin muscles after the manner of linen
threads; and thus you can represent them, one over another as nature
has placed them; and thus, too, you can name them according to the
limb they serve; for instance the motor of the point of the great
toe, of its middle bone, of its first bone, &c. And when you have
the knowledge you will draw, by the side of this, the true form and
size and position of each muscle. But remember to give the threads
which explain the situation of the muscles in the position which
corresponds to the central line of each muscle; and so these threads
will demonstrate the form of the leg and their distance in a plain
and clear manner.
I have removed the skin from a man who was so shrunk by illness that
the muscles were worn down and remained in a state like thin
membrane, in such a way that the sinews instead of merging in
muscles ended in wide membrane; and where the bones were covered by
the skin they had very little over their natural size.
[Footnote: The photograph No. 41 of Grosvenor Gallery Publications:
a drawing of the muscles of the foot, includes a complete facsimile
of the text of this passage.]
805.
Which nerve causes the motion of the eye so that the motion of one
eye moves the other?
Of frowning the brows, of raising the brows, of lowering the
brows,--of closing the eyes, of opening the eyes,--of raising the
nostrils, of opening the lips, with the teeth shut, of pouting with
the lips, of smiling, of astonishment.--
Describe the beginning of man when it is caused in the womb and why
an eight months child does not live. What sneezing is. What yawning
is. Falling sickness, spasms, paralysis, shivering with cold,
sweating, fatigue, hunger, sleepiness, thirst, lust.
Of the nerve which is the cause of movement from the shoulder to the
elbow, of the movement from the elbow to the hand, from the joint of
the hand to the springing of the fingers. From the springing of the
fingers to the middle joints, and from the middle joints to the
last.
Of the nerve which causes the movement of the thigh, and from the
knee to the foot, and from the joint of the foot to the toes, and
then to the middle of the toes and of the rotary motion of the leg.
806.
ANATOMY.
Which nerves or sinews of the hand are those which close and part
the fingers and toes latteraly?
807.
Remove by degrees all the parts of the front of a man in making your
dissection, till you come to the bones. Description of the parts of
the bust and of their motions.
808.
Give the anatomy of the leg up to the hip, in all views and in every
action and in every state; veins, arteries, nerves, sinews and
muscles, skin and bones; then the bones in sections to show the
thickness of the bones.
[Footnote: A straightened leg in profile is sketched by the side of
this text.]
On corpulency and leanness (809-811).
809.
Make the rule and give the measurement of each muscle, and give the
reasons of all their functions, and in which way they work and what
makes them work &c.
[4] First draw the spine of the back; then clothe it by degrees, one
after the other, with each of its muscles and put in the nerves and
arteries and veins to each muscle by itself; and besides these note
the vertebrae to which they are attached; which of the intestines
come in contact with them; and which bones and other organs &c.
The most prominent parts of lean people are most prominent in the
muscular, and equally so in fat persons. But concerning the
difference in the forms of the muscles in fat persons as compared
with muscular persons, it shall be described below.
[Footnote: The two drawings given on Pl. CVIII no. 1 come between
lines 3 and 4. A good and very early copy of this drawing without
the written text exists in the collection of drawings belonging to
Christ's College Oxford, where it is attributed to Leonardo.]
810.
Describe which muscles disappear in growing fat, and which become
visible in growing lean.
And observe that that part which on the surface of a fat person is
most concave, when he grows lean becomes more prominent.
Where the muscles separate one from another you must give profiles
and where they coalesce ...
811.
OF THE HUMAN FIGURE.
Which is the part in man, which, as he grows fatter, never gains
flesh?
Or what part which as a man grows lean never falls away with a too
perceptible diminution? And among the parts which grow fat which is
that which grows fattest?
Among those which grow lean which is that which grows leanest?
In very strong men which are the muscles which are thickest and most
prominent?
In your anatomy you must represent all the stages of the limbs from
man's creation to his death, and then till the death of the bone;
and which part of him is first decayed and which is preserved the
longest.
And in the same way of extreme leanness and extreme fatness.
The divisions of the head (812. 813).
812.
ANATOMY.
There are eleven elementary tissues:-- Cartilage, bones, nerves,
veins, arteries, fascia, ligament and sinews, skin, muscle and fat.
OF THE HEAD.
The divisions of the head are 10, viz. 5 external and 5 internal,
the external are the hair, skin, muscle, fascia and the skull; the
internal are the dura mater, the pia mater, [which enclose] the
brain. The pia mater and the dura mater come again underneath and
enclose the brain; then the rete mirabile, and the occipital bone,
which supports the brain from which the nerves spring.
813.
_a_. hair
_n_. skin
_c_. muscle
_m_. fascia
_o_. skull _i.e._ bone
_b_. dura mater
_d_. pia mater
_f_. brain
_r_. pia mater, below
_t_. dura mater
_l_. rete mirablile
_s_. the occipitul bone.
[Footnote: See Pl. CVIII, No. 3.]
Physiological problems (814. 815).
814.
Of the cause of breathing, of the cause of the motion of the heart,
of the cause of vomiting, of the cause of the descent of food from
the stomach, of the cause of emptying the intestines.
Of the cause of the movement of the superfluous matter through the
intestines.
Of the cause of swallowing, of the cause of coughing, of the cause
of yawning, of the cause of sneezing, of the cause of limbs getting
asleep.
Of the cause of losing sensibility in any limb.
Of the cause of tickling.
Of the cause of lust and other appetites of the body, of the cause
of urine and also of all the natural excretions of the body.
[Footnote: By the side of this text stands the pen and ink drawing
reproduced on Pl. CVIII, No. 4; a skull with indications of the
veins in the fleshy covering.]
815.
The tears come from the heart and not from the brain.
Define all the parts, of which the body is composed, beginning with
the skin with its outer cuticle which is often chapped by the
influence of the sun.
II.
ZOOLOGY AND COMPARATIVE ANATOMY.
The divisions of the animal kingdom (816. 817).
816.
_Man_. The description of man, which includes that of such creatures
as are of almost the same species, as Apes, Monkeys and the like,
which are many,
_The Lion_ and its kindred, as Panthers. [Footnote 3: _Leonza_--wild
cat? "_Secondo alcuni, lo stesso che Leonessa; e secondo altri con
piu certezza, lo stesso che Pantera_" FANFANI, _Vocabolario_ page
858.] Wildcats (?) Tigers, Leopards, Wolfs, Lynxes, Spanish cats,
common cats and the like.
_The Horse_ and its kindred, as Mule, Ass and the like, with incisor
teeth above and below.
_The Bull_ and its allies with horns and without upper incisors as
the Buffalo, Stag Fallow Deer, Wild Goat, Swine, Goat, wild Goats
Muskdeers, Chamois, Giraffe.
817.
Describe the various forms of the intestines of the human species,
of apes and such like. Then, in what way the leonine species differ,
and then the bovine, and finally birds; and arrange this description
after the manner of a disquisition.
Miscellaneous notes on the study of Zoology (818-821).
818.
Procure the placenta of a calf when it is born and observe the form
of the cotyledons, if their cotyledons are male or female.
819.
Describe the tongue of the woodpecker and the jaw of the crocodile.
820.
Of the flight of the 4th kind of butterflies that consume winged
ants. Of the three principal positions of the wings of birds in
downward flight.
[Footnote: A passing allusion is all I can here permit myself to
Leonardo's elaborate researches into the flight of birds. Compare
the observations on this subject in the Introduction to section
XVIII and in the Bibliography of Manuscripts at the end of the
work.]
821.
Of the way in which the tail of a fish acts in propelling the fish;
as in the eel, snake and leech.
[Footnote: A sketch of a fish, swimming upwards is in the original,
inserted above this text.--Compare No. 1114.]
Comparative study of the structure of bones and of the action of
muscles (822-826).
822.
OF THE PALM OF THE HAND.
Then I will discourse of the hands of each animal to show in what
they vary; as in the bear, which has the ligatures of the sinews of
the toes joined above the instep.
823.
A second demonstration inserted between anatomy and [the treatise
on] the living being.
You will represent here for a comparison, the legs of a frog, which
have a great resemblance to the legs of man, both in the bones and
in the muscles. Then, in continuation, the hind legs of the hare,
which are very muscular, with strong active muscles, because they
are not encumbered with fat.
[Footnote: This text is written by the side of a drawing in black
chalk of a nude male figure, but there is no connection between the
sketch and the text.]
824.
Here I make a note to demonstrate the difference there is between
man and the horse and in the same way with other animals. And first
I will begin with the bones, and then will go on to all the muscles
which spring from the bones without tendons and end in them in the
same way, and then go on to those which start with a single tendon
at one end.
[Footnote: See Pl. CVIII, No. 2.]
825.
Note on the bendings of joints and in what way the flesh grows upon
them in their flexions or extensions; and of this most important
study write a separate treatise: in the description of the movements
of animals with four feet; among which is man, who likewise in his
infancy crawls on all fours.
826.
OF THE WAY OF WALKING IN MAN.
The walking of man is always after the universal manner of walking
in animals with 4 legs, inasmuch as just as they move their feet
crosswise after the manner of a horse in trotting, so man moves his
4 limbs crosswise; that is, if he puts forward his right foot in
walking he puts forward, with it, his left arm and vice versa,
invariably.
III.
PHYSIOLOGY.
Comparative study of the organs of sense in men and animals.
827.
I have found that in the composition of the human body as compared
with the bodies of animals the organs of sense are duller and
coarser. Thus it is composed of less ingenious instruments, and of
spaces less capacious for receiving the faculties of sense. I have
seen in the Lion tribe that the sense of smell is connected with
part of the substance of the brain which comes down the nostrils,
which form a spacious receptacle for the sense of smell, which
enters by a great number of cartilaginous vesicles with several
passages leading up to where the brain, as before said, comes down.
The eyes in the Lion tribe have a large part of the head for their
sockets and the optic nerves communicate at once with the brain; but
the contrary is to be seen in man, for the sockets of the eyes are
but a small part of the head, and the optic nerves are very fine and
long and weak, and by the weakness of their action we see by day but
badly at night, while these animals can see as well at night as by
day. The proof that they can see is that they prowl for prey at
night and sleep by day, as nocturnal birds do also.
Advantages in the structure of the eye in certain animals (828-831).
828.
Every object we see will appear larger at midnight than at midday,
and larger in the morning than at midday.
This happens because the pupil of the eye is much smaller at midday
than at any other time.
In proportion as the eye or the pupil of the owl is larger in
proportion to the animal than that of man, so much the more light
can it see at night than man can; hence at midday it can see nothing
if its pupil does not diminish; and, in the same way, at night
things look larger to it than by day.
829.
OF THE EYES IN ANIMALS.
The eyes of all animals have their pupils adapted to dilate and
diminish of their own accord in proportion to the greater or less
light of the sun or other luminary. But in birds the variation is
much greater; and particularly in nocturnal birds, such as horned
owls, and in the eyes of one species of owl; in these the pupil
dilates in such away as to occupy nearly the whole eye, or
diminishes to the size of a grain of millet, and always preserves
the circular form. But in the Lion tribe, as panthers, pards,
ounces, tigers, lynxes, Spanish cats and other similar animals the
pupil diminishes from the perfect circle to the figure of a pointed
oval such as is shown in the margin. But man having a weaker sight
than any other animal is less hurt by a very strong light and his
pupil increases but little in dark places; but in the eyes of these
nocturnal animals, the horned owl--a bird which is the largest of
all nocturnal birds--the power of vision increases so much that in
the faintest nocturnal light (which we call darkness) it sees with
much more distinctness than we do in the splendour of noon day, at
which time these birds remain hidden in dark holes; or if indeed
they are compelled to come out into the open air lighted up by the
sun, they contract their pupils so much that their power of sight
diminishes together with the quantity of light admitted.
Study the anatomy of various eyes and see which are the muscles
which open and close the said pupils of the eyes of animals.
[Footnote: Compare No. 24, lines 8 and fol.]
830.
_a b n_ is the membrane which closes the eye from below, upwards,
with an opaque film, _c n b_ encloses the eye in front and behind
with a transparent membrane.
It closes from below, upwards, because it [the eye] comes downwards.
When the eye of a bird closes with its two lids, the first to close
is the nictitating membrane which closes from the lacrymal duct over
to the outer corner of the eye; and the outer lid closes from below
upwards, and these two intersecting motions begin first from the
lacrymatory duct, because we have already seen that in front and
below birds are protected and use only the upper portion of the eye
from fear of birds of prey which come down from above and behind;
and they uncover first the membrane from the outer corner, because
if the enemy comes from behind, they have the power of escaping to
the front; and again the muscle called the nictitating membrane is
transparent, because, if the eye had not such a screen, they could
not keep it open against the wind which strikes against the eye in
the rush of their rapid flight. And the pupil of the eye dilates and
contracts as it sees a less or greater light, that is to say intense
brilliancy.
831.
If at night your eye is placed between the light and the eye of a
cat, it will see the eye look like fire.
Remarks on the organs of speech
(832. 833).
832.
_a e i o u
ba be bi bo bu
ca ce ci co cu
da de di do du
fa fe fi fo fu
ga ge gi go gu
la le li lo lu
ma me mi mo mu
na ne ni no nu
pa pe pi po pu
qa qe qi qo qu
ra re ri ro ru
sa se si so su
ta te ti to tu_
The tongue is found to have 24 muscles which correspond to the six
muscles which compose the portion of the tongue which moves in the
mouth.
And when _a o u_ are spoken with a clear and rapid pronunciation, it
is necessary, in order to pronounce continuously, without any pause
between, that the opening of the lips should close by degrees; that
is, they are wide apart in saying _a_, closer in saying _o_, and
much closer still to pronounce _u_.
It may be shown how all the vowels are pronounced with the farthest
portion of the false palate which is above the epiglottis.
833.
If you draw in breath by the nose and send it out by the mouth you
will hear the sound made by the division that is the membrane in
[Footnote 5: The text here breaks off.]...
On the conditions of sight (834. 835).
834.
OF THE NATURE OF SIGHT.
I say that sight is exercised by all animals, by the medium of
light; and if any one adduces, as against this, the sight of
nocturnal animals, I must say that this in the same way is subject
to the very same natural laws. For it will easily be understood that
the senses which receive the images of things do not project from
themselves any visual virtue [Footnote 4: Compare No. 68.]. On the
contrary the atmospheric medium which exists between the object and
the sense incorporates in itself the figure of things, and by its
contact with the sense transmits the object to it. If the
object--whether by sound or by odour--presents its spiritual force
to the ear or the nose, then light is not required and does not act.
The forms of objects do not send their images into the air if they
are not illuminated [8]; and the eye being thus constituted cannot
receive that from the air, which the air does not possess, although
it touches its surface. If you choose to say that there are many
animals that prey at night, I answer that when the little light
which suffices the nature of their eyes is wanting, they direct
themselves by their strong sense of hearing and of smell, which are
not impeded by the darkness, and in which they are very far superior
to man. If you make a cat leap, by daylight, among a quantity of
jars and crocks you will see them remain unbroken, but if you do the
same at night, many will be broken. Night birds do not fly about
unless the moon shines full or in part; rather do they feed between
sun-down and the total darkness of the night.
[Footnote 8: See No. 58-67.]
No body can be apprehended without light and shade, and light and
shade are caused by light.
835.
WHY MEN ADVANCED IN AGE SEE BETTER AT A DISTANCE.
Sight is better from a distance than near in those men who are
advancing in age, because the same object transmits a smaller
impression of itself to the eye when it is distant than when it is
near.
The seat of the common sense.
836.
The Common Sense, is that which judges of things offered to it by
the other senses. The ancient speculators have concluded that that
part of man which constitutes his judgment is caused by a central
organ to which the other five senses refer everything by means of
impressibility; and to this centre they have given the name Common
Sense. And they say that this Sense is situated in the centre of the
head between Sensation and Memory. And this name of Common Sense is
given to it solely because it is the common judge of all the other
five senses _i.e._ Seeing, Hearing, Touch, Taste and Smell. This
Common Sense is acted upon by means of Sensation which is placed as
a medium between it and the senses. Sensation is acted upon by means
of the images of things presented to it by the external instruments,
that is to say the senses which are the medium between external
things and Sensation. In the same way the senses are acted upon by
objects. Surrounding things transmit their images to the senses and
the senses transfer them to the Sensation. Sensation sends them to
the Common Sense, and by it they are stamped upon the memory and are
there more or less retained according to the importance or force of
the impression. That sense is most rapid in its function which is
nearest to the sensitive medium and the eye, being the highest is
the chief of the others. Of this then only we will speak, and the
others we will leave in order not to make our matter too long.
Experience tells us that the eye apprehends ten different natures of
things, that is: Light and Darkness, one being the cause of the
perception of the nine others, and the other its absence:-- Colour
and substance, form and place, distance and nearness, motion and
stillness [Footnote 15: Compare No. 23.].
On the origin of the soul.
837.
Though human ingenuity may make various inventions which, by the
help of various machines answering the same end, it will never
devise any inventions more beautiful, nor more simple, nor more to
the purpose than Nature does; because in her inventions nothing is
wanting, and nothing is superfluous, and she needs no counterpoise
when she makes limbs proper for motion in the bodies of animals. But
she puts into them the soul of the body, which forms them that is
the soul of the mother which first constructs in the womb the form
of the man and in due time awakens the soul that is to inhabit it.
And this at first lies dormant and under the tutelage of the soul of
the mother, who nourishes and vivifies it by the umbilical vein,
with all its spiritual parts, and this happens because this
umbilicus is joined to the placenta and the cotyledons, by which the
child is attached to the mother. And these are the reason why a
wish, a strong craving or a fright or any other mental suffering in
the mother, has more influence on the child than on the mother; for
there are many cases when the child loses its life from them, &c.
This discourse is not in its place here, but will be wanted for the
one on the composition of animated bodies--and the rest of the
definition of the soul I leave to the imaginations of friars, those
fathers of the people who know all secrets by inspiration.
[Footnote 57: _lettere incoronate_. By this term Leonardo probably
understands not the Bible only, but the works of the early Fathers,
and all the books recognised as sacred by the Roman Church.] I leave
alone the sacred books; for they are supreme truth.
On the relations of the soul to the organs of sense.
838.
HOW THE FIVE SENSES ARE THE MINISTERS OF THE SOUL.
The soul seems to reside in the judgment, and the judgment would
seem to be seated in that part where all the senses meet; and this
is called the Common Sense and is not all-pervading throughout the
body, as many have thought. Rather is it entirely in one part.
Because, if it were all-pervading and the same in every part, there
would have been no need to make the instruments of the senses meet
in one centre and in one single spot; on the contrary it would have
sufficed that the eye should fulfil the function of its sensation on
its surface only, and not transmit the image of the things seen, to
the sense, by means of the optic nerves, so that the soul--for the
reason given above-- may perceive it in the surface of the eye. In
the same way as to the sense of hearing, it would have sufficed if
the voice had merely sounded in the porous cavity of the indurated
portion of the temporal bone which lies within the ear, without
making any farther transit from this bone to the common sense, where
the voice confers with and discourses to the common judgment. The
sense of smell, again, is compelled by necessity to refer itself to
that same judgment. Feeling passes through the perforated cords and
is conveyed to this common sense. These cords diverge with infinite
ramifications into the skin which encloses the members of the body
and the viscera. The perforated cords convey volition and sensation
to the subordinate limbs. These cords and the nerves direct the
motions of the muscles and sinews, between which they are placed;
these obey, and this obedience takes effect by reducing their
thickness; for in swelling, their length is reduced, and the nerves
shrink which are interwoven among the particles of the limbs; being
extended to the tips of the fingers, they transmit to the sense the
object which they touch.
The nerves with their muscles obey the tendons as soldiers obey the
officers, and the tendons obey the Common [central] Sense as the
officers obey the general. [27] Thus the joint of the bones obeys
the nerve, and the nerve the muscle, and the muscle the tendon and
the tendon the Common Sense. And the Common Sense is the seat of the
soul [28], and memory is its ammunition, and the impressibility is
its referendary since the sense waits on the soul and not the soul
on the sense. And where the sense that ministers to the soul is not
at the service of the soul, all the functions of that sense are also
wanting in that man's life, as is seen in those born mute and blind.
[Footnote: The peculiar use of the words _nervo_, _muscolo_,
_corda_, _senso comune_, which are here literally rendered by nerve,
muscle cord or tendon and Common Sense may be understood from lines
27 and 28.]
On involuntary muscular action.
839.
HOW THE NERVES SOMETIMES ACT OF THEMSELVES WITHOUT ANY COMMANDS FROM
THE OTHER FUNCTIONS OF THE SOUL.
This is most plainly seen; for you will see palsied and shivering
persons move, and their trembling limbs, as their head and hands,
quake without leave from their soul and their soul with all its
power cannot prevent their members from trembling. The same thing
happens in falling sickness, or in parts that have been cut off, as
in the tails of lizards. The idea or imagination is the helm and
guiding-rein of the senses, because the thing conceived of moves the
sense. Pre-imagining, is imagining the things that are to be.
Post-imagining, is imagining the things that are past.
Miscellaneous physiological observations (840-842).
840.
There are four Powers: memory and intellect, desire and
covetousness. The two first are mental and the others sensual. The
three senses: sight, hearing and smell cannot well be prevented;
touch and taste not at all. Smell is connected with taste in dogs
and other gluttonous animals.
841.
I reveal to men the origin of the first, or perhaps second cause of
their existence.
842.
Lust is the cause of generation.
Appetite is the support of life. Fear or timidity is the
prolongation of life and preservation of its instruments.
The laws of nutrition and the support of life (843-848).
843.
HOW THE BODY OF ANIMALS IS CONSTANTLY DYING AND BEING RENEWED.
The body of any thing whatever that takes nourishment constantly
dies and is constantly renewed; because nourishment can only enter
into places where the former nourishment has expired, and if it has
expired it no longer has life. And if you do not supply nourishment
equal to the nourishment which is gone, life will fail in vigour,
and if you take away this nourishment, the life is entirely
destroyed. But if you restore as much is destroyed day by day, then
as much of the life is renewed as is consumed, just as the flame of
the candle is fed by the nourishment afforded by the liquid of this
candle, which flame continually with a rapid supply restores to it
from below as much as is consumed in dying above: and from a
brilliant light is converted in dying into murky smoke; and this
death is continuous, as the smoke is continuous; and the continuance
of the smoke is equal to the continuance of the nourishment, and in
the same instant all the flame is dead and all regenerated,
simultaneously with the movement of its own nourishment.
844.
King of the animals--as thou hast described him--I should rather say
king of the beasts, thou being the greatest--because thou hast
spared slaying them, in order that they may give thee their children
for the benefit of the gullet, of which thou hast attempted to make
a sepulchre for all animals; and I would say still more, if it were
allowed me to speak the entire truth [5]. But we do not go outside
human matters in telling of one supreme wickedness, which does not
happen among the animals of the earth, inasmuch as among them are
found none who eat their own kind, unless through want of sense (few
indeed among them, and those being mothers, as with men, albeit they
be not many in number); and this happens only among the rapacious
animals, as with the leonine species, and leopards, panthers lynxes,
cats and the like, who sometimes eat their children; but thou,
besides thy children devourest father, mother, brothers and friends;
nor is this enough for thee, but thou goest to the chase on the
islands of others, taking other men and these half-naked, the ...
and the ... thou fattenest, and chasest them down thy own
throat[18]; now does not nature produce enough simples, for thee to
satisfy thyself? and if thou art not content with simples, canst
thou not by the mixture of them make infinite compounds, as Platina
wrote[Footnote 21: _Come scrisse il Platina_ (Bartolomeo Sacchi, a
famous humanist). The Italian edition of his treatise _De arte
coquinaria_, was published under the title _De la honestra
voluptate, e valetudine, Venezia_ 1487.], and other authors on
feeding?
[Footnote: We are led to believe that Leonardo himself was a
vegetarian from the following interesting passage in the first of
Andrea Corsali's letters to Giuliano de'Medici: _Alcuni gentili
chiamati Guzzarati non si cibano di cosa, alcuna che tenga sangue,
ne fra essi loro consentono che si noccia ad alcuna cosa animata,
come il nostro Leonardo da Vinci_.
5-18. Amerigo Vespucci, with whom Leonardo was personally
acquainted, writes in his second letter to Pietro Soderini, about
the inhabitants of the Canary Islands after having stayed there in
1503: "_Hanno una scelerata liberta di viuere; ... si cibano di
carne humana, di maniera che il padre magia il figliuolo, et
all'incontro il figliuolo il padre secondo che a caso e per sorte
auiene. Io viddi un certo huomo sceleratissimo che si vantaua, et si
teneua a non piccola gloria di hauer mangiato piu di trecento
huomini. Viddi anche vna certa citta, nella quale io dimorai forse
ventisette giorni, doue le carni humane, hauendole salate, eran
appicate alli traui, si come noi alli traui di cucina_ _appicchiamo
le carni di cinghali secche al sole o al fumo, et massimamente
salsiccie, et altre simil cose: anzi si marauigliauano gradem ete
che noi non magiaissimo della carne de nemici, le quali dicono
muouere appetito, et essere di marauiglioso sapore, et le lodano
come cibi soaui et delicati (Lettere due di Amerigo Vespucci
Fiorentino drizzate al magnifico Pietro Soderini, Gonfaloniere della
eccelsa Republica di Firenze_; various editions).]
845.
Our life is made by the death of others.
In dead matter insensible life remains, which, reunited to the
stomachs of living beings, resumes life, both sensual and
intellectual.
846.
Here nature appears with many animals to have been rather a cruel
stepmother than a mother, and with others not a stepmother, but a
most tender mother.
847.
Man and animals are really the passage and the conduit of food, the
sepulchre of animals and resting place of the dead, one causing the
death of the other, making themselves the covering for the
corruption of other dead [bodies].
On the circulation of the blood (848-850).
848.
Death in old men, when not from fever, is caused by the veins which
go from the spleen to the valve of the liver, and which thicken so
much in the walls that they become closed up and leave no passage
for the blood that nourishes it.
[6]The incessant current of the blood through the veins makes these
veins thicken and become callous, so that at last they close up and
prevent the passage of the blood.
849.
The waters return with constant motion from the lowest depths of the
sea to the utmost height of the mountains, not obeying the nature of
heavier bodies; and in this they resemble the blood of animated
beings which always moves from the sea of the heart and flows
towards the top of the head; and here it may burst a vein, as may be
seen when a vein bursts in the nose; all the blood rises from below
to the level of the burst vein. When the water rushes out from the
burst vein in the earth, it obeys the law of other bodies that are
heavier than the air since it always seeks low places.
[Footnote: From this passage it is quite plain that Leonardo had not
merely a general suspicion of the circulation of the blood but a
very clear conception of it. Leonardo's studies on the muscles of
the heart are to be found in the MS. W. An. III. but no information
about them has hitherto been made public. The limits of my plan in
this work exclude all purely anatomical writings, therefore only a
very brief excerpt from this note book can be given here. WILLIAM
HARVEY (born 1578 and Professor of Anatomy at Cambridge from 1615)
is always considered to have been the discoverer of the circulation
of the blood. He studied medicine at Padua in 1598, and in 1628
brought out his memorable and important work: _De motu cordis et
sanguinis_.]
850.
That the blood which returns when the heart opens again is not the
same as that which closes the valves of the heart.
Some notes on medicine (851-855).
851.
Make them give you the definition and remedies for the case ... and
you will see that men are selected to be doctors for diseases they
do not know.
852.
A remedy for scratches taught me by the Herald to the King of
France. 4 ounces of virgin wax, 4 ounces of colophony, 2 ounces of
incense. Keep each thing separate; and melt the wax, and then put in
the incense and then the colophony, make a mixture of it and put it
on the sore place.
853.
Medicine is the restoration of discordant elements; sickness is the
discord of the elements infused into the living body.
854.
Those who are annoyed by sickness at sea should drink extract of
wormwood.
855.
To keep in health, this rule is wise: Eat only when you want and
relish food. Chew thoroughly that it may do you good. Have it well
cooked, unspiced and undisguised. He who takes medicine is ill
advised.
[Footnote: This appears to be a sketch for a poem.]
856.
I teach you to preserve your health; and in this you will succed
better in proportion as you shun physicians, because their medicines
are the work of alchemists.
[Footnote: This passage is written on the back of the drawing Pl.
CVIII. Compare also No. 1184.]
_XV_.
_Astronomy_.
_Ever since the publication by Venturi in_ 1797 _and Libri in_ 1840
_of some few passages of Leonardo's astronomical notes, scientific
astronomers have frequently expressed the opinion, that they must
have been based on very important discoveries, and that the great
painter also deserved a conspicuous place in the history of this
science. In the passages here printed, a connected view is given of
his astronomical studies as they lie scattered through the
manuscripts, which have come down to us. Unlike his other purely
scientific labours, Leonardo devotes here a good deal of attention
to the opinions of the ancients, though he does not follow the
practice universal in his day of relying on them as authorities; he
only quotes them, as we shall see, in order to refute their
arguments. His researches throughout have the stamp of independent
thought. There is nothing in these writings to lead us to suppose
that they were merely an epitome of the general learning common to
the astronomers of the period. As early as in the XIVth century
there were chairs of astronomy in the universities of Padua and
Bologna, but so late as during the entire XVIth century Astronomy
and Astrology were still closely allied._
_It is impossible now to decide whether Leonardo, when living in
Florence, became acquainted in his youth with the doctrines of Paolo
Toscanelli the great astronomer and mathematician (died_ 1482_), of
whose influence and teaching but little is now known, beyond the
fact that he advised and encouraged Columbus to carry out his
project of sailing round the world. His name is nowhere mentioned by
Leonardo, and from the dates of the manuscripts from which the texts
on astronomy are taken, it seems highly probable that Leonardo
devoted his attention to astronomical studies less in his youth than
in his later years. It was evidently his purpose to treat of
Astronomy in a connected form and in a separate work (see the
beginning of Nos._ 866 _and_ 892_; compare also No._ 1167_). It is
quite in accordance with his general scientific thoroughness that he
should propose to write a special treatise on Optics as an
introduction to Astronomy (see Nos._ 867 _and_ 877_). Some of the
chapters belonging to this Section bear the title "Prospettiva"
_(see Nos._ 869 _and_ 870_), this being the term universally applied
at the time to Optics as well as Perspective (see Vol. I, p._ 10,
_note to No._ 13, _l._ 10_)_.
_At the beginning of the XVIth century the Ptolemaic theory of the
universe was still universally accepted as the true one, and
Leonardo conceives of the earth as fixed, with the moon and sun
revolving round it, as they are represented in the diagram to No._
897. _He does not go into any theory of the motions of the planets;
with regard to these and the fixed stars he only investigates the
phenomena of their luminosity. The spherical form of the earth he
takes for granted as an axiom from the first, and he anticipates
Newton by pointing out the universality of Gravitation not merely in
the earth, but even in the moon. Although his acute research into
the nature of the moon's light and the spots on the moon did not
bring to light many results of lasting importance beyond making it
evident that they were a refutation of the errors of his
contemporaries, they contain various explanations of facts which
modern science need not modify in any essential point, and
discoveries which history has hitherto assigned to a very much later
date_.
_The ingenious theory by which he tries to explain the nature of
what is known as earth shine, the reflection of the sun's rays by
the earth towards the moon, saying that it is a peculiar refraction,
originating in the innumerable curved surfaces of the waves of the
sea may be regarded as absurd; but it must not be forgotten that he
had no means of detecting the fundamental error on which he based
it, namely: the assumption that the moon was at a relatively short
distance from the earth. So long as the motion of the earth round
the sun remained unknown, it was of course impossible to form any
estimate of the moon's distance from the earth by a calculation of
its parallax_.
_Before the discovery of the telescope accurate astronomical
observations were only possible to a very limited extent. It would
appear however from certain passages in the notes here printed for
the first time, that Leonardo was in a position to study the spots
in the moon more closely than he could have done with the unaided
eye. So far as can be gathered from the mysterious language in which
the description of his instrument is wrapped, he made use of
magnifying glasses; these do not however seem to have been
constructed like a telescope--telescopes were first made about_
1600. _As LIBRI pointed out_ (Histoire des Sciences mathematiques
III, 101) _Fracastoro of Verona_ (1473-1553) _succeeded in
magnifying the moon's face by an arrangement of lenses (compare No._
910, _note), and this gives probability to Leonardo's invention at a
not much earlier date._
I.
THE EARTH AS A PLANET.
The earth's place in the universe (857. 858).
857.
The equator, the line of the horizon, the ecliptic, the meridian:
These lines are those which in all their parts are equidistant from
the centre of the globe.
858.
The earth is not in the centre of the Sun's orbit nor at the centre
of the universe, but in the centre of its companion elements, and
united with them. And any one standing on the moon, when it and the
sun are both beneath us, would see this our earth and the element of
water upon it just as we see the moon, and the earth would light it
as it lights us.
The fundamental laws of the solar system (859-864).
859.
Force arises from dearth or abundance; it is the child of physical
motion, and the grand-child of spiritual motion, and the mother and
origin of gravity. Gravity is limited to the elements of water and
earth; but this force is unlimited, and by it infinite worlds might
be moved if instruments could be made by which the force could be
generated.
Force, with physical motion, and gravity, with resistance are the
four external powers on which all actions of mortals depend.
Force has its origin in spiritual motion; and this motion, flowing
through the limbs of sentient animals, enlarges their muscles. Being
enlarged by this current the muscles are shrunk in length and
contract the tendons which are connected with them, and this is the
cause of the force of the limbs in man.
The quality and quantity of the force of a man are able to give
birth to other forces, which will be proportionally greater as the
motions produced by them last longer.
[Footnote: Only part of this passage belongs, strictly speaking, to
this section. The principle laid down in the second paragraph is
more directly connected with the notes given in the preceding
section on Physiology.]
860.
Why does not the weight _o_ remain in its place? It does not remain
because it has no resistance. Where will it move to? It will move
towards the centre [of gravity]. And why by no other line? Because a
weight which has no support falls by the shortest road to the lowest
point which is the centre of the world. And why does the weight know
how to find it by so short a line? Because it is not independant and
does not move about in various directions.
[Footnote: This text and the sketch belonging to it, are reproduced
on Pl. CXXI.]
861.
Let the earth turn on which side it may the surface of the waters
will never move from its spherical form, but will always remain
equidistant from the centre of the globe.
Granting that the earth might be removed from the centre of the
globe, what would happen to the water?
It would remain in a sphere round that centre equally thick, but the
sphere would have a smaller diameter than when it enclosed the
earth.
[Footnote: Compare No. 896, lines 48-64; and No. 936.]
862.
Supposing the earth at our antipodes which supports the ocean were
to rise and stand uncovered, far out of the sea, but remaining
almost level, by what means afterwards, in the course of time, would
mountains and vallies be formed?
And the rocks with their various strata?
863.
Each man is always in the middle of the surface of the earth and
under the zenith of his own hemisphere, and over the centre of the
earth.
864.
Mem.: That I must first show the distance of the sun from the earth;
and, by means of a ray passing through a small hole into a dark
chamber, detect its real size; and besides this, by means of the
aqueous sphere calculate the size of the globe ...
Here it will be shown, that when the sun is in the meridian of our
hemisphere [Footnote 10: _Antipodi orientali cogli occidentali_. The
word _Antipodes_ does not here bear its literal sense, but--as we
may infer from the simultaneous reference to inhabitants of the
North and South-- is used as meaning men living at a distance of 90
degrees from the zenith of the rational horizon of each observer.],
the antipodes to the East and to the West, alike, and at the same
time, see the sun mirrored in their waters; and the same is equally
true of the arctic and antarctic poles, if indeed they are
inhabited.
How to prove that the earth is a planet (865-867).
865.
That the earth is a star.
866.
In your discourse you must prove that the earth is a star much like
the moon, and the glory of our universe; and then you must treat of
the size of various stars, according to the authors.
867.
THE METHOD OF PROVING THAT THE EARTH IS A STAR.
First describe the eye; then show how the twinkling of a star is
really in the eye and why one star should twinkle more than another,
and how the rays from the stars originate in the eye; and add, that
if the twinkling of the stars were really in the stars --as it seems
to be--that this twinkling appears to be an extension as great as
the diameter of the body of the star; therefore, the star being
larger than the earth, this motion effected in an instant would be a
rapid doubling of the size of the star. Then prove that the surface
of the air where it lies contiguous to fire, and the surface of the
fire where it ends are those into which the solar rays penetrate,
and transmit the images of the heavenly bodies, large when they
rise, and small, when they are on the meridian. Let _a_ be the earth
and _n d m_ the surface of the air in contact with the sphere of
fire; _h f g_ is the orbit of the moon or, if you please, of the
sun; then I say that when the sun appears on the horizon _g_, its
rays are seen passing through the surface of the air at a slanting
angle, that is _o m_; this is not the case at _d k_. And so it
passes through a greater mass of air; all of _e m_ is a denser
atmosphere.
868.
Beyond the sun and us there is darkness and so the air appears blue.
[Footnote: Compare Vol. I, No. 301.]
869.
PERSPECTIVE.
It is possible to find means by which the eye shall not see remote
objects as much diminished as in natural perspective, which
diminishes them by reason of the convexity of the eye which
necessarily intersects, at its surface, the pyramid of every image
conveyed to the eye at a right angle on its spherical surface. But
by the method I here teach in the margin [9] these pyramids are
intersected at right angles close to the surface of the pupil. The
convex pupil of the eye can take in the whole of our hemisphere,
while this will show only a single star; but where many small stars
transmit their images to the surface of the pupil those stars are
extremely small; here only one star is seen but it will be large.
And so the moon will be seen larger and its spots of a more defined
form [Footnote 20 and fol.: Telescopes were not in use till a century
later. Compare No. 910 and page 136.]. You must place close to the
eye a glass filled with the water of which mention is made in number
4 of Book 113 "On natural substances" [Footnote 23: _libro_ 113.
This is perhaps the number of a book in some library catalogue. But
it may refer, on the other hand, to one of the 120 Books mentioned
in No. 796. l. 84.]; for this water makes objects which are enclosed
in balls of crystalline glass appear free from the glass.
OF THE EYE.
Among the smaller objects presented to the pupil of the eye, that
which is closest to it, will be least appreciable to the eye. And at
the same time, the experiments here made with the power of sight,
show that it is not reduced to speck if the &c. [32][Footnote 32:
Compare with this the passage in Vol. I, No. 52, written about
twenty years earlier.].
Read in the margin.
[34]Those objects are seen largest which come to the eye at the
largest angles.
But the images of the objects conveyed to the pupil of the eye are
distributed to the pupil exactly as they are distributed in the air:
and the proof of this is in what follows; that when we look at the
starry sky, without gazing more fixedly at one star than another,
the sky appears all strewn with stars; and their proportions to the
eye are the same as in the sky and likewise the spaces between them
[61].
[Footnote: 9. 32. _in margine:_ lines 34-61 are, in the original,
written on the margin and above them is the diagram to which
Leonardo seems to refer here.]
870.
PERSPECTIVE.
Among objects moved from the eye at equal distance, that undergoes
least diminution which at first was most remote.
When various objects are removed at equal distances farther from
their original position, that which was at first the farthest from
the eye will diminish least. And the proportion of the diminution
will be in proportion to the relative distance of the objects from
the eye before they were removed.
That is to say in the object _t_ and the object _e_ the proportion
of their distances from the eye _a_ is quintuple. I remove each from
its place and set it farther from the eye by one of the 5 parts into
which the proposition is divided. Hence it happens that the nearest
to the eye has doubled the distance and according to the last
proposition but one of this, is diminished by the half of its whole
size; and the body _e_, by the same motion, is diminished 1/5 of its
whole size. Therefore, by that same last proposition but one, that
which is said in this last proposition is true; and this I say of
the motions of the celestial bodies which are more distant by 3500
miles when setting than when overhead, and yet do not increase or
diminish in any sensible degree.
871.
_a b_ is the aperture through which the sun passes, and if you could
measure the size of the solar rays at _n m_, you could accurately
trace the real lines of the convergence of the solar rays, the
mirror being at _a b_, and then show the reflected rays at equal
angles to _n m_; but, as you want to have them at _n m_, take them
at the. inner side of the aperture at cd, where they maybe measured
at the spot where the solar rays fall. Then place your mirror at the
distance _a b_, making the rays _d b_, _c a_ fall and then be
reflected at equal angles towards _c d_; and this is the best
method, but you must use this mirror always in the same month, and
the same day, and hour and instant, and this will be better than at
no fixed time because when the sun is at a certain distance it
produces a certain pyramid of rays.
872.
_a_, the side of the body in light and shade _b_, faces the whole
portion of the hemisphere bed _e f_, and does not face any part of
the darkness of the earth. And the same occurs at the point _o_;
therefore the space a _o_ is throughout of one and the same
brightness, and s faces only four degrees of the hemisphere _d e f g
h_, and also the whole of the earth _s h_, which will render it
darker; and how much must be demonstrated by calculation. [Footnote:
This passage, which has perhaps a doubtful right to its place in
this connection, stands in the Manuscript between those given in
Vol. I as No. 117 and No. 427.]
873.
THE REASON OF THE INCREASED SIZE OF THE SUN IN THE WEST.
Some mathematicians explain that the sun looks larger as it sets,
because the eye always sees it through a denser atmosphere, alleging
that objects seen through mist or through water appear larger. To
these I reply: No; because objects seen through a mist are similar
in colour to those at a distance; but not being similarly diminished
they appear larger. Again, nothing increases in size in smooth
water; and the proof of this may be seen by throwing a light on a
board placed half under water. But the reason why the sun looks
larger is that every luminous body appears larger in proportion as
it is more remote. [Footnote: Lines 5 and 6 are thus rendered by M.
RAVAISSON in his edition of MS. A. "_De meme, aucune chose ne croit
dans l'eau plane, et tu en feras l'experience_ en calquant un ais
sous l'eau."--Compare the diagrams in Vol. I, p. 114.]
On the luminosity of the Earth in the universal space (874-878).
874.
In my book I propose to show, how the ocean and the other seas must,
by means of the sun, make our world shine with the appearance of a
moon, and to the remoter worlds it looks like a star; and this I
shall prove.
Show, first that every light at a distance from the eye throws out
rays which appear to increase the size of the luminous body; and
from this it follows that 2 ...[Footnote 10: Here the text breaks
off; lines 11 and fol. are written in the margin.].
[11]The moon is cold and moist. Water is cold and moist. Thus our
seas must appear to the moon as the moon does to us.
875.
The waves in water magnify the image of an object reflected in it.
Let _a_ be the sun, and _n m_ the ruffled water, _b_ the image of
the sun when the water is smooth. Let _f_ be the eye which sees the
image in all the waves included within the base of the triangle _c e
f_. Now the sun reflected in the unruffled surface occupied the
space _c d_, while in the ruffled surface it covers all the watery
space _c e_ (as is proved in the 4th of my "Perspective") [Footnote
9: _Nel quarto della mia prospettiva_. If this reference is to the
diagrams accompanying the text--as is usual with Leonardo--and not
to some particular work, the largest of the diagrams here given must
be meant. It is the lowest and actually the fifth, but he would have
called it the fourth, for the text here given is preceded on the
same page of the manuscript by a passage on whirlpools, with the
diagram belonging to it also reproduced here. The words _della mia
prospettiva_ may therefore indicate that the diagram to the
preceding chapter treating on a heterogeneal subject is to be
excluded. It is a further difficulty that this diagram belongs
properly to lines 9-10 and not to the preceding sentence. The
reflection of the sun in water is also discussed in the Theoretical
part of the Book on Painting; see Vol. I, No. 206, 207.] and it will
cover more of the water in proportion as the reflected image is
remote from the eye [10].
[Footnote: In the original sketch, inside the circle in the first
diagram, is written _Sole_ (sun), and to the right of it _luna_
(moon). Thus either of these heavenly bodies may be supposed to fill
that space. Within the lower circle is written _simulacro_ (image).
In the two next diagrams at the spot here marked _L_ the word _Luna_
is written, and in the last _sole_ is written in the top circle at
_a_.]
The image of the sun will be more brightly shown in small waves than
in large ones--and this is because the reflections or images of the
sun are more numerous in the small waves than in large ones, and the
more numerous reflections of its radiance give a larger light than
the fewer.
Waves which intersect like the scales of a fir cone reflect the
image of the sun with the greatest splendour; and this is the case
because the images are as many as the ridges of the waves on which
the sun shines, and the shadows between these waves are small and
not very dark; and the radiance of so many reflections together
becomes united in the image which is transmitted to the eye, so that
these shadows are imperceptible.
That reflection of the sun will cover most space on the surface of
the water which is most remote from the eye which sees it.
Let _a_ be the sun, _p q_ the reflection of the sun; _a b_ is the
surface of the water, in which the sun is mirrored, and _r_ the eye
which sees this reflection on the surface of the water occupying the
space _o m_. _c_ is the eye at a greater distance from the surface
of the water and also from the reflection; hence this reflection
covers a larger space of water, by the distance between _n_ and _o_.
876.
It is impossible that the side of a spherical mirror, illuminated by
the sun, should reflect its radiance unless this mirror were
undulating or filled with bubbles.
You see here the sun which lights up the moon, a spherical mirror,
and all of its surface, which faces the sun is rendered radiant.
Whence it may be concluded that what shines in the moon is water
like that of our seas, and in waves as that is; and that portion
which does not shine consists of islands and terra firma.
This diagram, of several spherical bodies interposed between the eye
and the sun, is given to show that, just as the reflection of the
sun is seen in each of these bodies, in the same way that image may
be seen in each curve of the waves of the sea; and as in these many
spheres many reflections of the sun are seen, so in many waves there
are many images, each of which at a great distance is much magnified
to the eye. And, as this happens with each wave, the spaces
interposed between the waves are concealed; and, for this reason, it
looks as though the many suns mirrored in the many waves were but
one continuous sun; and the shadows,, mixed up with the luminous
images, render this radiance less brilliant than that of the sun
mirrored in these waves.
[Footnote: In the original, at letter _A_ in the diagram "_Sole_"
(the sun) is written, and at _o_ "_occhio_" (the eye).]
877.
This will have before it the treatise on light and shade.
The edges in the moon will be most strongly lighted and reflect most
light, because, there, nothing will be visible but the tops of the
waves of the water [Footnote 5: I have thought it unnecessary to
reproduce the detailed explanation of the theory of reflection on
waves contained in the passage which follows this.].
878.
The sun will appear larger in moving water or on waves than in still
water; an example is the light reflected on the strings of a
monochord.
II.
THE SUN.
The question of the true and of the apparent size of the sun
(879-884).
879.
IN PRAISE OF THE SUN.
If you look at the stars, cutting off the rays (as may be done by
looking through a very small hole made with the extreme point of a
very fine needle, placed so as almost to touch the eye), you will
see those stars so minute that it would seem as though nothing could
be smaller; it is in fact their great distance which is the reason
of their diminution, for many of them are very many times larger
than the star which is the earth with water. Now reflect what this
our star must look like at such a distance, and then consider how
many stars might be added--both in longitude and latitude--between
those stars which are scattered over the darkened sky. But I cannot
forbear to condemn many of the ancients, who said that the sun was
no larger than it appears; among these was Epicurus, and I believe
that he founded his reason on the effects of a light placed in our
atmosphere equidistant from the centre of the earth. Any one looking
at it never sees it diminished in size at whatever distance; and the
rea-
[Footnote 879-882: What Leonardo says of Epicurus-- who according to
LEWIS, _The Astronomy of the ancients_, and MADLER, _Geschichte der
Himmelskunde_, did not devote much attention to the study of
celestial phenomena--, he probably derived from Book X of Diogenes
Laertius, whose _Vitae Philosophorum_ was not printed in Greek till
1533, but the Latin translation appeared in 1475.]
880.
sons of its size and power I shall reserve for Book 4. But I wonder
greatly that Socrates
[Footnote 2: _Socrates;_ I have little light to throw on this
reference. Plato's Socrates himself declares on more than one
occasion that in his youth he had turned his mind to the study of
celestial phenomena (METEWPA) but not in his later years (see G. C.
LEWIS, _The Astronomy of the ancients_, page 109; MADLER,
_Geschichte der Himmelskunde_, page 41). Here and there in Plato's
writings we find incidental notes on the sun and other heavenly
bodies. Leonardo may very well have known of these, since the Latin
version by Ficinus was printed as early as 1491; indeed an undated
edition exists which may very likely have appeared between 1480--90.
There is but one passage in Plato, Epinomis (p. 983) where he speaks
of the physical properties of the sun and says that it is larger
than the earth.
Aristotle who goes very fully into the subject says the same. A
complete edition of Aristotele's works was first printed in Venice
1495-98, but a Latin version of the Books _De Coelo et Mundo_ and
_De Physica_ had been printed in Venice as early as in 1483 (H.
MULLER-STRUBING).]
should have depreciated that solar body, saying that it was of the
nature of incandescent stone, and the one who opposed him as to that
error was not far wrong. But I only wish I had words to serve me to
blame those who are fain to extol the worship of men more than that
of the sun; for in the whole universe there is nowhere to be seen a
body of greater magnitude and power than the sun. Its light gives
light to all the celestial bodies which are distributed throughout
the universe; and from it descends all vital force, for the heat
that is in living beings comes from the soul [vital spark]; and
there is no other centre of heat and light in the universe as will
be shown in Book 4; and certainly those who have chosen to worship
men as gods--as Jove, Saturn, Mars and the like--have fallen into
the gravest error, seeing that even if a man were as large as our
earth, he would look no bigger than a little star which appears but
as a speck in the universe; and seeing again that these men are
mortal, and putrid and corrupt in their sepulchres.
Marcellus [Footnote 23: I have no means of identifying _Marcello_
who is named in the margin. It may be Nonius Marcellus, an obscure
Roman Grammarian of uncertain date (between the IInd and Vth
centuries A. C.) the author of the treatise _De compendiosa doctrina
per litteras ad filium_ in which he treats _de rebus omnibus et
quibusdam aliis_. This was much read in the middle ages. The _editto
princeps_ is dated 1470 (H. MULLER-STRUBING).] and many others
praise the sun.
881.
Epicurus perhaps saw the shadows cast by columns on the walls in
front of them equal in diameter to the columns from which the
shadows were cast; and the breadth of the shadows being parallel
from beginning to end, he thought he might infer that the sun also
was directly opposite to this parallel and that consequently its
breadth was not greater than that of the column; not perceiving that
the diminution in the shadow was insensibly slight by reason of the
remoteness of the sun. If the sun were smaller than the earth, the
stars on a great portion of our hemisphere would have no light,
which is evidence against Epicurus who says the sun is only as large
as it appears.
[Footnote: In the original the writing is across the diagram.]
882.
Epicurus says the sun is the size it looks. Hence as it looks about
a foot across we must consider that to be its size; it would follow
that when the moon eclipses the sun, the sun ought not to appear the
larger, as it does. Then, the moon being smaller than the sun, the
moon must be less than a foot, and consequently when our world
eclipses the moon, it must be less than a foot by a finger's
breadth; inasmuch as if the sun is a foot across, and our earth
casts a conical shadow on the moon, it is inevitable that the
luminous cause of the cone of shadow must be larger than the opaque
body which casts the cone of shadow.
883.
To measure how many times the diameter of the sun will go into its
course in 24 hours.
Make a circle and place it to face the south, after the manner of a
sundial, and place a rod in the middle in such a way as that its
length points to the centre of this circle, and mark the shadow cast
in the sunshine by this rod on the circumference of the circle, and
this shadow will be--let us say-- as broad as from _a_ to _n_. Now
measure how many times this shadow will go into this circumference
of a circle, and that will give you the number of times that the
solar body will go into its orbit in 24 hours. Thus you may see
whether Epicurus was [right in] saying that the sun was only as
large as it looked; for, as the apparent diameter of the sun is
about a foot, and as that sun would go a thousand times into the
length of its course in 24 hours, it would have gone a thousand
feet, that is 300 braccia, which is the sixth of a mile. Whence it
would follow that the course of the sun during the day would be the
sixth part of a mile and that this venerable snail, the sun will
have travelled 25 braccia an hour.
884.
Posidonius composed books on the size of the sun. [Footnote:
Poseidonius of Apamea, commonly called the Rhodian, because he
taught in Rhodes, was a Stoic philosopher, a contemporary and friend
of Cicero's, and the author of numerous works on natural science,
among them.
Strabo quotes no doubt from one of his works, when he says that
Poseidonius explained how it was that the sun looked larger when it
was rising or setting than during the rest of its course (III, p.
135). Kleomedes, a later Greek Naturalist also mentions this
observation of Poseidonius' without naming the title of his work;
however, as Kleomedes' Cyclia Theorica was not printed till 1535,
Leonardo must have derived his quotation from Strabo. He probably
wrote this note in 1508, and as the original Greek was first printed
in Venice in 1516, we must suppose him to quote here from the
translation by Guarinus Veronensis, which was printed as early as
1471, also at Venice (H. MULLER-STRUBING).]
Of the nature of Sunlight.
885.
OF THE PROOF THAT THE SUN IS HOT BY NATURE AND NOT BY VIRTUE.
Of the nature of Sunlight.
That the heat of the sun resides in its nature and not in its virtue
[or mode of action] is abundantly proved by the radiance of the
solar body on which the human eye cannot dwell and besides this no
less manifestly by the rays reflected from a concave mirror,
which--when they strike the eye with such splendour that the eye
cannot bear them--have a brilliancy equal to the sun in its own
place. And that this is true I prove by the fact that if the mirror
has its concavity formed exactly as is requisite for the collecting
and reflecting of these rays, no created being could endure the
heat that strikes from the reflected rays of such a mirror. And if
you argue that the mirror itself is cold and yet send forth hot
rays, I should reply that those rays come really from the sun and
that it is the ray of the concave mirror after having passed through
the window.
Considerations as to the size of the sun (886-891).
886.
The sun does not move. [Footnote: This sentence occurs incidentally
among mathematical notes, and is written in unusually large
letters.]
887.
PROOF THAT THE NEARER YOU ARE TO THE SOURCE OF THE SOLAR RAYS, THE
LARGER WILL THE REFLECTION OF THE SUN FROM THE SEA APPEAR TO YOU.
[Footnote: Lines 4 and fol. Compare Vol. I, Nos. 130, 131.] If it is
from the centre that the sun employs its radiance to intensify the
power of its whole mass, it is evident that the farther its rays
extend, the more widely they will be divided; and this being so,
you, whose eye is near the water that mirrors the sun, see but a
small portion of the rays of the sun strike the surface of the
water, and reflecting the form of the sun. But if you were near to
the sun--as would be the case when the sun is on the meridian and
the sea to the westward--you would see the sun, mirrored in the sea,
of a very great size; because, as you are nearer to the sun, your
eye taking in the rays nearer to the point of radiation takes more
of them in, and a great splendour is the result. And in this way it
can be proved that the moon must have seas which reflect the sun,
and that the parts which do not shine are land.
888.
Take the measure of the sun at the solstice in mid-June.
889.
WHY THE SUN APPEARS LARGER WHEN SETTING THAN AT NOON, WHEN IT IS
NEAR TO US.
Every object seen through a curved medium seems to be of larger size
than it is.
[Footnote: At A is written _sole_ (the sun), at B _terra_ (the
earth).]
890.
Because the eye is small it can only see the image of the sun as of
a small size. If the eye were as large as the sun it would see the
image of the sun in water of the same size as the real body of the
sun, so long as the water is smooth.
891.
A METHOD OF SEEING THE SUN ECLIPSED WITHOUT PAIN TO THE EYE.
Take a piece of paper and pierce holes in it with a needle, and look
at the sun through these holes.
III.
THE MOON.
On the luminousity of the moon (892-901).
892.
OF THE MOON.
As I propose to treat of the nature of the moon, it is necessary
that first I should describe the perspective of mirrors, whether
plane, concave or convex; and first what is meant by a luminous ray,
and how it is refracted by various kinds of media; then, when a
reflected ray is most powerful, whether when the angle of incidence
is acute, right, or obtuse, or from a convex, a plane, or a concave
surface; or from an opaque or a transparent body. Besides this, how
it is that the solar rays which fall on the waves of the sea, are
seen by the eye of the same width at the angle nearest to the eye,
as at the highest line of the waves on the horizon; but
notwithstanding this the solar rays reflected from the waves of the
sea assume the pyramidal form and consequently, at each degree of
distance increase proportionally in size, although to our sight,
they appear as parallel.
1st. Nothing that has very little weight is opaque.
2dly. Nothing that is excessively weighty can remain beneath that
which is heavier.
3dly. As to whether the moon is situated in the centre of its
elements or not.
And, if it has no proper place of its own, like the earth, in the
midst of its elements, why does it not fall to the centre of our
elements? [Footnote 26: The problem here propounded by Leonardo was
not satisfactorily answered till Newton in 1682 formulated the law
of universal attraction and gravitation. Compare No. 902, lines
5-15.]
And, if the moon is not in the centre of its own elements and yet
does not fall, it must then be lighter than any other element.
And, if the moon is lighter than the other elements why is it opaque
and not transparent?
When objects of various sizes, being placed at various distances,
look of equal size, there must be the same relative proportion in
the distances as in the magnitudes of the objects.
[Footnote: In the diagram Leonardo wrote _sole_ at the place marked
_A_.]
893.
OF THE MOON AND WHETHER IT IS POLISHED AND SPHERICAL.
The image of the sun in the moon is powerfully luminous, and is only
on a small portion of its surface. And the proof may be seen by
taking a ball of burnished gold and placing it in the dark with a
light at some distance from it; and then, although it will
illuminate about half of the ball, the eye will perceive its
reflection only in a small part of its surface, and all the rest of
the surface reflects the darkness which surrounds it; so that it is
only in that spot that the image of the light is seen, and all the
rest remains invisible, the eye being at a distance from the ball.
The same thing would happen on the surface of the moon if it were
polished, lustrous and opaque, like all bodies with a reflecting
surface.
Show how, if you were standing on the moon or on a star, our earth
would seem to reflect the sun as the moon does.
And show that the image of the sun in the sea cannot appear one and
undivided, as it appears in a perfectly plane mirror.
894.
How shadows are lost at great distances, as is shown by the shadow
side of the moon which is never seen. [Footnote: Compare also Vol.
I, Nos. 175-179.]
895.
Either the moon has intrinsic luminosity or not. If it has, why does
it not shine without the aid of the sun? But if it has not any light
in itself it must of necessity be a spherical mirror; and if it is a
mirror, is it not proved in Perspective that the image of a luminous
object will never be equal to the extent of surface of the
reflecting body that it illuminates? And if it be thus [Footnote 13:
At A, in the diagram, Leonardo wrote "_sole_" (the sun), and at B
"_luna o noi terra_" (the moon or our earth). Compare also the text
of No. 876.], as is here shown at _r s_ in the figure, whence comes
so great an extent of radiance as that of the full moon as we see
it, at the fifteenth day of the moon?
896.
OF THE MOON.
The moon has no light in itself; but so much of it as faces the sun
is illuminated, and of that illumined portion we see so much as
faces the earth. And the moon's night receives just as much light as
is lent it by our waters as they reflect the image of the sun, which
is mirrored in all those waters which are on the side towards the
sun. The outside or surface of the waters forming the seas of the
moon and of the seas of our globe is always ruffled little or much,
or more or less--and this roughness causes an extension of the
numberless images of the sun which are repeated in the ridges and
hollows, the sides and fronts of the innumerable waves; that is to
say in as many different spots on each wave as our eyes find
different positions to view them from. This could not happen, if the
aqueous sphere which covers a great part of the moon were uniformly
spherical, for then the images of the sun would be one to each
spectator, and its reflections would be separate and independent and
its radiance would always appear circular; as is plainly to be seen
in the gilt balls placed on the tops of high buildings. But if those
gilt balls were rugged or composed of several little balls, like
mulberries, which are a black fruit composed of minute round
globules, then each portion of these little balls, when seen in the
sun, would display to the eye the lustre resulting from the
reflection of the sun, and thus, in one and the same body many tiny
suns would be seen; and these often combine at a long distance and
appear as one. The lustre of the new moon is brighter and stronger,
than when the moon is full; and the reason of this is that the angle
of incidence is more obtuse in the new than in the full moon, in
which the angles [of incidence and reflection] are highly acute. The
waves of the moon therefore mirror the sun in the hollows of the
waves as well as on the ridges, and the sides remain in shadow. But
at the sides of the moon the hollows of the waves do not catch the
sunlight, but only their crests; and thus the images are fewer and
more mixed up with the shadows in the hollows; and this
intermingling of the shaded and illuminated spots comes to the eye
with a mitigated splendour, so that the edges will be darker,
because the curves of the sides of the waves are insufficient to
reflect to the eye the rays that fall upon them. Now the new moon
naturally reflects the solar rays more directly towards the eye from
the crests of the waves than from any other part, as is shown by the
form of the moon, whose rays a strike the waves _b_ and are
reflected in the line _b d_, the eye being situated at _d_. This
cannot happen at the full moon, when the solar rays, being in the
west, fall on the extreme waters of the moon to the East from _n_ to
_m_, and are not reflected to the eye in the West, but are thrown
back eastwards, with but slight deflection from the straight course
of the solar ray; and thus the angle of incidence is very wide
indeed.
The moon is an opaque and solid body and if, on the contrary, it
were transparent, it would not receive the light of the sun.
The yellow or yolk of an egg remains in the middle of the albumen,
without moving on either side; now it is either lighter or heavier
than this albumen, or equal to it; if it is lighter, it ought to
rise above all the albumen and stop in contact with the shell of the
egg; and if it is heavier, it ought to sink, and if it is equal, it
might just as well be at one of the ends, as in the middle or below
[54].
[Footnote 48-64: Compare No. 861.]
The innumerable images of the solar rays reflected from the
innumerable waves of the sea, as they fall upon those waves, are
what cause us to see the very broad and continuous radiance on the
surface of the sea.
897.
That the sun could not be mirrored in the body of the moon, which is
a convex mirror, in such a way as that so much of its surface as is
illuminated by the sun, should reflect the sun unless the moon had a
surface adapted to reflect it--in waves and ridges, like the surface
of the sea when its surface is moved by the wind.
[Footnote: In the original diagrams _sole_ is written at the place
marked _A; luna_ at _C,_ and _terra_ at the two spots marked _B_.]
The waves in water multiply the image of the object reflected in it.
These waves reflect light, each by its own line, as the surface of
the fir cone does [Footnote 14: See the diagram p. 145.]
These are 2 figures one different from the other; one with
undulating water and the other with smooth water.
It is impossible that at any distance the image of the sun cast on
the surface of a spherical body should occupy the half of the
sphere.
Here you must prove that the earth produces all the same effects
with regard to the moon, as the moon with regard to the earth.
The moon, with its reflected light, does not shine like the sun,
because the light of the moon is not a continuous reflection of that
of the sun on its whole surface, but only on the crests and hollows
of the waves of its waters; and thus the sun being confusedly
reflected, from the admixture of the shadows that lie between the
lustrous waves, its light is not pure and clear as the sun is.
[Footnote 38: This refers to the small diagram placed between _B_
and _B_.--]. The earth between the moon on the fifteenth day and the
sun. [Footnote 39: See the diagram below the one referred to in the
preceding note.] Here the sun is in the East and the moon on the
fifteenth day in the West. [Footnote 40.41: Refers to the diagram
below the others.] The moon on the fifteenth [day] between the earth
and the sun. [41]Here it is the moon which has the sun to the West
and the earth to the East.
898.
WHAT SORT OF THING THE MOON IS.
The moon is not of itself luminous, but is highly fitted to
assimilate the character of light after the manner of a mirror, or
of water, or of any other reflecting body; and it grows larger in
the East and in the West, like the sun and the other planets. And
the reason is that every luminous body looks larger in proportion as
it is remote. It is easy to understand that every planet and star is
farther from us when in the West than when it is overhead, by about
3500 miles, as is proved on the margin [Footnote 7: refers to the
first diagram.--A = _sole_ (the sun), B = _terra_ (the earth), C =
_luna_ (the moon).], and if you see the sun or moon mirrored in the
water near to you, it looks to you of the same size in the water as
in the sky. But if you recede to the distance of a mile, it will
look 100 times larger; and if you see the sun reflected in the sea
at sunset, its image would look to you more than 10 miles long;
because that reflected image extends over more than 10 miles of sea.
And if you could stand where the moon is, the sun would look to you,
as if it were reflected from all the sea that it illuminates by day;
and the land amid the water would appear just like the dark spots
that are on the moon, which, when looked at from our earth, appears
to men the same as our earth would appear to any men who might dwell
in the moon.
[Footnote: This text has already been published by LIBRI: _Histoire
des Sciences,_ III, pp. 224, 225.]
OF THE NATURE OF THE MOON.
When the moon is entirely lighted up to our sight, we see its full
daylight; and at that time, owing to the reflection of the solar
rays which fall on it and are thrown off towards us, its ocean casts
off less moisture towards us; and the less light it gives the more
injurious it is.
899.
OF THE MOON.
I say that as the moon has no light in itself and yet is luminous,
it is inevitable but that its light is caused by some other body.
900.
OF THE MOON.
All my opponent's arguments to say that there is no water in the
moon. [Footnote: The objections are very minutely noted down in the
manuscript, but they hardly seem to have a place here.]
901.
Answer to Maestro Andrea da Imola, who said that the solar rays
reflected from a convex mirror are mingled and lost at a short
distance; whereby it is altogether denied that the luminous side of
the moon is of the nature of a mirror, and that consequently the
light is not produced by the innumerable multitude of the waves of
that sea, which I declared to be the portion of the moon which is
illuminated by the solar rays.
Let _o p_ be the body of the sun, _c n s_ the moon, and _b_ the eye
which, above the base _c n_ of the cathetus _c n m_, sees the body
of the sun reflected at equal angles _c n_; and the same again on
moving the eye from _b_ to _a_. [Footnote: The large diagram on the
margin of page 161 belongs to this chapter.]
Explanation of the lumen cinereum in the moon.
902.
OF THE MOON.
No solid body is less heavy than the atmosphere.
[Footnote: 1. On the margin are the words _tola romantina,
tola--ferro stagnato_ (tinned iron); _romantina_ is some special
kind of sheet-iron no longer known by that name.]
Having proved that the part of the moon that shines consists of
water, which mirrors the body of the sun and reflects the radiance
it receives from it; and that, if these waters were devoid of waves,
it would appear small, but of a radiance almost like the sun; --[5]
It must now be shown whether the moon is a heavy or a light body:
for, if it were a heavy body--admitting that at every grade of
distance from the earth greater levity must prevail, so that water
is lighter than the earth, and air than water, and fire than air and
so on successively--it would seem that if the moon had density as it
really has, it would have weight, and having weight, that it could
not be sustained in the space where it is, and consequently that it
would fall towards the centre of the universe and become united to
the earth; or if not the moon itself, at least its waters would fall
away and be lost from it, and descend towards the centre, leaving
the moon without any and so devoid of lustre. But as this does not
happen, as might in reason be expected, it is a manifest sign that
the moon is surrounded by its own elements: that is to say water,
air and fire; and thus is, of itself and by itself, suspended in
that part of space, as our earth with its element is in this part of
space; and that heavy bodies act in the midst of its elements just
as other heavy bodies do in ours [Footnote 15: This passage would
certainly seem to establish Leonardo's claim to be regarded as the
original discoverer of the cause of the ashy colour of the new moon
(_lumen cinereum_). His observations however, having hitherto
remained unknown to astronomers, Moestlin and Kepler have been
credited with the discoveries which they made independently a
century later.
Some disconnected notes treat of the same subject in MS. C. A. 239b;
718b and 719b; "_Perche la luna cinta della parte alluminata dal
sole in ponente, tra maggior splendore in mezzo a tal cerchio, che
quando essa eclissava il sole. Questo accade perche nell' eclissare
il sole ella ombrava il nostro oceano, il qual caso non accade
essendo in ponente, quando il sole alluma esso oceano_." The editors
of the "_Saggio_" who first published this passage (page 12) add
another short one about the seasons in the moon which I confess not
to have seen in the original manuscript: "_La luna ha ogni mese un
verno e una state, e ha maggiori freddi e maggiori caldi, e i suoi
equinozii son piu freddi de' nostri._"]
When the eye is in the East and sees the moon in the West near to
the setting sun, it sees it with its shaded portion surrounded by
luminous portions; and the lateral and upper portion of this light
is derived from the sun, and the lower portion from the ocean in the
West, which receives the solar rays and reflects them on the lower
waters of the moon, and indeed affords the part of the moon that is
in shadow as much radiance as the moon gives the earth at midnight.
Therefore it is not totally dark, and hence some have believed that
the moon must in parts have a light of its own besides that which is
given it by the sun; and this light is due, as has been said, to the
above- mentioned cause,--that our seas are illuminated by the sun.
Again, it might be said that the circle of radiance shown by the
moon when it and the sun are both in the West is wholly borrowed
from the sun, when it, and the sun, and the eye are situated as is
shown above.
[Footnote 23. 24: The larger of the two diagrams reproduced above
stands between these two lines, and the smaller one is sketched in
the margin. At the spot marked _A_ Leonardo wrote _corpo solare_
(solar body) in the larger diagram and _Sole_ (sun) in the smaller
one. At _C luna_ (moon) is written and at _B terra_ (the earth).]
Some might say that the air surrounding the moon as an element,
catches the light of the sun as our atmosphere does, and that it is
this which completes the luminous circle on the body of the moon.
Some have thought that the moon has a light of its own, but this
opinion is false, because they have founded it on that dim light
seen between the hornes of the new moon, which looks dark where it
is close to the bright part, while against the darkness of the
background it looks so light that many have taken it to be a ring of
new radiance completing the circle where the tips of the horns
illuminated by the sun cease to shine [Footnote 34: See Pl. CVIII,
No. 5.]. And this difference of background arises from the fact that
the portion of that background which is conterminous with the bright
part of the moon, by comparison with that brightness looks darker
than it is; while at the upper part, where a portion of the luminous
circle is to be seen of uniform width, the result is that the moon,
being brighter there than the medium or background on which it is
seen by comparison with that darkness it looks more luminous at that
edge than it is. And that brightness at such a time itself is
derived from our ocean and other inland-seas. These are, at that
time, illuminated by the sun which is already setting in such a way
as that the sea then fulfils the same function to the dark side of
the moon as the moon at its fifteenth day does to us when the sun is
set. And the small amount of light which the dark side of the moon
receives bears the same proportion to the light of that side which
is illuminated, as that... [Footnote 42: Here the text breaks off;
lines 43-52 are written on the margin.].
If you want to see how much brighter the shaded portion of the moon
is than the background on which it is seen, conceal the luminous
portion of the moon with your hand or with some other more distant
object.
On the spots in the moon (903-907).
903.
THE SPOTS ON THE MOON.
Some have said that vapours rise from the moon, after the manner of
clouds and are interposed between the moon and our eyes. But, if
this were the case, these spots would never be permanent, either as
to position or form; and, seeing the moon from various aspects, even
if these spots did not move they would change in form, as objects do
which are seen from different sides.
904.
OF THE SPOTS ON THE MOON.
Others say that the moon is composed of more or less transparent
parts; as though one part were something like alabaster and others
like crystal or glass. It would follow from this that the sun
casting its rays on the less transparent portions, the light would
remain on the surface, and so the denser part would be illuminated,
and the transparent portions would display the shadow of their
darker depths; and this is their account of the structure and nature
of the moon. And this opinion has found favour with many
philosophers, and particularly with Aristotle, and yet it is a false
view--for, in the various phases and frequent changes of the moon
and sun to our eyes, we should see these spots vary, at one time
looking dark and at another light: they would be dark when the sun
is in the West and the moon in the middle of the sky; for then the
transparent hollows would be in shadow as far as the tops of the
edges of those transparent hollows, because the sun could not then
fling his rays into the mouth of the hollows, which however, at full
moon, would be seen in bright light, at which time the moon is in
the East and faces the sun in the West; then the sun would
illuminate even the lowest depths of these transparent places and
thus, as there would be no shadows cast, the moon at these times
would not show us the spots in question; and so it would be, now
more and now less, according to the changes in the position of the
sun to the moon, and of the moon to our eyes, as I have said above.
905.
OF THE SPOTS ON THE MOON.
It has been asserted, that the spots on the moon result from the
moon being of varying thinness or density; but if this were so, when
there is an eclipse of the moon the solar rays would pierce through
the portions which were thin as is alleged [Footnote 3-5: _Eclissi_.
This word, as it seems to me, here means eclipses of the sun; and
the sense of the passage, as I understand it, is that by the
foregoing hypothesis the moon, when it comes between the sun and the
earth must appear as if pierced,--we may say like a sieve.]. But as
we do not see this effect the opinion must be false.
Others say that the surface of the moon is smooth and polished and
that, like a mirror, it reflects in itself the image of our earth.
This view is also false, inasmuch as the land, where it is not
covered with water, presents various aspects and forms. Hence when
the moon is in the East it would reflect different spots from those
it would show when it is above us or in the West; now the spots on
the moon, as they are seen at full moon, never vary in the course of
its motion over our hemisphere. A second reason is that an object
reflected in a convex body takes up but a small portion of that
body, as is proved in perspective [Footnote 18: _come e provato_.
This alludes to the accompanying diagram.]. The third reason is that
when the moon is full, it only faces half the hemisphere of the
illuminated earth, on which only the ocean and other waters reflect
bright light, while the land makes spots on that brightness; thus
half of our earth would be seen girt round with the brightness of
the sea lighted up by the sun, and in the moon this reflection would
be the smallest part of that moon. Fourthly, a radiant body cannot
be reflected from another equally radiant; therefore the sea, since
it borrows its brightness from the sun,--as the moon does--, could
not cause the earth to be reflected in it, nor indeed could the body
of the sun be seen reflected in it, nor indeed any star opposite to
it.
906.
If you keep the details of the spots of the moon under observation
you will often find great variation in them, and this I myself have
proved by drawing them. And this is caused by the clouds that rise
from the waters in the moon, which come between the sun and those
waters, and by their shadow deprive these waters of the sun's rays.
Thus those waters remain dark, not being able to reflect the solar
body.
907.
How the spots on the moon must have varied from what they formerly
were, by reason of the course of its waters.
On the moon's halo.
908.
OF HALOS ROUND THE MOON.
I have found, that the circles which at night seem to surround the
moon, of various sizes, and degrees of density are caused by various
gradations in the densities of the vapours which exist at different
altitudes between the moon and our eyes. And of these halos the
largest and least red is caused by the lowest of these vapours; the
second, smaller one, is higher up, and looks redder because it is
seen through two vapours. And so on, as they are higher they will
appear smaller and redder, because, between the eye and them, there
is thicker vapour. Whence it is proved that where they are seen to
be reddest, the vapours are most dense.
On instruments for observing the moon (909. 910).
909.
If you want to prove why the moon appears larger than it is, when it
reaches the horizon; take a lens which is highly convex on one
surface and concave on the opposite, and place the concave side next
the eye, and look at the object beyond the convex surface; by this
means you will have produced an exact imitation of the atmosphere
included beneath the sphere of fire and outside that of water; for
this atmosphere is concave on the side next the earth, and convex
towards the fire.
910.
Construct glasses to see the moon magnified.
[Footnote: See the Introduction, p. 136, Fracastoro says in his work
Homocentres: "_Per dua specilla ocularla si quis perspiciat, alteri
altero superposito, majora multo et propinquiora videbit
omnia.--Quin imo quaedam specilla ocularia fiunt tantae densitatis,
ut si per ea quis aut lunam, aut aliud siderum spectet, adeo
propinqua illa iudicet, ut ne turres ipsas excedant_" (sect. II c. 8
and sect. III, c. 23).]
******** 911 - 912 MISSING ***
when the sun is seen through the boughs of trees bare of their
leaves, at some distance the branches do not conceal any portion of
the sun from our eye. The same thing happens with the above
mentioned planets which, though they have no light of their own, do
not--as has been said--conceal any part of the sun from our eye
[18].
SECOND ARGUMENT.
Some say that the stars appear most brilliant at night in proportion
as they are higher up; and that if they had no light of their own,
the shadow of the earth which comes between them and the sun, would
darken them, since they would not face nor be faced by the solar
body. But those persons have not considered that the conical shadow
of the earth cannot reach many of the stars; and even as to those it
does reach, the cone is so much diminished that it covers very
little of the star's mass, and all the rest is illuminated by the
sun.
913.
Why the planets appear larger in the East than they do overhead,
whereas the contrary should be the case, as they are 3500 miles
nearer to us when in mid sky than when on the horizon.
All the degrees of the elements, through which the images of the
celestial bodies pass to reach the eye, are equal curves and the
angles by which the central line of those images passes through
them, are unequal angles [Footnote 13: _inequali_, here and
elsewhere does not mean unequal in the sense of not being equal to
each other, but angles which are not right angles.]; and the
distance is greater, as is shown by the excess of _a b_ beyond _a
d_; and the enlargement of these celestial bodies on the horizon is
shown by the 9th of the 7th.
Observations on the stars.
914.
To see the real nature of the planets open the covering and note at
the base [Footnote 4: _basa_. This probably alludes to some
instrument, perhaps the Camera obscura.] one single planet, and the
reflected movement of this base will show the nature of the said
planet; but arrange that the base may face only one at the time.
On history of astronomy.
915.
Cicero says in [his book] De Divinatione that Astrology has been
practised five hundred seventy thousand years before the Trojan war.
57000.
[Footnote: The statement that CICERO, _De Divin._ ascribes the
discovery of astrology to a period 57000 years before the Trojan war
I believe to be quite erroneous. According to ERNESTI, _Clavis
Ciceroniana,_ CH. G. SCHULZ (_Lexic. Cicer._) and the edition of _De
Divin._ by GIESE the word Astrologia occurs only twice in CICERO:
_De Divin. II_, 42. _Ad Chaldaeorum monstra veniamus, de quibus
Eudoxus, Platonis auditor, in astrologia judicio doctissimorum
hominum facile princeps, sic opinatur (id quod scriptum reliquit):
Chaldaeis in praedictione et in notatione cujusque vitae ex natali
die minime esse credendum._" He then quotes the condemnatory verdict
of other philosophers as to the teaching of the Chaldaeans but says
nothing as to the antiquity and origin of astronomy. CICERO further
notes _De oratore_ I, 16 that Aratus was "_ignarus astrologiae_" but
that is all. So far as I know the word occurs nowhere else in
CICERO; and the word _Astronomia_ he does not seem to have used at
all. (H. MULLER-STRUBING.)]
Of time and its divisions (916-918).
916.
Although time is included in the class of Continuous Quantities,
being indivisible and immaterial, it does not come entirely under
the head of Geometry, which represents its divisions by means of
figures and bodies of infinite variety, such as are seen to be
continuous in their visible and material properties. But only with
its first principles does it agree, that is with the Point and the
Line; the point may be compared to an instant of time, and the line
may be likened to the length of a certain quantity of time, and just
as a line begins and terminates in a point, so such a space of time.
begins and terminates in an instant. And whereas a line is
infinitely divisible, the divisibility of a space of time is of the
same nature; and as the divisions of the line may bear a certain
proportion to each other, so may the divisions of time.
[Footnote: This passage is repeated word for word on page 190b of
the same manuscript and this is accounted for by the text in Vol. I,
No. 4. Compare also No. 1216.]
917.
Describe the nature of Time as distinguished from the Geometrical
definitions.
918.
Divide an hour into 3000 parts, and this you can do with a clock by
making the pendulum lighter or heavier.
_XVI.
Physical Geography.
Leonardo's researches as to the structure of the earth and sea were
made at a time, when the extended voyages of the Spaniards and
Portuguese had also excited a special interest in geographical
questions in Italy, and particularly in Tuscany. Still, it need
scarcely surprise us to find that in deeper questions, as to the
structure of the globe, the primitive state of the earth's surface,
and the like, he was far in advance of his time.
The number of passages which treat of such matters is relatively
considerable; like almost all Leonardo's scientific notes they deal
partly with theoretical and partly with practical questions. Some of
his theoretical views of the motion of water were collected in a
copied manuscript volume by an early transcriber, but without any
acknowledgment of the source whence they were derived. This copy is
now in the Library of the Barberini palace at Rome and was published
under the title: "De moto e misura dell'acqua," by FRANCESCO
CARDINALI, Bologna_ 1828. _In this work the texts are arranged under
the following titles:_ Libr. I. Della spera dell'acqua; Libr. II.
Del moto dell'acqua; Libr. III. Dell'onda dell'acqua; Libr. IV. Dei
retrosi d'acqua; Libr. V. Dell'acqua cadente; Libr. VI. Delle
rotture fatte dall'acqua; Libr. VII Delle cose portate dall'acqua;
Libr. VIII. Dell'oncia dell'acqua e delle canne; Libr. IX. De molini
e d'altri ordigni d'acqua.
_The large number of isolated observations scattered through the
manuscripts, accounts for our so frequently finding notes of new
schemes for the arrangement of those relating to water and its
motions, particularly in the Codex Atlanticus: I have printed
several of these plans as an introduction to the Physical Geography,
and I have actually arranged the texts in accordance with the clue
afforded by one of them which is undoubtedly one of the latest notes
referring to the subject (No._ 920_). The text given as No._ 930
_which is also taken from a late note-book of Leonardo's, served as
a basis for the arrangement of the first of the seven books--or
sections--, bearing the title: Of the Nature of Water_ (Dell'acque
in se).
_As I have not made it any part of this undertaking to print the
passages which refer to purely physical principles, it has also been
necessary to exclude those practical researches which, in accordance
with indications given in_ 920, _ought to come in as Books_ 13, 14
_and_ 15. _I can only incidentally mention here that Leonardo--as it
seems to me, especially in his youth--devoted a great deal of
attention to the construction of mills. This is proved by a number
of drawings of very careful and minute execution, which are to be
found in the Codex Atlanticus. Nor was it possible to include his
considerations on the regulation of rivers, the making of canals and
so forth (No._ 920, _Books_ 10, 11 _and_ 12_); but those passages in
which the structure of a canal is directly connected with notices of
particular places will be found duly inserted under section XVII
(Topographical notes). In Vol. I, No._ 5 _the text refers to
canal-making in general._
_On one point only can the collection of passages included under the
general heading of Physical Geography claim to be complete. When
comparing and sorting the materials for this work I took particular
care not to exclude or omit any text in which a geographical name
was mentioned even incidentally, since in all such researches the
chief interest, as it appeared to me, attached to the question
whether these acute observations on the various local
characteristics of mountains, rivers or seas, had been made by
Leonardo himself, and on the spot. It is self-evident that the few
general and somewhat superficial observations on the Rhine and the
Danube, on England and Flanders, must have been obtained from maps
or from some informants, and in the case of Flanders Leonardo
himself acknowledges this (see No._ 1008_). But that most of the
other and more exact observations were made, on the spot, by
Leonardo himself, may be safely assumed from their method and the
style in which he writes of them; and we should bear it in mind that
in all investigations, of whatever kind, experience is always spoken
of as the only basis on which he relies. Incidentally, as in No._
984, _he thinks it necessary to allude to the total absence of all
recorded observations._
I.
INTRODUCTION.
Schemes for the arrangement of the materials (919-928).
919.
These books contain in the beginning: Of the nature of water itself
in its motions; the others treat of the effects of its currents,
which change the world in its centre and its shape.
920.
DIVISIONS OF THE BOOK.