The Notebooks of Leonardo Da Vinci, Volume 2
by
Leonardo Da Vinci
Part 2 out of 10
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.
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