The Notebooks of Leonardo Da Vinci, Volume 2 by Leonardo Da Vinci

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_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.

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