It never looks well to see the roofs of a church; they should rather
be flat and the water should run off by gutters made in the frieze.

[Footnote: This text is to the left of the domed church reproduced
on Pl. LXXXVII, No. 2.]

_B. The theory of Dome Architecture.

This subject has been more extensively treated by Leonardo in
drawings than in writing. Still we may fairly assume that it was his
purpose, ultimately to embody the results of his investigation in a_
"Trattato delle Cupole." _The amount of materials is remarkably
extensive. MS. B is particularly rich in plans and elevations of
churches with one or more domes--from the simplest form to the most
complicated that can be imagined. Considering the evident connexion
between a great number of these sketches, as well as the
impossibility of seeing in them designs or preparatory sketches for
any building intended to be erected, the conclusion is obvious that
they were not designed for any particular monument, but were
theoretical and ideal researches, made in order to obtain a clear
understanding of the laws which must govern the construction of a
great central dome, with smaller ones grouped round it; and with or
without the addition of spires, so that each of these parts by
itself and in its juxtaposition to the other parts should produce
the grandest possible effect.

In these sketches Leonardo seems to have exhausted every imaginable
combination. [Footnote 1: In MS. B, 32b (see Pl. C III, No. 2) we
find eight geometrical patterns, each drawn in a square; and in MS.
C.A., fol. 87 to 98 form a whole series of patterns done with the
same intention.] The results of some of these problems are perhaps
not quite satisfactory; still they cannot be considered to give
evidence of a want of taste or of any other defect in Leonardo s
architectural capacity. They were no doubt intended exclusively for
his own instruction, and, before all, as it seems, to illustrate the
features or consequences resulting from a given principle._

_I have already, in another place,_ [Footnote 1: Les Projets
Primitifs pour la Basilique de St. Pierre de Rome, par Bramante,
Raphael etc.,Vol. I, p. 2.] _pointed out the law of construction for
buildings crowned by a large dome: namely, that such a dome, to
produce the greatest effect possible, should rise either from the
centre of a Greek cross, or from the centre of a structure of which
the plan has some symmetrical affinity to a circle, this circle
being at the same time the centre of the whole plan of the building.

Leonardo's sketches show that he was fully aware, as was to be
expected, of this truth. Few of them exhibit the form of a Latin
cross, and when this is met with, it generally gives evidence of the
determination to assign as prominent a part as possible to the dome
in the general effect of the building.

While it is evident, on the one hand, that the greater number of
these domes had no particular purpose, not being designed for
execution, on the other hand several reasons may be found for
Leonardo's perseverance in his studies of the subject.

Besides the theoretical interest of the question for Leonardo and
his_ Trattato _and besides the taste for domes prevailing at that
time, it seems likely that the intended erection of some building of
the first importance like the Duomos of Pavia and Como, the church
of Sta. Maria delle Grazie at Milan, and the construction of a Dome
or central Tower_ (Tiburio) _on the cathedral of Milan, may have
stimulated Leonardo to undertake a general and thorough
investigation of the subject; whilst Leonardo's intercourse with
Bramante for ten years or more, can hardly have remained without
influence in this matter. In fact now that some of this great
Architect's studies for S. Peter's at Rome have at last become
known, he must be considered henceforth as the greatest master of
Dome-Architecture that ever existed. His influence, direct or
indirect even on a genius like Leonardo seems the more likely, since
Leonardo's sketches reveal a style most similar to that of Bramante,
whose name indeed, occurs twice in Leonardo's manuscript notes. It
must not be forgotten that Leonardo was a Florentine; the
characteristic form of the two principal domes of Florence, Sta.
Maria del Fiore and the Battisterio, constantly appear as leading
features in his sketches.

The church of San Lorenzo at Milan, was at that time still intact.
The dome is to this day one of the most wonderful cupolas ever
constructed, and with its two smaller domes might well attract the
attention and study of a never resting genius such as Leonardo. A
whole class of these sketches betray in fact the direct influence of
the church of S. Lorenzo, and this also seems to have suggested the
plan of Bramante's dome of St. Peter's at Rome.

In the following pages the various sketches for the construction of
domes have been classified and discussed from a general point of
view. On two sheets: Pl. LXXXIV (C.A. 354b; 118a) and Pl. LXXXV,
Nos. 1-11 (Ash. II, 6b) we see various dissimilar types, grouped
together; thus these two sheets may be regarded as a sort of
nomenclature of the different types, on which we shall now have to
treat._

_1. Churches formed on the plan of a Greek cross.

Group I.

Domes rising from a circular base.

The simplest type of central building is a circular edifice.

Pl. LXXXIV, No. 9. Plan of a circular building surrounded by a
colonnade.

Pl. LXXXIV, No. 8. Elevation of the former, with a conical roof.

Pl. XC. No. 5. A dodecagon, as most nearly approaching the circle.

Pl. LXXXVI, No. 1, 2, 3. Four round chapels are added at the
extremities of the two principal axes;--compare this plan with fig.
1 on p. 44 and fig. 3 on p. 47 (W. P. 5b) where the outer wall is
octagonal.

Group II.

Domes rising from a square base.

The plan is a square surrounded by a colonnade, and the dome seems
to be octagonal.

Pl. LXXXIV. The square plan below the circular building No. 8, and
its elevation to the left, above the plan: here the ground-plan is
square, the upper storey octagonal. A further development of this
type is shown in two sketches C. A. 3a (not reproduced here), and in

Pl. LXXXVI, No. 5 (which possibly belongs to No. 7 on Pl. LXXXIV).

Pl, LXXXV, No. 4, and p. 45, Fig. 3, a Greek cross, repeated p. 45,
Fig. 3, is another development of the square central plan.

The remainder of these studies show two different systems; in the
first the dome rises from a square plan,--in the second from an
octagonal base._

_Group III.

Domes rising from a square base and four pillars. [Footnote 1: The
ancient chapel San Satiro, via del Falcone, Milan, is a specimen of
this type.]_

a) First type. _A Dome resting on four pillars in the centre of a
square edifice, with an apse in the middle, of each of the four
sides. We have eleven variations of this type.

aa) Pl. LXXXVIII, No. 3.

bb) Pl. LXXX, No. 5.

cc) Pl. LXXXV, Nos. 2, 3, 5.

dd) Pl. LXXXIV, No. 1 and 4 beneath.

ee) Pl. LXXXV, Nos. 1, 7, 10, 11._

b) Second type. _This consists in adding aisles to the whole plan of
the first type; columns are placed between the apses and the aisles;
the plan thus obtained is very nearly identical with that of S.
Lorenzo at Milan.

Fig. 1 on p. 56. (MS. B, 75a) shows the result of this treatment
adapted to a peculiar purpose about which we shall have to say a few
words later on.

Pl. XCV, No. 1, shows the same plan but with the addition of a short
nave. This plan seems to have been suggested by the general
arrangement of S. Sepolcro at Milan.

MS. B. 57b (see the sketch reproduced on p.51). By adding towers in
the four outer angles to the last named plan, we obtain a plan which
bears the general features of Bramante's plans for S. Peter's at
Rome. [Footnote 2: See_ Les projets primitifs _etc., Pl. 9-12.] (See
p. 51 Fig. 1.)

Group IV.

Domes rising from an octagonal base.

This system, developed according to two different schemes, has given
rise to two classes with many varieties.

In a) On each side of the octagon chapels of equal form are added.

In b) The chapels are dissimilar; those which terminate the
principal axes being different in form from those which are added on
the diagonal sides of the octagon.

a. First Class.

The Chapel_ "degli Angeli," _at Florence, built only to a height of
about 20 feet by Brunellesco, may be considered as the prototype of
this group; and, indeed it probably suggested it. The fact that we
see in MS. B. 11b (Pl. XCIV, No. 3) by the side of Brunellesco's
plan for the Basilica of Sto. Spirito at Florence, a plan almost
identical with that of the_ Capella degli Angeli, _confirms this
supposition. Only two small differences, or we may say improvements,
have been introduced by Leonardo. Firstly the back of the chapels
contains a third niche, and each angle of the Octagon a folded
pilaster like those in Bramante's_ Sagrestia di S. M. presso San
Satiro _at Milan, instead of an interval between the two pilasters
as seen in the Battistero at Florence and in the Sacristy of Sto.
Spirito in the same town and also in the above named chapel by
Brunellesco.

The first set of sketches which come under consideration have at
first sight the appearance of mere geometrical studies. They seem to
have been suggested by the plan given on page 44 Fig. 2 (MS. B, 55a)
in the centre of which is written_ "Santa Maria in perticha da
Pavia", _at the place marked A on the reproduction.

a) (MS. B, 34b, page 44 Fig. 3). In the middle of each side a column
is added, and in the axes of the intercolumnar spaces a second row
of columns forms an aisle round the octagon. These are placed at the
intersection of a system of semicircles, of which the sixteen
columns on the sides of the octagon are the centres.

b) The preceding diagram is completed and becomes more monumental in
style in the sketch next to it (MS. B, 35a, see p. 45 Fig. 1). An
outer aisle is added by circles, having for radius the distance
between the columns in the middle sides of the octagon.

c) (MS. B. 96b, see p. 45 Fig. 2). Octagon with an aisle round it;
the angles of both are formed by columns. The outer sides are formed
by 8 niches forming chapels. The exterior is likewise octagonal,
with the angles corresponding to the centre of each of the interior
chapels.

Pl. XCII, No. 2 (MS. B. 96b). Detail and modification of the
preceding plan--half columns against piers--an arrangement by which
the chapels of the aisle have the same width of opening as the inner
arches between the half columns. Underneath this sketch the
following note occurs:_ questo vole - avere 12 facce - co 12
tabernaculi - come - _a_ - _b_. _(This will have twelve sides with
twelve tabernacles as_ a b._) In the remaining sketches of this
class the octagon is not formed by columns at the angles.

The simplest type shows a niche in the middle of each side and is
repeated on several sheets, viz: MS. B 3; MS. C.A. 354b (see Pl.
LXXXIV, No. 11) and MS. Ash II 6b; (see Pl. LXXXV, No. 9 and the
elevations No. 8; Pl. XCII, No. 3; MS. B. 4b [not reproduced here]
and Pl. LXXXIV, No. 2)._

_Pl. XCII, 3 (MS. B, 56b) corresponds to a plan like the one in MS.
B 35a, in which the niches would be visible outside or, as in the
following sketch, with the addition of a niche in the middle of each
chapel.

Pl. XC, No. 6. The niches themselves are surrounded by smaller
niches (see also No. 1 on the same plate).

Octagon expanded on each side.

A. by a square chapel:

MS. B. 34b (not reproduced here).

B. by a square with 3 niches:

MS. B. 11b (see Pl. XCIV, No. 3).

C. by octagonal chapels:

a) MS. B, 21a; Pl. LXXXVIII, No. 4.

b) No. 2 on the same plate. Underneath there is the remark:_
"quest'e come le 8 cappele ano a essere facte" _(this is how the
eight chapels are to be executed).

c) Pl. LXXXVIII, No. 5. Elevation to the plans on the same sheet, it
is accompanied by the note:_ "ciasscuno de' 9 tiburi no'uole -
passare l'alteza - di - 2 - quadri" _(neither of the 9 domes must
exceed the height of two squares).

d) Pl. LXXXVIII, No. 1. Inside of the same octagon. MS. B, 30a, and
34b; these are three repetitions of parts of the same plan with very
slight variations.

D. by a circular chapel:

MS. B, 18a (see Fig. 1 on page 47) gives the plan of this
arrangement in which the exterior is square on the ground floor with
only four of the chapels projecting, as is explained in the next
sketch.

Pl. LXXXIX, MS. B, 17b. Elevation to the preceding plan sketched on
the opposite side of the sheet, and also marked A. It is accompanied
by the following remark, indicating the theoretical character of
these studies:_ questo - edifitio - anchora - starebbe - bene
affarlo dalla linja - _a_ - _b_ - _c_ - _d_ - insu. _("This edifice
would also produce a good effect if only the part above the lines_ a
b, c d, _were executed").

Pl. LXXXIV, No. 11. The exterior has the form of an octagon, but the
chapels project partly beyond it. On the left side of the sketch
they appear larger than on the right side.

Pl. XC, No. 1, (MS. B, 25b); Repetition of Pl. LXXXIV, No. 11.

Pl. XC, No. 2. Elevation to the plan No. 1, and also to No. 6 of the
same sheet._

_E. By chapels formed by four niches:

Pl. LXXXIV, No. 7 (the circular plan on the left below) shows this
arrangement in which the central dome has become circular inside and
might therefore be classed after this group. [Footnote 1: This plan
and some others of this class remind us of the plan of the Mausoleum
of Augustus as it is represented for instance by Durand. See_ Cab.
des Estampes, Bibliotheque Nationale, Paris, Topographie de Rome, V,
6, 82._]

The sketch on the right hand side gives most likely the elevation
for the last named plan.

F. By chapels of still richer combinations, which necessitate an
octagon of larger dimensions:

Pl. XCI, No. 2 (MS. Ash. 11. 8b) [Footnote 2: The note accompanying
this plan is given under No. 754.]; on this plan the chapels
themselves appear to be central buildings formed like the first type
of the third group. Pl. LXXXVIII, No. 3.

Pl. XCI, No. 2 above; the exterior of the preceding figure,
particularly interesting on account of the alternation of apses and
niches, the latter containing statues of a gigantic size, in
proportion to the dimension of the niches.

b. Second Class.

Composite plans of this class are generally obtained by combining
two types of the first class--the one worked out on the principal
axes, the other on the diagonal ones.

MS. B. 22 shows an elementary combination, without any additions on
the diagonal axes, but with the dimensions of the squares on the two
principal axes exceeding those of the sides of the octagon.

In the drawing W. P. 5b (see page 44 Fig. 1) the exterior only of
the edifice is octagonal, the interior being formed by a circular
colonnade; round chapels are placed against the four sides of the
principal axes.

The elevation, drawn on the same sheet (see page 47 Fig. 3), shows
the whole arrangement which is closely related with the one on Pl.
LXXXVI No. 1, 2.

MS. B. 21a shows:

a) four sides with rectangular chapels crowned by pediments Pl.
LXXXVII No. 3 (plan and elevation);

b) four sides with square chapels crowned by octagonal domes. Pl.
LXXXVII No. 4; the plan underneath.

MS. B. 18a shows a variation obtained by replacing the round chapels
in the principal axes of the sketch MS. B. l8a by square ones, with
an apse. Leonardo repeated both ideas for better comparison side by
side, see page 47. Fig. 2.

Pl. LXXXIX (MS. B. 17b). Elevation for the preceding figure. The
comparison of the drawing marked M with the plan on page 47 Fig. 2,
bearing the same mark, and of the elevation on Pl. LXXXIX below
(marked A) with the corresponding plan on page 47 is highly
instructive, as illustrating the spirit in which Leonardo pursued
these studies.

Pl. LXXXIV No. 12 shows the design Pl. LXXXVII No. 3 combined with
apses, with the addition of round chapels on the diagonal sides.

Pl. LXXXIV No. 13 is a variation of the preceding sketch.

Pl. XC No. 3. MS. B. 25b. The round chapels of the preceding sketch
are replaced by octagonal chapels, above which rise campaniles.

Pl. XC No. 4 is the elevation for the preceding plan.

Pl. XCII No. 1. (MS. B. 39b.); the plan below. On the principal as
well as on the diagonal axes are diagonal chapels, but the latter
are separated from the dome by semicircular recesses. The
communication between these eight chapels forms a square aisle round
the central dome.

Above this figure is the elevation, showing four campaniles on the
angles. [Footnote 1: The note accompanying this drawing is
reproduced under No. 753.]

Pl. LXXXIV No. 3. On the principal axes are square chapels with
three niches; on the diagonals octagonal chapels with niches. Cod.
Atl. 340b gives a somewhat similar arrangement.

MS. B. 30. The principal development is thrown on the diagonal axes
by square chapels with three niches; on the principal axes are inner
recesses communicating with outer ones.

The plan Pl. XCIII No. 2 (MS. B. 22) differs from this only in so
far as the outer semicircles have become circular chapels,
projecting from the external square as apses; one of them serves as
the entrance by a semicircular portico.

The elevation is drawn on the left side of the plan.

MS. B. 19. A further development of MS. B. 18, by employing for the
four principal chapels the type Pl. LXXXVIII No. 3, as we have
already seen in Pl. XCI No. 2; the exterior presents two varieties.

a) The outer contour follows the inner. [Footnote 2: These chapels
are here sketched in two different sizes; it is the smaller type
which is thus formed.]

b) It is semicircular.

Pl. LXXXVII No. 2 (MS. B. 18b) Elevation to the first variation MS.
B. 19. If we were not certain that this sketch was by Leonardo, we
might feel tempted to take it as a study by Bramante for St. Peter's
at Rome. [Footnote 3: See_ Les projets primitifs Pl. 43._]_

_MS. P. V. 39b. In the principal axes the chapels of MS. B. 19, and
semicircular niches on the diagonals. The exterior of the whole
edifice is also an octagon, concealing the form of the interior
chapels, but with its angles on their axes.

Group V.

Suggested by San Lorenzo at Milan.

In MS. C. A. 266 IIb, 8l2b there is a plan almost identical with
that of San Lorenzo. The diagonal sides of the irregular octagon are
not indicated.

If it could be proved that the arches which, in the actual church,
exist on these sides in the first story, were added in 1574 by
Martimo Bassi, then this plan and the following section would be
still nearer the original state of San Lorenzo than at present. A
reproduction of this slightly sketched plan has not been possible.
It may however be understood from Pl. LXXXVIII No. 3, by suppressing
the four pillars corresponding to the apses.

Pl. LXXXVII No. 1 shows the section in elevation corresponding with
the above-named plan. The recessed chapels are decorated with large
shells in the halfdomes like the arrangement in San Lorenzo, but
with proportions like those of Bramante's Sacristy of Santa Maria
presso S. Satiro.

MS. C. A. 266; a sheet containing three views of exteriors of Domes.
On the same sheet there is a plan similar to the one above-named but
with uninterrupted aisles and with the addition of round chapels in
the axes (compare Pl. XCVII No. 3 and page 44 Fig. 1), perhaps a
reminiscence of the two chapels annexed to San Lorenzo.--Leonardo
has here sketched the way of transforming this plan into a Latin
cross by means of a nave with side aisles.

Pl. XCI No. 1. Plan showing a type deprived of aisles and comprised
in a square building which is surrounded by a portico. It is
accompanied by the following text:_