Ten Books on Architecture

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6. An account must now be given of the eustyle, which is the most
approved class, and is arranged on principles developed with a view to
convenience, beauty, and strength. The intervals should be made as wide
as the thickness of two columns and a quarter, but the middle
intercolumniations, one in front and the other in the rear, should be of
the thickness of three columns. Thus built, the effect of the design
will be beautiful, there will be no obstruction at the entrance, and the
walk round the cella will be dignified.

[Illustration: THE EUSTYLE TEMPLE OF VITRUVIUS COMPARED WITH THE TEMPLE
OF TEOS]

7. The rule of this arrangement may be set forth as follows. If a
tetrastyle is to be built, let the width of the front which shall have
already been determined for the temple, be divided into eleven parts and
a half, not including the substructures and the projections of the
bases; if it is to be of six columns, into eighteen parts. If an
octastyle is to be constructed, let the front be divided into
twenty-four parts and a half. Then, whether the temple is to be
tetrastyle, hexastyle, or octastyle, let one of these parts be taken,
and it will be the module. The thickness of the columns will be equal to
one module. Each of the intercolumniations, except those in the middle,
will measure two modules and a quarter. The middle intercolumniations in
front and in the rear will each measure three modules. The columns
themselves will be nine modules and a half in height. As a result of
this division, the intercolumniations and the heights of the columns
will be in due proportion.

8. We have no example of this in Rome, but at Teos in Asia Minor there
is one which is hexastyle, dedicated to Father Bacchus.

These rules for symmetry were established by Hermogenes, who was also
the first to devise the principle of the pseudodipteral octastyle. He
did so by dispensing with the inner rows of thirty-eight columns which
belonged to the symmetry of the dipteral temple, and in this way he made
a saving in expense and labour. He thus provided a much wider space for
the walk round the cella between it and the columns, and without
detracting at all from the general effect, or making one feel the loss
of what had been really superfluous, he preserved the dignity of the
whole work by his new treatment of it.

9. For the idea of the pteroma and the arrangement of the columns round
a temple were devised in order that the intercolumniations might give
the imposing effect of high relief; and also, in case a multitude of
people should be caught in a heavy shower and detained, that they might
have in the temple and round the cella a wide free space in which to
wait. These ideas are developed, as I have described, in the
pseudodipteral arrangement of a temple. It appears, therefore, that
Hermogenes produced results which exhibit much acute ingenuity, and
that he left sources from which those who came after him could derive
instructive principles.

[Illustration: VITRUVIUS' RULES FOR THE DIAMETER AND HEIGHT OF COLUMNS
IN THE DIFFERENT CLASSES OF TEMPLE COMPARED WITH ACTUAL EXAMPLES]

10. In araeostyle temples, the columns should be constructed so that
their thickness is one eighth part of their height. In the diastyle, the
height of a column should be measured off into eight and a half parts,
and the thickness of the column fixed at one of these parts. In the
systyle, let the height be divided into nine and a half parts, and one
of these given to the thickness of the column. In the pycnostyle, the
height should be divided into ten parts, and one of these used for the
thickness of the column. In the eustyle temple, let the height of a
column be divided, as in the systyle, into nine and a half parts, and
let one part be taken for the thickness at the bottom of the shaft. With
these dimensions we shall be taking into account the proportions of the
intercolumniations.

11. For the thickness of the shafts must be enlarged in proportion to
the increase of the distance between the columns. In the araeostyle, for
instance, if only a ninth or tenth part is given to the thickness, the
column will look thin and mean, because the width of the
intercolumniations is such that the air seems to eat away and diminish
the thickness of such shafts. On the other hand, in pycnostyles, if an
eighth part is given to the thickness, it will make the shaft look
swollen and ungraceful, because the intercolumniations are so close to
each other and so narrow. We must therefore follow the rules of symmetry
required by each kind of building. Then, too, the columns at the corners
should be made thicker than the others by a fiftieth of their own
diameter, because they are sharply outlined by the unobstructed air
round them, and seem to the beholder more slender than they are. Hence,
we must counteract the ocular deception by an adjustment of proportions.

[Illustration: THE DIMINUTION OF COLUMNS IN RELATION TO THEIR DIMENSIONS
OF HEIGHT]

12. Moreover, the diminution in the top of a column at the necking seems
to be regulated on the following principles: if a column is fifteen feet
or under, let the thickness at the bottom be divided into six parts,
and let five of those parts form the thickness at the top. If it is from
fifteen feet to twenty feet, let the bottom of the shaft be divided into
six and a half parts, and let five and a half of those parts be the
upper thickness of the column. In a column of from twenty feet to thirty
feet, let the bottom of the shaft be divided into seven parts, and let
the diminished top measure six of these. A column of from thirty to
forty feet should be divided at the bottom into seven and a half parts,
and, on the principle of diminution, have six and a half of these at the
top. Columns of from forty feet to fifty should be divided into eight
parts, and diminish to seven of these at the top of the shaft under the
capital. In the case of higher columns, let the diminution be determined
proportionally, on the same principles.

13. These proportionate enlargements are made in the thickness of
columns on account of the different heights to which the eye has to
climb. For the eye is always in search of beauty, and if we do not
gratify its desire for pleasure by a proportionate enlargement in these
measures, and thus make compensation for ocular deception, a clumsy and
awkward appearance will be presented to the beholder. With regard to the
enlargement made at the middle of columns, which among the Greeks is
called [Greek: entasis], at the end of the book a figure and calculation
will be subjoined, showing how an agreeable and appropriate effect may
be produced by it.

CHAPTER IV

THE FOUNDATIONS AND SUBSTRUCTURES OF TEMPLES

1. The foundations of these works should be dug out of the solid ground,
if it can be found, and carried down into solid ground as far as the
magnitude of the work shall seem to require, and the whole substructure
should be as solid as it can possibly be laid. Above ground, let walls
be laid under the columns, thicker by one half than the columns are to
be, so that the lower may be stronger than the higher. Hence they are
called "stereobates"; for they take the load. And the projections of the
bases should not extend beyond this solid foundation. The wall-thickness
is similarly to be preserved above ground likewise, and the intervals
between these walls should be vaulted over, or filled with earth rammed
down hard, to keep the walls well apart.

[Illustration: THE ENTASIS OF COLUMNS

1. The entasis as given by Fra Giocondo in the edition of 1511.

2. The entasis from the temple of Mars Ultor in Rome compared with
Vignola's rule for entasis.]

2. If, however, solid ground cannot be found, but the place proves to be
nothing but a heap of loose earth to the very bottom, or a marsh, then
it must be dug up and cleared out and set with piles made of charred
alder or olive wood or oak, and these must be driven down by machinery,
very closely together like bridge-piles, and the intervals between them
filled in with charcoal, and finally the foundations are to be laid on
them in the most solid form of construction. The foundations having been
brought up to the level, the stylobates are next to be put in place.

3. The columns are then to be distributed over the stylobates in the
manner above described: close together in the pycnostyle; in the
systyle, diastyle, or eustyle, as they are described and arranged above.
In araeostyle temples one is free to arrange them as far apart as one
likes. Still, in peripterals, the columns should be so placed that there
are twice as many intercolumniations on the sides as there are in front;
for thus the length of the work will be twice its breadth. Those who
make the number of columns double, seem to be in error, because then the
length seems to be one intercolumniation longer than it ought to be.

4. The steps in front must be arranged so that there shall always be an
odd number of them; for thus the right foot, with which one mounts the
first step, will also be the first to reach the level of the temple
itself. The rise of such steps should, I think, be limited to not more
than ten nor less than nine inches; for then the ascent will not be
difficult. The treads of the steps ought to be made not less than a foot
and a half, and not more than two feet deep. If there are to be steps
running all round the temple, they should be built of the same size.

5. But if a podium is to be built on three sides round the temple, it
should be so constructed that its plinths, bases, dies, coronae, and
cymatiumare appropriate to the actual stylobate which is to be under the
bases of the columns.

[Illustration: FRA GIOCONDO'S IDEA OF THE "SCAMILLI IMPARES"

(From his edition of Vitruvius, Venice, 1511)]

The level of the stylobate must be increased along the middle by the
scamilli impares; for if it is laid perfectly level, it will look to the
eye as though it were hollowed a little. At the end of the book a figure
will be found, with a description showing how the scamilli may be made
to suit this purpose.

CHAPTER V

PROPORTIONS OF THE BASE, CAPITALS, AND ENTABLATURE IN THE IONIC ORDER

1. This finished, let the bases of the columns be set in place, and
constructed in such proportions that their height, including the plinth,
may be half the thickness of a column, and their projection (called in
Greek [Greek: ekphora]) the same.[1] Thus in both length and breadth it
will be one and one half thicknesses of a column.

[Note 1: Reading _aeque tantam_ as in new _Rose._ Codd. _sextantem;_
Schn. _quadrantem._]

2. If the base is to be in the Attic style, let its height be so divided
that the upper part shall be one third part of the thickness of the
column, and the rest left for the plinth. Then, excluding the plinth,
let the rest be divided into four parts, and of these let one fourth
constitute the upper torus, and let the other three be divided equally,
one part composing the lower torus, and the other, with its fillets, the
scotia, which the Greeks call [Greek: trochilos].

3. But if Ionic bases are to be built, their proportions shall be so
determined that the base may be each way equal in breadth to the
thickness of a column plus three eighths of the thickness; its height
that of the Attic base, and so too its plinth; excluding the plinth, let
the rest, which will be a third part of the thickness of a column, be
divided into seven parts. Three of these parts constitute the torus at
the top, and the other four are to be divided equally, one part
constituting the upper trochilus with its astragals and overhang, the
other left for the lower trochilus. But the lower will seem to be
larger, because it will project to the edge of the plinth. The astragals
must be one eighth of the trochilus. The projection of the base will be
three sixteenths of the thickness of a column.

[Illustration: THE IONIC ORDER ACCORDING TO VITRUVIUS COMPARED WITH THE
ORDER OF THE MAUSOLEUM AT HALICARNASSUS

The difference between the Roman and the Greek relation of the
baluster-side of the capital to the echinus is to be noted.]

4. The bases being thus finished and put in place, the columns are to be
put in place: the middle columns of the front and rear porticoes
perpendicular to their own centre; the corner columns, and those which
are to extend in a line from them along the sides of the temple to the
right and left, are to be set so that their inner sides, which face
toward the cella wall, are perpendicular, but their outer sides in the
manner which I have described in speaking of their diminution. Thus, in
the design of the temple the lines will be adjusted with due regard to
the diminution.

5. The shafts of the columns having been erected, the rule for the
capitals will be as follows. If they are to be cushion-shaped, they
should be so proportioned that the abacus is in length and breadth
equivalent to the thickness of the shaft at its bottom plus one
eighteenth thereof, and the height of the capital, including the
volutes, one half of that amount. The faces of the volutes must recede
from the edge of the abacus inwards by one and a half eighteenths of
that same amount. Then, the height of the capital is to be divided into
nine and a half parts, and down along the abacus on the four sides of
the volutes, down along the fillet at the edge of the abacus, lines
called "catheti" are to be let fall. Then, of the nine and a half parts
let one and a half be reserved for the height of the abacus, and let the
other eight be used for the volutes.

6. Then let another line be drawn, beginning at a point situated at a
distance of one and a half parts toward the inside from the line
previously let fall down along the edge of the abacus. Next, let these
lines be divided in such a way as to leave four and a half parts under
the abacus; then, at the point which forms the division between the four
and a half parts and the remaining three and a half, fix the centre of
the eye, and from that centre describe a circle with a diameter equal to
one of the eight parts. This will be the size of the eye, and in it draw
a diameter on the line of the "cathetus." Then, in describing the
quadrants, let the size of each be successively less, by half the
diameter of the eye, than that which begins under the abacus, and
proceed from the eye until that same quadrant under the abacus is
reached.

7. The height of the capital is to be such that, of the nine and a half
parts, three parts are below the level of the astragal at the top of the
shaft, and the rest, omitting the abacus and the channel, belongs to
its echinus. The projection of the echinus beyond the fillet of the
abacus should be equal to the size of the eye. The projection of the
bands of the cushions should be thus obtained: place one leg of a pair
of compasses in the centre of the capital and open out the other to the
edge of the echinus; bring this leg round and it will touch the outer
edge of the bands. The axes of the volutes should not be thicker than
the size of the eye, and the volutes themselves should be channelled out
to a depth which is one twelfth of their height. These will be the
symmetrical proportions for capitals of columns twenty-five feet high
and less. For higher columns the other proportions will be the same, but
the length and breadth of the abacus will be the thickness of the lower
diameter of a column plus one ninth part thereof; thus, just as the
higher the column the less the diminution, so the projection of its
capital is proportionately increased and its breadth[2] is
correspondingly enlarged.

[Note 2: Codd. _altitudo_.]

8. With regard to the method of describing volutes, at the end of the
book a figure will be subjoined and a calculation showing how they may
be described so that their spirals may be true to the compass.

The capitals having been finished and set up in due proportion to the
columns (not exactly level on the columns, however, but with the same
measured adjustment, so that in the upper members there may be an
increase corresponding to that which was made in the stylobates), the
rule for the architraves is to be as follows. If the columns are at
least twelve feet and not more than fifteen feet high, let the height of
the architrave be equal to half the thickness of a column at the bottom.
If they are from fifteen feet to twenty, let the height of a column be
measured off into thirteen parts, and let one of these be the height of
the architrave. If they are from twenty to twenty-five feet, let this
height be divided into twelve and one half parts, and let one of them
form the height of the architrave. If they are from twenty-five feet to
thirty, let it be divided into twelve parts, and let one of them form
the height. If they are higher, the heights of the architraves are to be
worked out proportionately in the same manner from the height of the
columns.

9. For the higher that the eye has to climb, the less easily can it make
its way through the thicker and thicker mass of air. So it fails when
the height is great, its strength is sucked out of it, and it conveys to
the mind only a confused estimate of the dimensions. Hence there must
always be a corresponding increase in the symmetrical proportions of the
members, so that whether the buildings are on unusually lofty sites or
are themselves somewhat colossal, the size of the parts may seem in due
proportion. The depth of the architrave on its under side just above the
capital, is to be equivalent to the thickness of the top of the column
just under the capital, and on its uppermost side equivalent to the foot
of the shaft.

10. The cymatium of the architrave should be one seventh of the height
of the whole architrave, and its projection the same. Omitting the
cymatium, the rest of the architrave is to be divided into twelve parts,
and three of these will form the lowest fascia, four, the next, and
five, the highest fascia. The frieze, above the architrave, is one
fourth less high than the architrave, but if there are to be reliefs
upon it, it is one fourth higher than the architrave, so that the
sculptures may be more imposing. Its cymatium is one seventh of the
whole height of the frieze, and the projection of the cymatium is the
same as its height.

11. Over the frieze comes the line of dentils, made of the same height
as the middle fascia of the architrave and with a projection equal to
their height. The intersection (or in Greek [Greek: metope]) is
apportioned so that the face of each dentil is half as wide as its
height and the cavity of each intersection two thirds of this face in
width. The cymatium here is one sixth of the whole height of this part.
The corona with its cymatium, but not including the sima, has the height
of the middle fascia of the architrave, and the total projection of the
corona and dentils should be equal to the height from the frieze to the
cymatium at the top of the corona.

[Illustration: A COMPARISON OF THE IONIC ORDER ACCORDING TO VITRUVIUS
WITH ACTUAL EXAMPLES AND WITH VIGNOLA'S ORDER

A: Showing the orders reduced to equal lower diameters. B: Showing the
orders to a uniform scale.]

And as a general rule, all projecting parts have greater beauty when
their projection is equal to their height.

12. The height of the tympanum, which is in the pediment, is to be
obtained thus: let the front of the corona, from the two ends of its
cymatium, be measured off into nine parts, and let one of these parts be
set up in the middle at the peak of the tympanum, taking care that it is
perpendicular to the entablature and the neckings of the columns. The
coronae over the tympanum are to be made of equal size with the coronae
under it, not including the simae. Above the coronae are the simae (in
Greek [Greek: epaietides]), which should be made one eighth higher than
the height of the coronae. The acroteria at the corners have the height
of the centre of the tympanum, and those in the middle are one eighth
part higher than those at the corners.

13. All the members which are to be above the capitals of the columns,
that is, architraves, friezes, coronae, tympana, gables, and acroteria,
should be inclined to the front a twelfth part of their own height, for
the reason that when we stand in front of them, if two lines are drawn
from the eye, one reaching to the bottom of the building and the other
to the top, that which reaches to the top will be the longer. Hence, as
the line of sight to the upper part is the longer, it makes that part
look as if it were leaning back. But when the members are inclined to
the front, as described above, they will seem to the beholder to be
plumb and perpendicular.

14. Each column should have twenty-four flutes, channelled out in such a
way that if a carpenter's square be placed in the hollow of a flute and
turned, the arm will touch the corners of the fillets on the right and
left, and the tip of the square may keep touching some point in the
concave surface as it moves through it. The breadth of the flutes is to
be equivalent to the enlargement in the middle of a column, which will
be found in the figure.

15. In the simae which are over the coronae on the sides of the temple,
lion's heads are to be carved and arranged at intervals thus: First one
head is marked out directly over the axis of each column, and then the
others are arranged at equal distances apart, and so that there shall be
one at the middle of every roof-tiling. Those that are over the columns
should have holes bored through them to the gutter which receives the
rainwater from the tiles, but those between them should be solid. Thus
the mass of water that falls by way of the tiles into the gutter will
not be thrown down along the intercolumniations nor drench people who
are passing through them, while the lion's heads that are over the
columns will appear to be vomiting as they discharge streams of water
from their mouths.

In this book I have written as clearly as I could on the arrangements of
Ionic temples. In the next I shall explain the proportions of Doric and
Corinthian temples.

BOOK IV

INTRODUCTION

1. I have observed, Emperor, that many in their treatises and volumes of
commentaries on architecture have not presented the subject with
well-ordered completeness, but have merely made a beginning and left, as
it were, only desultory fragments. I have therefore thought that it
would be a worthy and very useful thing to reduce the whole of this
great art to a complete and orderly form of presentation, and then in
different books to lay down and explain the required characteristics of
different departments. Hence, Caesar, in my first book I have set forth
to you the function of the architect and the things in which he ought to
be trained. In the second I have discussed the supplies of material of
which buildings are constructed. In the third, which deals with the
arrangements of temples and their variety of form, I showed the nature
and number of their classes, with the adjustments proper to each form
according to the usage of the Ionic order, one of the three which
exhibit the greatest delicacy of proportion in their symmetrical
measurements. In the present book I shall speak of the established rules
for the Doric and Corinthian orders, and shall explain their differences
and peculiarities.

CHAPTER I

THE ORIGINS OF THE THREE ORDERS, AND THE PROPORTIONS OF THE CORINTHIAN
CAPITAL

1. Corinthian columns are, excepting in their capitals, of the same
proportions in all respects as Ionic; but the height of their capitals
gives them proportionately a taller and more slender effect. This is
because the height of the Ionic capital is only one third of the
thickness of the column, while that of the Corinthian is the entire
thickness of the shaft. Hence, as two thirds are added in Corinthian
capitals, their tallness gives a more slender appearance to the columns
themselves.

2. The other members which are placed above the columns, are, for
Corinthian columns, composed either of the Doric proportions or
according to the Ionic usages; for the Corinthian order never had any
scheme peculiar to itself for its cornices or other ornaments, but may
have mutules in the coronae and guttae on the architraves according to
the triglyph system of the Doric style, or, according to Ionic
practices, it may be arranged with a frieze adorned with sculptures and
accompanied with dentils and coronae.

3. Thus a third architectural order, distinguished by its capital, was
produced out of the two other orders. To the forms of their columns are
due the names of the three orders, Doric, Ionic, and Corinthian, of
which the Doric was the first to arise, and in early times. For Dorus,
the son of Hellen and the nymph Phthia, was king of Achaea and all the
Peloponnesus, and he built a fane, which chanced to be of this order, in
the precinct of Juno at Argolis, a very ancient city, and subsequently
others of the same order in the other cities of Achaea, although the
rules of symmetry were not yet in existence.

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