kat's and mon's theory presentation

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Book III: Temples and the Order of Architecture Marcus Vitruvius Pollio de Architectura

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Chapter I

The Planning of Temples

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1. The design of Temples depends on symmetry, the rules of which Architects

should be most careful to observe. Symmetry arises from proportion, which the

Greeks call ajnalogiva. Proportion is a due adjustment of the size of the different

parts to each other and to the whole; on this proper adjustment symmetry

depends. Hence no building can be said to be well designed which wants

symmetry and proportion. In truth they are as necessary to the beauty of a

building as to that of a well formed human figure,

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2. Nature has so fashioned, that in the face, from the chin to the top of theforehead, or to the roots of the hair, is a tenth part of the height of the wholebody. From the chin to the crown of the head is an eighth part of the whole

height, and from the nape of the neck to the crown of the head the same. Fromthe upper part of the breast to the roots of the hair a sixth; to the crown of thehead a fourth. A third part of the height of the face is equal to that from the chinto under side of the nostrils, and thence to the middle of the eyebrows the same;from the last to the roots of the hair, where the forehead ends, the remainingthird part. The length of the foot is a sixth part of the height of the body. Thefore-arm a fourth part. The width of the breast a fourth part. Similarly have othermembers their due proportions, by attention to which the ancient Painters andSculptors obtained so much reputation.

3. Just so the parts of Temples should correspond with each other, and with thewhole. The navel is naturally placed in the centre of the human body, and, if in aman lying with his face upward, and his hands and feet extended, from his navelas the centre, a circle be described, it will touch his fingers and toes. It is notalone by a circle, that the human body is thus circumscribed, as maybe seen byplacing it within a square. For measuring from the feet to the crown of the head,and then across the arms fully extended, we find the latter measure equal to theformer; so that lines at right angles to each other, enclosing the figure, will form asquare.

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4. If Nature, therefore, has made the human body so that the different members of 

it are measures of the whole, so the ancients have, with great propriety,

determined that in all perfect works, each part should be some aliquot part of the whole; and since they direct, that this be observed in all works, it must be

most strictly attended to in temples of the gods, wherein the faults as well as the

beauties remain to the end of time.

5. It is worthy of remark, that the measures necessarily used in all buildings and

other works, are derived from the members of the human body, as the digit, thepalm, the foot, the cubit, and that these form a perfect number, called by the

Greeks tevleioV. The ancients considered ten a perfect number, because the

fingers are ten in number, and the palm is derived from them, and from the palm

is derived the foot. Plato, therefore, called ten a perfect number, Nature having

formed the hands with ten fingers, and also because it is composed of units

called monavdeV in Greek, which also advancing beyond ten, as to eleven,

twelve, &c. cannot be perfect until another ten are included, units being the

parts whereof such numbers are composed.

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6. The mathematicians, on the other hand, contend for the perfection of the

number six, because, according to their reasoning, its divisors equal its number:

for a sixth part is one, a third two, a half three, two-thirds four, which they call

divmoiroV; the fifth in order, which they call pentavmoiro, five, and then the

perfect number six. When it advances beyond that, a sixth being added, which iscalled e[fektoV, we have the number seven. Eight are formed by adding a third,

called triens, and by the Greeks, ejpivtrito. Nine are formed by the addition of a

half, and thence called sesquilateral; by the Greeks hJmiovlio; if we add the two

aliquot parts of it, which form ten, it is called bes alterus, or in Greek

ejpidivmoiroV. The number eleven, being compounded of the original number,

and the fifth in order is called ejpipentavmoiroV . The number twelve, being thesum of the two simple numbers, is called diplasivwn.

7. Moreover, as the foot is the sixth part of a man’s height, they contend, that this

number, namely six, the number of feet in height, is perfect: the cubit, also, being

six palms, consequently consists of twenty-four digits. Hence the states of Greeceappear to have divided the drachma, like the cubit, that is into six parts, which

were small equal sized pieces of brass, similar to the asses, which they called

oboli; and, in imitation of the twenty-four digits, they divided the obolus into four

parts, which some call dichalca, others trichalca.

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8. Our ancestors, however, were better pleased with the number ten, and hence

made the denarius to consist of ten brass asses, and the money to this day

retains the name of denarius. The sestertius, a fourth part of a denarius, was so

called, because composed of two asses, and half of another. Thus finding the

numbers six and ten perfect, they added them together, and formed sixteen, a

still more perfect number. The foot measure gave rise to this, for subtracting two

palms from the cubit, four remains, which is the length of a foot; and as each

palm contains four digits, the foot will consequently contain sixteen, so the

denarius was made to contain an equal number of asses.

9. If it therefore appear, that numbers had their origin from the human body, and

proportion is the result of a due adjustment of the different parts to each other,

and to the whole, they are especially to be commended, who, in designing

temples to the gods, so arrange the parts that the whole may harmonize in their

proportions and symmetry.

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• It is assumed that

proportions of the circle

and square reflect Golden

Division. Here we present

analysis that shows that

this assumption is

incorrect.

Fig. 1 Comparison of true Golden

Rectangle with Vitruvian Man

drawing

Fig. 2 Circle and square based on

Golden Section 

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Fig. 3 The simplest way to describe

the geometrical construction of the Vitruvian

Man. 

Fig. 4 Superimposed image of Fig.6 and 

Leonardo's drawing. 

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• The mathematicians argued that six(6) was the perfect number for that its divisors

equal its number.

 – It is perfect because it can be divided by 1, 2, 3 and sum up to 6 again. In

Vitruvius’ words, a sixth is one; a third is two; a half is three. A rather simpleway of saying it is 1+2+3 = 6. They called such numbers “perfect”, because

they contain themselves.

• Thus finding the number 10 and 6 perfect, they added them together forming 16,

a still more perfect number. The foot measure gave rise to this, for subtracting twopalms from the cubit, four remains, which is the length of a foot; and as each palm

contains four digits, the foot will consequently contain sixteen.

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CHAPTER II

ON THE KINDS OF TEMPLES

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It has pilasters in front of the walls which enclose the cell, with columns in between the

pilasters, and crowned with a pediment built to symmetry to be set forth in this book.

SAMPLE PLAN OF

IN ANTIS TEMPLE

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It has columns instead of pilasters in front, which are placed opposite to the pilasters at

the angles, of the cell, and support the entablature.

SAMPLE PLAN OF

PROSTYLOS TEMPLE

TEMPLE OF AGUSTUS

PULA, CROATIA

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AMPHIPROSTYLOS

It is similar to the  prostylos, only that the columns and pediment in the front are

repeated at the rear of the temple.

TEMPLE OF ATHENA NIKE

BY CALLICRATES 427  – 424 B.C.

ACROPOLIS, ATHENS

SAMPLE PLAN OFAMPHIPROSTYLOS TEMPLE

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It has six columns in the front and rear, and eleven on the left and right, counting in

the two columns at the angles. The columns are placed that their distance from the

wall is equal to an intercolumniation, and thus forming a walk around the cell of the

temple.

SAMPLE PLAN OF

PERIPTEROS TEMPLE

TEMPLE OF ATHENA, PAESTUM

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PSUEDODIPTEROS

It is constructed with eight columns in front and rear and with fifteen on the sides,

including those at the angles. The walls of the cell are opposite to the four in the

middle columns of the front and rear. Hence from the walls to the front of the lower

part of the columns, there will be an intercolumniation and the thickness of a column

all around.

TEMPLE OF ARTEMIS IN MAGNESIA (MINIATURE)

BY HERMOGENES OF ALABANDA

SAMPLE PLAN OF

PSUEDODIPTEROS TEMPLE

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DIPTEROS

It has eight columns in front and at the back, but has double rows of columns round

the sanctuary.

SAMPLE PLAN OF

DIPTEROS TEMPLE

TEMPLE OF ARTEMIS IN EPHESUS

BY HERMOGENES OF ALABANDA

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It has ten columns in front and at the back. For the rest it has everything like the

dipteral, except that in the interior it will have two stories of columns, at a distance

from the walls all round like a colonnade of a prostylos. The centre has no roof and is

open to the sky. There are folding doors in front and at the back.

SAMPLE PLAN OF

HYPAETHEROS TEMPLE

TEMPLE OF APOLLO IN DYDYMA

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1. There are five species of temples, whose names are, PYCNOSTYLOS, that is, thickset with columns: SYSTYLOS, in which the columns are not so close: DIASTYLOS,

where they are still wider apart: ARÆOSTYLOS , when placed more distant from

each other than in fact they ought to be: EUSTYLOS, when the intercolumniation,

or space between the columns, is of the best proportion.

2. Nature has so fashioned, that in the face, from the chin to the top of the forehead,or to the roots of the hair, is a tenth part of the height of the whole body. From the

chin to the crown of the head is an eighth part of the whole height, and from the

nape of the neck to the crown of the head the same. From the upper part of the

breast to the roots of the hair a sixth; to the crown of the head a fourth. A third

part of the height of the face is equal to that from the chin to under side of the

nostrils, and thence to the middle of the eyebrows the same; from the last to theroots of the hair, where the forehead ends, the remaining third part. The length of 

the foot is a sixth part of the height of the body. The fore-arm a fourth part. The

width of the breast a fourth part. Similarly have other members their due

proportions, by attention to which the ancient Painters and Sculptors obtained so

much reputation.

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4. DIASTYLOS has intercolumniations of three diameters, as in the temple of Apollo

and Diana. The inconvenience of this species is, that the epistylia or architraves

over the columns frequently fail, from their bearings being too long.

5. In the ARÆOSTYLOS the architraves are of wood, and not of stone or marble; the

different species of temples of this sort are clumsy, heavy roofed, low and wide,

and their pediments are usually ornamented with statues of clay or brass, gilt in

the Tuscan fashion. Of this species is the temple of Ceres, near the CircusMaximus, that of Hercules, erected by Pompey, and that of Jupiter Capitolinus.

6. We now proceed to the EUSTYLOS, which is preferable, as well in respect of 

convenience, as of beauty and strength. Its intercolumniations are of two

diameters and a quarter. The center intercolumniation, in front and in the

posticum, is three diameters. It has not only a beautiful effect, but is convenient,

from the unobstructed passage it affords to the door of the temple, and the great

room allowed for walking round the cell.

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Chapter III

On the Elevation of Temples

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7. The rule for designing it is as follows. The extent of the front being given, it is, if 

tetrastylos , to be divided into eleven parts and a half, not including the

projections of the base and plinth at each end: if hexastylos, into eighteen parts: if octastylos, into twenty-four parts and a half. One of either of these parts,

according to the case, whether tetrastylos , hexastylos, or octastylos, will be a

measure equal to the diameter of one of the columns. Each intercolumniation,

except the middle one, front and rear, will be equal to two of these measures and

one quarter, and the middle intercolumniation three. The heights of the columns

will be eight parts and a half. Thus the intercolumniations and the heights of thecolumns will have proper proportions.

8. There is no example of eustylos in Rome; but there is one at Teos in Asia, which is

octastylos, and dedicated to Bacchus. Its proportions were discovered by

Hermogenes, who was also the inventor of the octastylos or pseudodipteral

formation. It was he who first omitted the inner ranges of columns in the dipteros,

which, being in number thirty-eight, afforded the opportunity of avoiding

considerable expense. By it a great space was obtained for walking all round the

cell, and the effect of the temple was not injured because the omission of the

columns was not perceptible; neither was the grandeur of the work destroyed.

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9. The pteromata, or wings, and the disposition of columns about a temple, were

contrived for the purpose of increasing the effect, by the varied appearance of the

returning columns, as seen through the front intercolumniations, and also for

providing plenty of room for the numbers frequently detained by rain, so that theymight walk about, under shelter, round the cell. I have been thus particular on the

pseudodipteros, because it displays the skill and ingenuity with which Hermogenes

designed those his works; which cannot be but acknowledged as the sources

whence his successors have derived their best principles.

10. In aræostyle temples the diameter of the columns must be an eighth part of the

height. In diastylos, the height of the columns is to be divided into eight parts and

a half; one of which is to be taken for the diameter of the column. In systylos, let

the height be divided into nine parts and a half; one of those parts will be the

diameter of a column. In pycnostylos, one-tenth part of the height is the diameter

of the columns. In the eustylos, as well as in the diastylos, the height of thecolumns is divided into eight parts and a half; one of which is to be taken for the

thickness of the column. These, then, are the rules for the severaz

intercolumniations.

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11. For, as the distances between the columns increase, so must the shafts of thecolumns increase in thickness. If, for instance, in the aræostylos, they were a ninth

or a tenth part of the height, they would appear too delicate and slender; because

the air interposed between the columns destroys and apparently diminishes, their

thickness. On the other hand, if, in the pycnostylos, their thickness or diameter

were an eighth part of the height, the effect would be heavy and unpleasant, on

account of the frequent repetition of the columns, and the smallness of theintercolumniations. The arrangement is therefore indicated by the species

adopted. Columns at the angles, on account of the unobstructed play of air round

them, should be one-fiftieth part of a diameter thicker than the rest, that they may

have a more graceful effect. The deception which the eye undergoes should be

allowed for in execution.

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12. The diminution of columns taken at the hypotrachelium , is to be so ordered, that

for columns of fifteen feet and under, it should be one-sixth of the lower diameter.

From fifteen to twenty feet in height, the lower diameter is to be divided into six

parts and a half; and five parts and a half are to be assigned for the upper

thickness of the column. When columns are from twenty to thirty feet high, the

lower diameter of the shaft must be divided into seven parts, six of which are

given to the upper diameter. From thirty to forty feet high, the lower diameter is

divided into seven parts and a half, and six and a half given to the top. From forty

to fifty feet, the lower diameter of the shaft is to be divided into eight parts, seven

of which must be given to the thickness under the hypotrachelium . If the

proportion for greater heights be required, the thickness at top must be found

after the preceding method;

13. Always remembering, that as the upper parts of columns are more distant from

the eye, they deceive it when viewed from below, and that we must, therefore,

actually add what they apparently lose. The eye is constantly seeking after beauty;and if we do not endeavour to gratify it by proper proportions and an increase of 

size, where necessary, and thus remedy the defect of vision, a work will always be

clumsy and disagreeable. Of the swelling which is made in the middle of columns,

which the Greeks call e[ntasiV, so that it may be pleasing and appropriate, I shall

speak at the end of the book.

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PYCNOSTYLOS

•is that arrangement wherein the columns areonly once and a half their thickness apart

•Temple of Julius

SYSTYLOS

•is the distribution of columns with anintercolumniation of two diameters: thedistance between their plinths is then equal totheir front faces

•Fortuna Equestris

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DIASTYLOS

•has intercolumniations of three diameters

•Temple of Apollo and Diana

ARÆOSTYLOS

•the architraves are of wood, and not of stone

or marble the different

•species of temples of this sort are clumsy,

heavy roofed, low and wide, and their

pediments are usually ornamented with

statues of clay or brass

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EUSTYLOS

•preferable, as well in respect of 

convenience, as of beauty and

strength

•It has not only a beautiful effect,

but is convenient, from the

unobstructed passage it affords to

the door of the temple, and the

great room allowed for walking

round the cell.

•Temple of Bacchus

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Chapter 4

On the Foundation of Temples

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1. If solid ground can be come to, the foundations should go down to it and into it,according to the magnitude of the work, and the substruction should be built up

as solid as possible. Above the ground the wall should be one-half thicker than the

columns it is to receive, so that lower parts which carry the greatest weight, may

be stronger than the upper part, which is called the stereobata: nor must the

mouldings of the bases of the columns project beyond the solid. Thus, also, should

be regulated the thickness of all walls above ground. The intervals between the

foundations brought up under the columns, should be either rammed down hard,

or arched, so as to prevent the foundation piers from swerving.

2. If solid ground cannot be come to, and the ground be loose or marshy, the place

must be excavated, cleared, and either alder, olive, or oak piles, previouslycharred, must be driven with a machine, as close to each other as possible, and

the intervals, between the piles, filled with ashes. The heaviest foundations may

be laid on such a base.

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3. When they are brought up level, the stylobatæ (plinths) are placed thereon,

according to the arrangement used, and above described for the pycnostylos,

systylos, diastylos or eustylos , as the case may be. In the aræostylos it is only

necessary to preserve, in a peripteral building, twice the number of 

intercolumniations on the flanks that there are in front, so that the length may be

twice the breadth. Those who use twice the number of columns for the length,

appear to err, because they thus make one intercolumniation more than should be

used.

4. The number of steps in front should always be odd, since, in that case, the right

foot, which begins the ascent, will be that which first alights on the landing of the

temple. The thickness of the steps should not, I think, be more than ten inches,

nor less than nine, which will give an easy ascent. The treads not less than onefoot and a half, nor more than two feet; and if the steps areto go all round the

temple, they are to be formed in the same manner.

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5. But if there is to be a podium on three sides of the temple, the plinths, bases of 

the columns, columns, coronæ, and cymatium, may accord with the stylobata ,

under the bases of the columns. The stylobata should be so adjusted, that, by

means of small steps or stools, it may be highest in the middle. For if it be set out

level, it will have the appearance of having sunk in the centre. The mode of 

adjusting the steps (scamilli impares), in a proper manner, will be shown at theend of the book.

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CHAPTER 5

ON THE IONIC ORDER

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1. After preparing the foundation, the bases of the columns may be laid, theirheight being equal to half the radius of the column including the plinth, and

their projection, which the Greeks call elkfora, one half the raidus of the column.

Thus the height and breadth added together, will amount to one diameter and a

half.

2. If the attic base be used, must be one-third the thickness of a column, and thatthe remainder left for the height of the plinth. Taking the plinth away, the

remainder is to be divided into four parts, and the upper torus is to be one-

fourth: the remaining three-fourths are to be equally divided so that one is the

lower torus and the other the scotia (which the Greeks call trochilus) with

its fillets.

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3. But if the bases are to be Ionic, they are to be set out that the breath of the base

each way is one and three-eigths of the thickness of a column. The height is to be

like the Attic base; so also its plinth. The remainder beside the plinth, which will

be the third part of the column's diameter, is to be divided into seven parts: of 

these the torus at the top is to be three parts; the remaining four are to be

equally divided; one half to the upper hollow with its astragals and top moulding,

the other half is to be left to the lower trochilus; but the lower will seem greater

because it will have a projection to the edge of the plinth. The astragals are to be

one-eighth part of the scotia. The projections of the base will be three-sixteenths

of the thickness of the column.

4. When the bases are complete and in position, the middle columns in front and at

the back are to be set up to a perpendicular, but the corner columns and those

which are in line with them on the flanks of the temple right and left are to be set

up so that the inside parts which look to the sanctuary, have their faces

perpendicular, but the outside parts so as to declare their diminution. In this way

the intention of the design of the temple will be completed by such contraction.

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5. When the shafts of the columns are fixed, the proportions of the Ionic capitals

are to be conformed to this symmetries: namely, that in adding the eighteenth

part of the thickest part of the shaft, the abacus my find its length and breadth;

the height of the capital with the volutes, half of that. There must be a set-back

from the edge of the abacus inwards on the front of the volutes of aneighteenth part and a half. Then the height of the capital is to be divided into

nine and a half parts, and lines (which are called cathetoe) are to be let fall

down the abacus, at the four corners of the volutes, following a perpendicular

from the edge of the abacus. Then of nine parts and a half, one part and a half 

are to be left as the thickness of the abacus, and the remaining eight parts are

to be allotted to the volutes.

6. Then within a vertical line which is let fall at the extreme corner of the abacus,

let fall another line at a distance of one part and a half. Next let these lines be

so divided that four parts and a half are left under the abacus. Then that point

which divides the four and a half and the three and a half is the centre of theeye of the volute: and let there be drawn from that centre a complete circle

with a diameter of one part out of the eight parts. That will be the magnitude

of the eye. Through the centre let there be drawn a vertical diameter. Then

beginning from the top under the abacus, let the radius be successively

diminished by half the diameter of the eye in describing the quadrants, until it

comes into the quadrant which is under the abacus.

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7. Now the height of the capital is to be so arranged that of the nine and a half 

parts, three parts are below the astragal at the top of the shaft. The remaining

part is for the cymatium , when the abacus and channel are taken away. The

projection of the cymatium beyond the abacus is to be the size of the eye. Let

the bands of the pillow have the following projection: one point of the

compasses is placed in the centre of the eye, and the other point is taken to the

top of the cymatium; The circle thus described will mark the furthest part of the

pillow band. The axes of the volutes should not be further apart than the

diameter of the eye, and the volutes themselves are to be channelled to the

twelfth part of their height. These will be the proportions of capitals when thecolumns shall be up to twenty-five feet. Those which are more will have their

other proportions after the same fashion. The length and breadth of the abacus

will be the thickness of the column at its base with the addition of one-ninth:

inasmuch as its diminution is less as the heigtht is greater, the capital must not

have less addition in projection and height.

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8. At the end of the book a diagram and formula will be furnished for the drawing

of the volutes so that they may be correctly turned by the compass. When the

capitals are completed they are to be set, not level through the range of 

columns, but with a corresponding adjustment; so that the architraves in the

upper members may correspond to the addition in the stylobates. the

proportion of the architraves should be as follows: if the columns are from

twelve to fifteen feet, the height of the architrave should be half the thickness of 

the column at the bottom; from fifteen to twenty feet let the height of the

column be divided into thirteen parts, and the height of the architrave be one

part; from twenty to twenty-five feet, let the height be divided into twelve parts

and a half, and let the architrave be one part of that in height; also from twenty-

five to thirty let it be divided into twelve parts, and let the height be made of 

one part. Thus the height of the architraves are to be determined in accordance

with the height of the columns.

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9. For the higher the glance of the eye rises, it perces with the more difficulty the

denseness of the air; therefore it fails owing to the amount and power of the

height, and reports to the senses the assemblage of the uncertain quantity of 

the modules. And so we must always add a supplement to the proportion in thecase of the symmetrical parts, so that works which are either in higher positions

or themselves more grandiose may have proportionate dimensions. The

breadth of the architrave at the bottom where it rests upon the capital should

equal the diameter of the top of the column under the capital: the top of the

architrave should be as wide as the lower diameter of the shaft.

10. The cymatium of the architrave should be made one-seventh of its height and

the projection of it the same. The remainder apart from the cymatium is to be

divided into twelve parts of which the lowest fascia is to have three; the

second, four; and the top, five. The frieze also above the architrave is to be a

fourth less than the architrave; but if figures are to be introduced, a fourth

higher, so that the carvings may be effective. The cymatium a seventh part of its

height; the projection of the cymatium as much as the thickness.

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11. Above the frieze the dentil is to be made as high as the middle fascia of the

architrave; its projection as much as its height. The interval, which in Greek is

called metope, is to be arranged so that the dentil is half as wide as it is high; The

hollow of the interval is two-thirds of the front of the dentil; the cymatium of 

this, one-sixth its height. The cornice with its cymatium, but without the sima, isto be equal to the middle fascia of the architrave. The projection of the cornice

with the dentil is to be made equal to the height from the frieze to the top of the

cymatium of the cornice; and generally all projections have a more graceful

appearance when they are equal to the height of the feature.

12. The height of the tympanum which is in the pediment is to be such, that the

whole front of the cornice from the outside of the cymatia is to be measured into

nine parts; and of these one is to be set up in the middle for the summit of the

tympanum. The architraves and hypotrachelia of the columns are vertically under

it. The cornices above the tympana are to be made equal to those below,

omitting the simae. Above the cornices the simae, which the Greekscall epaietides, are to be made higher by one-height than the coronae. The

angle acroteria are to be as high as the middle of the tympanum; the middle ones

are to be one-eighth higher than those at the angles.

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13. All the features which are to be above the capitals of the columns, that is to say,

architraves, friezes, cornices, tympana, pediments, acroteria, are to be inclined

towards their front by a twelfth part of their height; because when we stand

against the fronts, if two lines are drawn from the eye, and one touches hte

lowest part of the work, and the other the highest, that which touches the

highest, will be the longer. Thus because the longer line of vision goes to the

upper part, it gives the appearance of leaning backwards. When however, as

written above, the line in inclined to the front, then the parts will seem vertical

and to measure.

14. The flutes of the columns are to be twenty four, hollowed out in such a way that

if a set square is placed into the hollow of a flute and moved round its ends, it

will touch the fillets on the right and left, and the point of the square will touch

the curve as it moves round. The width of the flutes is to be altered so as to suitthe addition produced by the swelling of the column.

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15. On the mouldings which are above the cornice on the sides of temples, lions'

heads are to be carved, and arranged firstly so as to be set over against the tops

of the several columns; the others at equal intervals so as to answer to the

middle of the roof tiling. But these which will be against the columns are to be

pierced for a gutter which takes the rainwater from the tiles. The intervening

heads are to be solid so that the water which falls over the tiles into the gutter,may not fall down through the intercolumniations upon the passers by. But those

which are against the columns are to seem to vomit and let fall streams of water

from their mouths.