The composition of a temple is based on symmetry, whose principles architects should take the greatest care to master. Symmetry derives from proportion, which is called analogia in Greek. Proportion is the mutual calibration of each element of the work and of the whole, from which the proportional system is achieved. No temple can have any compositional system without symmetry and proportion, unless, as it were, it has an exact system of correspondence to the likeness of a well-formed human being. For Nature composed the human body in such a way that the face, from the chin to the top of the forehead and the lowermost roots of the hairline should be one-tenth [of the total height of the body]; the palm of the hand form the wrist to the tip of the middle finger should measure likewise; the head from the chin to the crown, one-eighth; from the top of the chest to the hairline including the base of the neck, one-sixth; from the center of the chest to the crown of the head, one-fourth. Of the height of the face itself, one-third goes from the base of the chin to the lowermost part of the nostrils, another third from the base of the nostrils to a point between the eyebrows, and from that point to the hairline, the forehead also measures one-third. The foot should be one-sixth the height, the cubit, one-fourth, the chest also one-fourth. The other limbs, as well, have their own commensurate proportions, which the famous ancient painters and sculptors employed to attain great and unending praise. Similarly, indeed, the elements of holy temples should have dimensions for each individual part that agree with the full magnitude of the work. So, too, for example, the center and midpoint of the human body is, naturally, the navel. For if a person is imagined lying back with outstretch arms and feet within a circle whose center is at the navel, the fingers and toes will trace the circumference of this circle as they move about. But to whatever extent a circular scheme may be present in the body, a square design may also be discerned there. For if we measure from the soles of the feet to the crown of the head, and this measurement is compared with that of the outstretched hands, one discovers that this breadth equals the height, just as in areas which have been squared off by use of the set square. And so, if Nature has composed the human body so that in its proportions the separate individual elements answer to the total form, then the ancients seem to have had reason to decide that bringing their creations to full completion likewise required a correspondence between the measure of individual elements and the appearance of the work as a whole. Therefore, when they were handing down proportional sequences for every type of work, they did so especially for the dwellings of the gods, as the successes and failures of those works tend to remain forever. In the same way, they gathered the principles of measure, which seem to be necessary in any sort of project, from the components of the human body: the digit, palm, and cubit, for example, and grouped these units of measure into the perfect number which the Greeks call teleion. The ancients decided that the number called ten was perfect, because it was discovered from the number of digits on both hands. And if the number of digits on both hands is perfect by nature, it pleased Plato to state that the number was also perfect for this reason, that the decad (10) is achieved by adding together those [four] individual elements which the Greeks call monades. As soon as they reach eleven or twelve, because they will have passed ten [and beyond the four of the tetrad] they cannot be perfect until they reach the next decad. In a manner of speaking, the first four integers are the components of the perfect number. However, mathematicians who take the opposing side of the argument have said that the number which is called six is perfect, because that number has six components, all of which agree in their ratios with the number six. One-sixth of six (sextans = n/6) equals one. One-third of six (triens = n/3) equals two. Half of six (semissis = n/2) equals three. Two-thirds of six (bessis = 2n/3) equal four. Five-sixths of six (pentemoiros = 5n/6) equal five, and the complete number, the perfect number, is six. Now, if one increases the numbers in the direction of double six, by adding another unit, that is another sixth of six (n + n/6), one obtains seven, called ephekton, eight is reached, by the addition of another third of six to six (n + n/3), the sesquitertium (4:3) is obtained, which is called epitritos, adding one-half of six to six (3:2), which is called hemiolios. Adding two more units to make the decad (n + 2n/3) yields bes altertum, which they call epidimoiros, in the number eleven, because five units have been added (n + 5n/6), a fifth is made which is called epipemptos, but twelve, which is made by two whole numbers (i.e., 2 x 6; also 6 + 6) is called “the double,” diplasios. They also hold that that number perfect because, just as the foot occupies the sixth part of human height, so, too, the number that brings the dimension of the feet to completion, when multiplied by six, delimits the height of the body. Furthermore the ancients observed that the cubit is composed of six palms and twenty-four digits. On the basis of these observations, it seems that Greek cities have made it a rule that just as a cubit consists of six palms, so in the drachma, which they would use as a coin, there should be six equal stamped bronze coins, like our pounds, which they call obols, and to have decided on quarter-obols, which some cities call dicalcha and several call tricalcha, with twenty-four in the drachma, in due ratio to the fingers as they correspond to the palm. It was our ancestors who first fixed on the ancient number and invented the denarius of ten pounds, and this is why the name of our coinage to this day is denarius. And the quarter-denarius, which is composed of two and one-half pounds, they called a sestertius. Later, when they had observed that both numbers, six and ten, were perfect, they combined them to obtain the most perfect number of all (i.e., sixteen). The source of this discovery was the foot. For if two palms are subtracted from a cubit, a foot measuring four palms is left, and the palm, of course, is formed of four digits. Thus it came about that the foot measures sixteen digits, and the bronze denarius, likewise, is composed of sixteen pounds. Therefore it is agreed that from the limbs of the human body number was discovered, and also the fact that a correspondence of dimension exists among individual elements and the appearance of the entire body in each of its parts, then it is left for us to recognize that the ancients, who also established the houses of the immortal gods, ordered the elements of those works so that, in both their shape and their symmetries, fitting dimensions of separate elements and of the work as a whole might be created.