the Kanon of Polykleitos

His aesthetic theories of the mathematical bases of artistic perfection.
The aim of the Canon, was not simply to explain a statue but also to achieve to kallos, "the beautiful” and to eu (the perfect or the good) in it. The secret of achieving to kallos and to eu lay in the mastery of symmetria, the perfect "commensurability" of all parts of the statue to one another and to the whole.

A Reconstructed Outline of the Kanon of Polykleitos
From the quotations, paraphrases, and comments on the Canon extant from antiquity, an outline of the Canon treatise can be reasonably inferred as follows:

1. Perfection comes about little by little through many numbers (Philo of Byzantium, Belopoeica 4.1).
2. The numbers must all come to a congruence through some system of commensurability and harmony, for ugliness is immediately ready to come into being if only one chance element is omitted or inserted out of place (Plutarch, Moralia 45C).
3. Perfection is the exact Mean in each particular case —human, horse, ox, lion, and so on (Galen, de Temperamentis 1.9; Ars medica 14; de Optima nostri corporis constitutione 4).
4. So the perfect human body should be neither too tall nor too short, nor too stout or too thin, but exactly well proportioned (Galen, Ars medica; Lucian, de Saltatione 75).
5. Such perfection in proportion comes about via an exact commensurability of all the body’s parts to one another: of finger to finger and of these to the hand and wrist, of these to the forearm, of the forearm to the upper arm; of the equivalent parts of the leg; and of everything to everything else (Galen, de Temperamentis 1.9; Ars medica 14; de Placitis Hippocratis et Platonis; de Usu partium 17.1; de Optima nostri corporis constitutione 4).
6. This perfection requires scrupulous attention to replicating the body’s anatomy; not a single error can be tolerated (Galen, de Usu partium 17.1).
7. In bronze work, such precision is most difficult when the clay is on/at the nail (Plutarch, Moralia 86A and 636B-C; cf. Galen, de Usu partium 17.1).

Polyclitus's idea of symmetria and the pursuit of the to kallos and to eu was influenced by exposure to the ideas of Pythagoras of Samos.
Aristotle, Metaphysics, I.5.986a22: “Members of this school [the Pythagoreans] say there are ten principles, which they arrange into two columns of cognates, thus:

limited and unlimited
odd and even
one and plurality
right and left
male and female
rest and movement
straight and curved
light and darkness
good and bad
square and oblong