Did a Greek sculptor write down the formula for the perfect body?

Almost certainly, yes, and then the book was lost. Polykleitos, an ancient Greek sculptor active in the 5th century BCE, is particularly known for his lost treatise, the Canon, a canon of body proportions that set out a mathematical basis for an idealised male body. His Canon was probably represented by his statue the Doryphoros, or "Spear Bearer". None of his original sculptures are known to survive: the Doryphoros comes down to us only in numerous Roman marble copies of the lost bronze.

Of the treatise, we have scraps. He is quoted as saying that "Perfection ... comes about little by little through many numbers", meaning that a statue should be made of clearly definable parts, all related to one another through a system of ideal mathematical proportions and balance. Galen later explained that the Canon got its name because it had a precise commensurability, symmetria, of all the parts to one another: of finger to finger, fingers to palm and wrist, and forearm to upper arm.

So the principle is clear and the numbers are not. Modern scholars have found an absence of any general agreement on how the Canon was applied in works of art. Rhys Carpenter called it a curiosity of archaeological scholarship that no one has extracted the recipe of the written canon from its visible embodiment.

The pose that came with the Canon, rigorously calculated, found in almost all works attributed to Polykleitos, did become a standard formula in Greco-Roman and later western European art.