Vitruvius and siege weapons

Detail from the column of Trajanus - Dacians defending them self with a scorpion.

"I shall now proceed to an explanation of those instruments which have been invented for defence from danger, and for the purposes of self-preservation; I mean the construction of scorpions, catapultæ, and balistæ, and their proportions. And first of catapultæ and scorpions. Their proportions depend on the length of the arrow which instrument is to throw"

Vitruvius - de Architectura (On Architecture) X.10.1
Translated by J. Gwilt