Commentary on Proposition V.12

Back to Proposition V.12.

[Folio 0166 | p. 160]

Algebraically, if $a : a' = b : b' = c : c'$ etc., each ratio is equal to the ratio $(a + b + c + \dots) : (a' + b' + c' + \dots)$.

This theorem is quoted by Aristotle, Eth. Nic. V. 7, 1131 b 14, in the shortened form “the whole is to the whole what each part is to each part (respectively).”