Commentary on Proposition V.11

Back to Proposition V.11.

[Folio 0165 | p. 159]

Algebraically, if

$$\begin{aligned} a : b &= c : d, \\ \text{and}\qquad c : d &= e : f, \\ \text{then}\qquad a : b &= e : f. \end{aligned}$$

The idiomatic use of the imperfect in quoting a result previously obtained is noteworthy. Instead of saying “But it was proved that, if H is in excess of M, G is also in excess of L,” the Greek text has “But if H was in excess of M, G was also in excess of L,” ἀλλὰ εἰ ὑπερεῖχε τὸ Θ τοῦ Μ, ὑπερεῖχε καὶ τὸ Η τοῦ Λ.

This proposition is tacitly used in combination with v. 16 and v. 24 in the geometrical passage in Aristotle, $Meteorologica$ III. 5, 376 a 22—26.