Commentary on Proposition VII.18

Back to Proposition VII.18.

[Folio 0324 | p. 318]

It is here proved that

$$a : b = ac : bc.$$

The argument is as follows.

$$\begin{aligned} ac &= ca. & \text{[VII. 16]} \\ \text{Similarly}\qquad bc &= cb. \\ \text{And}\qquad a : b &= ca : cb; & \text{[VII. 17]} \\ \text{therefore}\qquad a : b &= ac : bc. \end{aligned}$$