Commentary on Proposition VIII.26

Back to Proposition VIII.26.

[Folio 0388 | p. 382]

If $a, b$ are similar “plane numbers,” let $c$ be the mean proportional between them. [VIII. 18]

Take $\alpha, \beta, \gamma$ the smallest numbers in the ratio of $a, c, b$. [VII. 33 or VIII. 2]

Then $\alpha, \gamma$ are squares. [VIII. 2, Por.]

Therefore $a, b$ are in the ratio of a square to a square.