Commentary on Proposition X.83

Back to Proposition X.83.

[Folio 0178 | p. 174]

Suppose, with the same notation, that

$$x - y = x' - y'. \qquad (x > x')$$

Here, $(x^2 + y^2)$, $(x'^2 + y'^2)$ being both medial areas, and $2xy$, $2x'y'$ both rational areas, while

$$(x^2 + y^2) - (x'^2 + y'^2) = 2xy - 2x'y',$$

24. 26 is contradicted again.

Therefore etc.