Source — Euclid's Elements, encoded as an rrxiv paper

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X.114 Proposition X.114

If an area be contained by an apotome and the binomial the terms of which are commensurable with the terms of the apotome and in the same ratio, the side of the area is rational.

Proof

The rectangle on

(a - b)

and

(a^{'} + b^{'})

with

a^{'} = k a

,

b^{'} = k b

equals

k (a^{2} - b^{2})

, which is rational.

lines 74–74 in main.tex