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

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X.20 Proposition X.20

If a rational area be applied to a rational straight line, it produces as breadth a straight line rational and commensurable in length with the straight line to which it is applied.

Proof

A = ℓ \cdot b

with

A

and

ℓ

rational forces

b

rational by X.19 / X.9.

lines 74–74 in main.tex