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

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VIII.11 Proposition VIII.11

Between two square numbers there is one mean proportional number, and the square has to the square the ratio duplicate of that which the side has to the side.

Proof

For squares

a^{2}

,

b^{2}

: the mean proportional is

ab

(since

a^{2} : ab = ab : b^{2} = a : b

), and

a^{2} : b^{2}

is the duplicate of

a : b

.

lines 74–74 in main.tex