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

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

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VIII.22 Proposition VIII.22

If three numbers be in continued proportion, and the first be square, the third will also be square.

Proof

If

a^{2} : m = m : c

, then

m^{2} = a^{2} c

so

c = (m / a)^{2}

, hence

c

is square. VII.19 ensures the division produces an integer.

lines 74–74 in main.tex