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

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XIII.4 Proposition XIII.4

If a straight line be cut in extreme and mean ratio, the square on the whole and the square on the lesser segment together are triple of the square on the greater segment.

Proof

A B^{2} + C B^{2} = 3 \cdot A C^{2}

where

C

cuts

A B

in extreme-and-mean ratio (greater

A C

). Use

A C^{2} = A B \cdot C B

and II.4 to verify the identity.

lines 74–74 in main.tex