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

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XII.9 Proposition XII.9

In equal pyramids which have triangular bases the bases are reciprocally proportional to the heights; and those pyramids which have triangular bases in which the bases are reciprocally proportional to the heights are equal.

Proof

3D analogue of VI.15 for pyramids; via XII.5 / XII.6 the area-times- height proportion factors into the reciprocal proportion of bases and heights.

lines 74–74 in main.tex