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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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XI.37 Proposition XI.37

If four straight lines be proportional, the similar and similarly described parallelepipedal solids upon them will also be proportional; and if the similar and similarly described parallelepipedal solids upon them be proportional, the straight lines will themselves also be proportional.

Proof

3D analogue of VI.22: similar parallelepipeds are in the triplicate ratio of edges; equality of triplicate ratios is equivalent to equality of edge ratios.

lines 74–74 in main.tex

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XI.37 Proposition XI.37

Proof

3D analogue of VI.22: similar parallelepipeds are in the triplicate ratio of edges; equality of triplicate ratios is equivalent to equality of edge ratios.

lines 74–74 in main.tex