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

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VIII.19 Proposition VIII.19

Between two similar solid numbers there fall two mean proportional numbers, and the solid number has to the solid number the ratio triplicate of that which the corresponding side has to the corresponding side.

Proof

For similar solid numbers

ab c

and

d e f

: the two means are

ab f

and

a e f

(or symmetric variants); together they give a continued proportion in triplicate ratio.

lines 74–74 in main.tex