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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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VII.18 Proposition VII.18

If two numbers by multiplying any number make certain numbers, the numbers so produced will have the same ratio as the multipliers.

Proof

a \cdot c : b \cdot c = a : b

by VII.16 (swap to put

c

on the left) and VII.17.

lines 74–74 in main.tex