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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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V.7 Proposition V.7

Equal magnitudes have to the same the same ratio, as also has the same to equal magnitudes.

Proof

Let

a = b

and

c

arbitrary. For any equimultiples

ma

,

mb

of

a

,

b

, and

n c

of

c

, the test of V.5 succeeds vacuously because

ma = mb

. Therefore

a : c = b : c

and

c : a = c : b

.

lines 74–74 in main.tex