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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.18 Proposition V.18

If magnitudes separated be proportional, they will also be proportional componendo.

Proof

The converse of V.17: if

a : b = c : d

, then by V.2 plus V.4 combined,

(a + b) : b = (c + d) : d

.

lines 74–74 in main.tex