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

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VII.7 Proposition VII.7

If a number be the same part of a number that a subtracted number is of a subtracted number, the remainder will also be the same part of the remainder that the whole is of the whole.

Proof

If

a = b / n

and

a^{'} = b^{'} / n

then

a - a^{'} = (b - b^{'}) / n

by Common Notion 3 applied to each of the

n

pieces.

lines 74–74 in main.tex