Proposition VII.7 — If a number be the same part of a number that a subtracted n…

Proof

a = b / n

and

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

then

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

by Common Notion 3 applied to each of the

n

pieces.

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Depends on (2)

3Common notion 3If equals be subtracted from equals, the remainders are equal.
VII.3Definition VII.3A number is a part of a number, the less of the greater, when it measures the greater.

Required by (dependents) (2)

VII.8Proposition VII.8If a number be the same parts of a number that a subtracted number is of a subtracted number, the remainder will also…
VII.11Proposition VII.11If, as whole is to whole, so is a number subtracted to a number subtracted, the remainder will also be to the remainder…

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