Proposition V.5 — If a magnitude be the same multiple of a magnitude that a su…

Proof

a = mb

and

a^{'} = m b^{'}

with

a^{'} < a

, then

a - a^{'} = m (b - b^{'})

by Common Notion 3 applied to each of the

m

copies.

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Depends on (2)

3Common notion 3If equals be subtracted from equals, the remainders are equal.
V.2Definition V.2The greater is a multiple of the less when it is measured by the less.

Required by (dependents) (2)

V.6Proposition V.6If two magnitudes be equimultiples of two magnitudes, and any magnitudes subtracted from them be equimultiples of the…
V.17Proposition V.17If magnitudes composed be proportional, they will also be proportional separando.

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