Proposition V.2 — If a first magnitude be the same multiple of a second that a…

Proof

a = mb

and

c = m d

e = nb

and

f = n d

, then

a + e = (m + n) b

and

c + f = (m + n) d

by Common Notion 2.

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Depends on (3)

V.1Proposition V.1If there be any number of magnitudes whatever which are, respectively, equimultiples of any magnitudes equal in…
2Common notion 2If equals be added to equals, the wholes 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.12Proposition V.12If any number of magnitudes be proportional, as one of the antecedents is to one of the consequents, so will all the…
V.18Proposition V.18If magnitudes separated be proportional, they will also be proportional componendo.

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