Proposition V.24 — If a first magnitude have to a second the same ratio as a th…

Proof

With

a : b = c : d

and

e : b = f : d

: by V.12 applied to the two proportions side-by-side,

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

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Depends on (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.22Proposition V.22If there be any number of magnitudes whatever, and others equal to them in multitude, which taken two and two together…

Required by (dependents) (1)

VI.31Proposition VI.31In right-angled triangles the figure on the side subtending the right angle is equal to the similar and similarly…

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