Proposition V.22 — If there be any number of magnitudes whatever, and others eq…

Proof

Apply V.20 inductively across the chain

a_{1} : a_{2} = b_{1} : b_{2}

a_{2} : a_{3} = b_{2} : b_{3}

\dots

a_{n - 1} : a_{n} = b_{n - 1} : b_{n}

to conclude

a_{1} : a_{n} = b_{1} : b_{n}

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Depends on (2)

V.20Proposition V.20If there be three magnitudes, and others equal to them in multitude, which taken two and two are in the same ratio, and…
V.17Definition V.17A ratio ex aequali arises when, there being several magnitudes and another set equal to them in multitude which taken…

Required by (dependents) (1)

V.24Proposition V.24If a first magnitude have to a second the same ratio as a third has to a fourth, and also a fifth have to the second…

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