Proposition V.20 — If there be three magnitudes, and others equal to them in mu…

Proof

With

a : b = d : e

and

b : c = e : f

, the relative order of

a

versus

c

matches the relative order of

d

versus

f

by repeated application of V.13 and V.14 across the three pairs.

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Depends on (2)

V.13Proposition V.13If a first magnitude have to a second the same ratio as a third to a fourth, and the third have to the fourth a greater…
V.14Proposition V.14If a first magnitude have to a second the same ratio as a third to a fourth, and the first be greater than the third,…

Required by (dependents) (1)

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

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