Proposition V.21 — If there be three magnitudes, and others equal to them in mu…

Proof

A perturbed version of V.20: with

a : b = e : f

and

b : c = d : e

the ratio chain still imposes the same ordering between

a

versus

c

and

d

versus

f

, by V.13 and V.14.

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Depends on (3)

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,…
V.18Definition V.18A perturbed proportion arises when, there being three magnitudes and another set equal to them in multitude, as…

Required by (dependents) (1)

V.23Proposition V.23If there be any number of magnitudes whatever, and others equal to them in multitude, which taken two and two together…

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