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Source — Euclid's Elements, encoded as an rrxiv paper — rrxiv

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Source — Euclid's Elements, encoded as an rrxiv paper

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V.20 Proposition V.20

If there be three magnitudes, and others equal to them in multitude, which taken two and two are in the same ratio, and if ex aequali the first be greater than the third, the fourth will also be greater than the sixth; and if equal, equal; and if less, less.

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.

lines 74–74 in main.tex

58 files·489.1 KB·

· 58 files

← Claims Full view

V.20 Proposition V.20

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.

lines 74–74 in main.tex