Proposition V.25 — If four magnitudes be proportional, the greatest and least a…

Proof

Let

a : b = c : d

with

a

greatest. By V.14

b > d

, so considering

a - c

and

d - b

or vice versa, the difference

a - c

equals

b - d

in ratio, and rearrangement (with Common Notion 5) yields

a + d > b + c

Knowledge graph · drag to pan, scroll to zoom, click a node to navigate

Full neighborhood

Depends on (3)

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.19Proposition V.19If, as a whole is to a whole, so is a part subtracted to a part subtracted, the remainder will also be to the remainder…
5Common notion 5The whole is greater than the part.

Discussion

No replications, contradictions, or comments registered yet for this claim.

Replicate or annotate this claim

Replicate to register a fresh attempt; contradict, extend, or comment otherwise. Authors can post a claim-retraction with the reason taxonomy from RRP-0020.