Proposition V.13 — If a first magnitude have to a second the same ratio as a th…

Proof

Combine V.11 (sameness transitivity) with Definition V.7 (greater ratio): the witness equimultiples for

c : d > e : f

work for

a : b

via the V.5 sameness of

a : b

and

c : d

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

Full neighborhood

Depends on (3)

V.11Proposition V.11Ratios which are the same with the same ratio are also the same with one another.
V.5Definition V.5Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any…
V.7Definition V.7When, of the equimultiples, the multiple of the first magnitude exceeds the multiple of the second, but the multiple of…

Required by (dependents) (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.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.21Proposition V.21If there be three magnitudes, and others equal to them in multitude, which taken two and two together are in the same…

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.