Proposition VIII.5 — Plane numbers have to one another the ratio compounded of th…

Proof

For plane numbers

ab

and

c d

ab : c d = (a : c) \cdot (b : d)

in the language of compound ratios. Verified by direct computation using VII.17 / VII.18.

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

Full neighborhood

Depends on (3)

VII.17Proposition VII.17If a number by multiplying two numbers make certain numbers, the numbers so produced will have the same ratio as the…
VII.18Proposition VII.18If two numbers by multiplying any number make certain numbers, the numbers so produced will have the same ratio as the…
VII.16Definition VII.16When two numbers having multiplied one another make some number, the number so produced is called plane, and its sides…

Required by (dependents) (1)

VIII.18Proposition VIII.18Between two similar plane numbers there is one mean proportional number, and the plane number has to the plane number…

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.