Proposition X.3 — Given two commensurable magnitudes, to find their greatest c…

Proof

Apply anthyphairesis (the Euclidean algorithm on magnitudes); by X.2 the algorithm terminates exactly when a common measure exists.

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

Full neighborhood

Depends on (2)

X.2Proposition X.2If, when the lesser of two unequal magnitudes is continually subtracted in turn from the greater, that which is left…
X.1Definition X.1Those magnitudes are said to be commensurable which are measured by the same measure, and those incommensurable which…

Required by (dependents) (1)

X.4Proposition X.4Given three commensurable magnitudes, to find their greatest common measure.

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.