Proof
If (integers) then ; converse
holds by VIII.14 applied to integers and VI.22 applied to magnitudes.
Knowledge graph · drag to pan, scroll to zoom, click a node to navigate
Full neighborhood
Depends on (4)
- VI.22Proposition VI.22If four straight lines be proportional, the rectilineal figures similar and similarly described upon them will also be…
- VIII.14Proposition VIII.14If a square measure a square, the side will also measure the side; and if the side measure the side, the square will…
- X.5Proposition X.5Commensurable magnitudes have to one another the ratio which a number has to a number.
- X.6Proposition X.6If two magnitudes have to one another the ratio which a number has to a number, the magnitudes will be commensurable.
Required by (dependents) (3)
- X.10Proposition X.10To find two straight lines incommensurable, the one in length only, the other in square also, with an assigned straight…
- X.19Proposition X.19The rectangle contained by rational straight lines commensurable in length is rational.
- X.21Proposition X.21The rectangle contained by rational straight lines commensurable in square only is irrational, and the side of the…
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.
Sign in with ORCID to annotate this claim.