Proposition X.19 — The rectangle contained by rational straight lines commensur…

Proof

Rational sides commensurable in length have integer ratios; product of two such sides is in rational ratio to the assigned-square area.

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

Full neighborhood

Depends on (3)

X.9Proposition X.9The squares on straight lines commensurable in length have to one another the ratio which a square number has to a…
X.3Definition X.3With these hypotheses, it is proved that there exist straight lines infinite in multitude which are commensurable and…
X.4Definition X.4And let the square on the assigned straight line be called rational and those areas which are commensurable with it…

Required by (dependents) (1)

X.20Proposition X.20If a rational area be applied to a rational straight line, it produces as breadth a straight line rational and…

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.