Proof
The intersection line lies in both planes; by Definition XI.4 the
perpendiculars from any point of the intersection within each plane
are perpendicular to the base plane; XI.13 then forces the
intersection line itself to be perpendicular.
Knowledge graph · drag to pan, scroll to zoom, click a node to navigate
Full neighborhood
Depends on (3)
- XI.13Proposition XI.13From the same point two straight lines cannot be set up at right angles to the same plane on the same side.
- XI.18Proposition XI.18If a straight line be at right angles to any plane, all the planes through it will also be at right angles to the same…
- XI.4Definition XI.4A plane is at right angles to a plane when the straight lines drawn in one of the planes at right angles to the common…
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.