Proposition I.9 — To bisect a given rectilineal angle.

Proof

Apply I.1 to construct an equilateral triangle on a chord between the angle's sides; the line from the vertex to the equilateral's apex bisects the angle by I.8.

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

Full neighborhood

Depends on (2)

I.1Proposition I.1On a given finite straight line to construct an equilateral triangle.
I.8Proposition I.8If two triangles have the two sides equal to two sides respectively, and have also the base equal to the base, they…

Required by (dependents) (4)

I.10Proposition I.10To bisect a given finite straight line.
IV.4Proposition IV.4In a given triangle to inscribe a circle.
IV.11Proposition IV.11In a given circle to inscribe an equilateral and equiangular pentagon.
IV.13Proposition IV.13In a given pentagon, which is equilateral and equiangular, to inscribe a circle.

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.