Proof
Apply I.23 to reproduce the alternate angle at the given point and
I.27 to conclude parallelism.
Knowledge graph · drag to pan, scroll to zoom, click a node to navigate
Full neighborhood
Depends on (2)
Required by (dependents) (20)
- I.32Proposition I.32In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles,…
- I.37Proposition I.37Triangles which are on the same base and in the same parallels are equal to one another.
- I.38Proposition I.38Triangles which are on equal bases and in the same parallels are equal to one another.
- I.39Proposition I.39Equal triangles which are on the same base and on the same side are also in the same parallels.
- I.40Proposition I.40Equal triangles which are on equal bases and on the same side are also in the same parallels.
- I.42Proposition I.42To construct, in a given rectilineal angle, a parallelogram equal to a given triangle.
- I.46Proposition I.46On a given straight line to describe a square.
- I.47Proposition I.47In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides…
- II.1Proposition II.1If there be two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by…
- II.2Proposition II.2If a straight line be cut at random, the rectangle contained by the whole and both of the segments is equal to the…
- II.4Proposition II.4If a straight line be cut at random, the square on the whole is equal to the squares on the segments and twice the…
- II.5Proposition II.5If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole…
- II.6Proposition II.6If a straight line be bisected and a straight line be added to it in a straight line, the rectangle contained by the…
- II.9Proposition II.9If a straight line be cut into equal and unequal segments, the squares on the unequal segments of the whole are double…
- II.10Proposition II.10If a straight line be bisected and a straight line be added to it in a straight line, the square on the whole with the…
- VI.3Proposition VI.3If an angle of a triangle be bisected and the straight line cutting the angle cut the base also, the segments of the…
- VI.9Proposition VI.9From a given straight line to cut off a prescribed part.
- VI.10Proposition VI.10To cut a given uncut straight line similarly to a given cut straight line.
- VI.11Proposition VI.11To two given straight lines to find a third proportional.
- VI.12Proposition VI.12To three given straight lines to find a fourth proportional.
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.