Proof
Suppose the sides unequal; cut off (by I.3) the greater equal to the
less; by I.4 the resulting smaller triangle equals the whole, which
contradicts Common Notion 5. Therefore the sides are equal.
Knowledge graph · drag to pan, scroll to zoom, click a node to navigate
Full neighborhood
Depends on (3)
- I.3Proposition I.3Given two unequal straight lines, to cut off from the greater a straight line equal to the less.
- I.4Proposition I.4If two triangles have two sides equal to two sides respectively, and have the angles contained by the equal straight…
- 5Common notion 5The whole is greater than the part.
Required by (dependents) (3)
- 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…
- IV.9Proposition IV.9About a given square to circumscribe a circle.
- 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…
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.