Home Geometry Euclid's Elements Post a comment Proposition 5 Proposition 7       By Antonio Gutierrez
Euclid's Elements Book I, Proposition 6:
If in a triangle two angles be equal to one another, the sides which subtend the equal angles will also be equal to one another.

Let ABC be a triangle having the angle BAC equal to the angle ACB;

I say that the side AB is also equal to the side BC. "Proof by contradiction," also called reductio ad absurdum.

Euclid's Elements Book 1,I, Proposition 6

Geometrical conversion

Proposition I.6 is the geometrical, but not the logical, converse of proposition I.5. 

The Elements: Books I-XIII

Euclid's Elements is the oldest mathematical and geometric treatise consisting of 13 books written by Euclid in Alexandria c. 300 BC. It is a collection of definitions, postulates, axioms, 467 propositions (theorems and constructions), and mathematical proofs of the propositions.

  Recent Additions