The following is as given in Sir Thomas L. Heath's translation, which can be found in the book The Thirteen Books of The Elements, Vol. 1.
|Book I||Book II||Book IX|
|Definitions, Postulates, and Common Notions||Definitions||Proposition 20|
|Proposition 1, Proposition 3,||Proposition 14||Proposition 36|
|Proposition 5, Proposition 6,|
|Proposition 29, Proposition 47|
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 ABC equal to the angle ACB;
I say that the side AB is also equal to the side AC.
For, if AB is unequal to AC, one of them is greater.
Let AB be greater; and from AB the greater let DB be cut off equal to AC the less;
let DC be joined.
Then, since DB is equal to AC,
the two sides DB, BC are equal to the two sides AC, CB respectively;
and the triangle DBC will be equal to the triangle ACB,
which is absurd.
Therefore AB is not unequal to AC;