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`,

and `BC` is common,

the two sides `DB`, `BC` are equal to the two sides `AC`, `CB` respectively;

and the angle `DBC` is equal to the angle `ACB`;

therefore the base `DC` is equal to the base `AB`,

and the triangle `DBC` will be equal to the triangle `ACB`,

the less to the greater;

which is absurd.

Therefore `AB` is not unequal to `AC`;

it is therefore equal to it.

Therefore etc.

Q.E.D.