Euclid, Elements of Geometry, Book I, Proposition 17
(Edited by Dionysius Lardner, 1855)

Proposition XVII. Theorem.
[Euclid, ed. Lardner, 1855, on Google Books]

(95) Any two angles of a triangle (B A C) are together less than two right angles.

Produce any side B C, then the angle A C D is greater than either of the angles A or B (XVI), A B C D therefore A C B together with either A or B is less than the same angle A C B together with A C D; that is, less than two right angles (VIII). In the same manner, if C B be produced from the point B, it can be demonstrated that the angle A B C together the angle A is less than two right angles; therefore any two angles of the triangle are less than two right angles.

This proposition and the sixteenth are included in the thirty-second. which proves that the three angles are together equal to two right angles.

Book I: Euclid, Book I (ed. Dionysius Lardner, 11th Edition, 1855)

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