Euclid, Elements, volume 1, page 282

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Let the angle ACB be added to each; therefore the angles ACD, ACB are greater than the angles ABC, BCA. But the angles ACD, ACB are equal to two right angles. [I. 13]

Therefore the angles ABC, BCA are less than two right angles.

Similarly we can prove that the angles BAC, ACB are also less than two right angles, and so are the angles CAB, ABC as well.

Therefore etc.

Q. E. D.

1 πάντη μεταλαμβανόμεναι, i.e. any pair added together.

Euclid. Euclid's Elements. Sir Thomas Little Heath. New York. Dover. 1956.

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