Euclid, Elements
Thomas L. Heath, Sir Thomas Little Heath, Ed.

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But the angle ECD is greater than the angle ECF; [C. N. 5]

therefore the angle ACD is greater than the angle BAE.

Similarly also, if BC be bisected, the angle BCG, that is, the angle ACD [I. 15], can be proved greater than the angle ABC as well.

Therefore etc.

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Q. E. D.

^{1 2 3 4}

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Proposition 17.

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In any triangle two angles taken together in any manner are less than two right angles.

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Let ABC be a triangle; I say that two angles of the triangle ABC taken together in any manner are less than two right angles.

For let BC be produced to D. [Post. 2]

Then, since the angle ACD is an exterior angle of the triangle ABC,

it is greater than the interior and opposite angle ABC. [I. 16]