In any triangle the greater side subtends the greater angle.
For let ABC be a triangle having
the side AC greater than
I say that the angle ABC is also greater than the angle BCA.
For, since AC is greater than AB, let AD be made equal to AB [I. 3] , and let BD be joined.
Then, since the angle ADB
is an exterior angle of the triangle
it is greater than the interior and opposite angle DCB. [I. 16]
But the angle ADB is equal to the
since the side AB is equal to AD;
therefore the angle ABD is also greater than the angle ACB;
therefore the angle ABC is much greater than the angle ACB.
Therefore etc. Q.E.D.
Book I: Euclid, Book I (ed. Sir Thomas L. Heath 1st Edition, 1908)
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