(Edited by Sir Thomas L. Heath, 1908)

[Euclid, ed. Heath, 1908, on

In any triangle the greater side subtends the greater angle.

For let ABC be a triangle having
the side AC greater than
AB;

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
BCD,

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

But the angle ADB is equal to the
angle ABD,

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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