(Edited by Sir Thomas L. Heath, 1908)

[Euclid, ed. Heath, 1908, on

In any triangle the greater angle is subtended by the greater side.

Let ABC be a triangle having
the angle ABC greater
than the angle BCA;

I say that the side AC
is also greater than the side
AB.

For, if not, AC is either equal to AB or less.

Now AC is not equal
to AB;

for then the angle ABC
would also have been equal
to the angle ACB;
[I. 5]

but it is not;

therefore AC
is not equal to AB.

Neither is AC less than
AB,

for then the angle ABC
would also have been less
than the angle ACB;
[I. 18]

but it is not;

therefore AC
is not less than AB.

And it was proved that it is not equal either.

Therefore AC is
greater than AB.

Therefore etc. Q.E.D.

Book I: Euclid, Book I (ed. Sir Thomas L. Heath 1st Edition, 1908)

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