(Edited by Sir Thomas L. Heath, 1908)

[Euclid, ed. Heath, 1908, on

If two triangles have the two sides equal to two sides respectively, but have the base greater than the base, they will also have the one of the angles contained by the equal straight lines greater than the other.

Let ABC, DEF
be two triangles having the two sides
AB, AC
equal to the two sides DE,
DF respectively, namely
AB to DE
and AC to DF;
and let the base BC be
greater than the
base EF;

I say that the angle BAC is also
greater than the angle EDF.

For, if not, it is either equal to it or less.

Now the angle BAC is not equal to
the angle EDF;

for then the base BC would also have been
equal to the base EF,
[I. 4]

but it is not;

therefore the angle BAC is not equal to
the angle DEF.

Neither again is the angle BAC
less than the angle EDF;

for then the base BC would also have been
less than the base EF,
[I. 24]

but it is not;

therefore the angle BAC is not
less than the angle EDF.

But it was proved that it is not equal either;

therefore the angle BAC
is greater than the angle EDF.

Therefore, etc. Q.E.D.

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

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