(Edited by Sir Thomas L. Heath, 1908)

[Euclid, ed. Heath, 1908, on

To bisect a given finite straight line.

Let AB be the given finite straight line.

Thus it is required to bisect the given straight line AB.

Let the equilateral triangle ABC
be constructed on it,
[I. 1]

and let the angle ACB be bisected
by the straight
line CD;
[I. 9]

I say that the straight line AB
has been bisected at the point D.

For, since AC is equal to
CB, and CD
is common,

the two sides AC,
CD are equal to the
two sides BC,
CD
respectively;

and the angle ACD is equal
to the angle BCD;

therefore the base AD is equal
to the base BD;
[I. 4]

Therefore the given finite straight line AB has been bisected at D. Q.E.F.

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

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