(Edited by Sir Thomas L. Heath, 1908)

[Euclid, ed. Heath, 1908, on

To bisect a given rectilineal angle.

Let the angle BAC be the given rectilineal angle.

Thus it is required to bisect it.

Let a point D be taken
at random on AB;

let AE be cut off from
AC equal to
AD;
[I. 3]

let DE be joined, and on
DE let the equilateral triangle
DEF be constructed;

let AF be joined.

I say that the angle BAC has been bisected by the straight line AF.

For, since AD is equal to
AE,

and AF is common,

the two sides DA,
AF are equal to the
two sides EA,
AF
respectively.

And the base DF is equal to
the base EF;

therefore the angle DAF is equal
to the angle.
EAF
[I. 8]

Therefore the given rectilineal angle BAC has been bisected by the straight line AF. Q.E.F.

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

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