From a given straight line to cut off a prescribed part.
Let AB be the given straight line;
thus it is required to cut off from AB a prescribed part. Let the third part
be that prescribed.
Let a straight line AC be drawn through from A containing with AB any angle;
let a point D be taken at random on AC, and let DE, EC be made equal to AD.
Let BC be joined, and through D let DF be drawn parallel to it.
Then, since FD has been drawn parallel to BC, one of the sides of the triangle
ABC, therefore, proportionally, as CD is to DA, so is BF to FA.
But CD is double of DA; therefore BF is also double of FA; therefore BA is
triple of AF.
Therefore from the given straight line AB the prescribed third part AF has
been cut off.
Therefore etc.
Q.E.D