PROPOSITION 1.
To find the centre of a given circle. Let ABC be the given circle; thus it is required to find the centre of the circle ABC. Let a straight line AB be drawnthrough it at random, and let it be bisected at the point D; from D let DC be drawn at right angles to AB and let it be drawn through to E; let CE be bisected at F;
I say that F is the centre of the circle ABC. For suppose it is not, but, if possible, let G be the centre, and let GA, GD, GB be joined.
Then, since AD is equal to DB, and DG is common,
radii;
Similarly we can prove that neither is any other point except F.
PORISM.
From this it is manifest that, if in a circle a straight line cut a straight line into two equal parts and atright angles, the centre of the circle is on the cutting straight line. Q. E. F. 1 2