. PROP. LXII. THEOR. 35. 3 Eu. If two straight lines within a circle cut one

another, the rectangle contained by the segments of one of them, is equal to the rectangle contained by the segments of the other.

Let the two str. lines AC, BD cut each other in E within O ABCD: then AE. EC=

PROP. LXIII. THEOR. 36. 3 Eu.

If from any point without a circle two straight

lines be drawn, one of which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

PROP. LXIV. PROB. 5. 4 Eu. To describe a circle about a given triangle.

Let the given a be ABC; it is required to describe a O about the A ABC, so that the O may pass through the angular points A, B, C of the A.