PART II CONTAINING THE THIRD AND FOURTH BOOKS OF EUCLID WITH EXERCISES AND NOTES BY J. HAMBLIN SMITH, M. A GONVILLE AND CAIUS COLLEGE, AND LATE LECTURER AT ST PBTER'S COLLEGE, CAMBRIDGE BOOK III. POSTULATE. A POINT is within, or without, a circle, according as its distance from the centre is less, or greater than, the radius of the circle. DEFINITIONS. I. A straight line, as PQ, drawn so as to cut a circle ABCD, is called a SECANT. That such a line can only meet the circumference in two points may be shewn thus : Some point within the circle is the centre; let this be 0. Join OA. Then (Ex. 1, 1. 16) we can draw one, and only one, straight line from 0, to meet the straight line PQ, such that it shall be equal to 0 A. Let this line be OC. Then A and C are the only points in PQ, which are on the circumference of the circle. 9 S. E. II. |