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, 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 O A. 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. 8. E. II. |