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RIVINGTONS

London Orford Cambridge

Waterloo Place High Street Trinity Street

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,

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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.

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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 0 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. S. E. II.

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