Page images
PDF
EPUB

Rivington's Mathematical Series

ELEMENTS OF GEOMETRY

RIVINGTONS

London Oxford 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,

[ocr errors]

CAMBRIDGE

[blocks in formation]

Cambridge:

PRINTED BY C. J. CLAY, M.A. AT THE UNIVERSITY PRESS.

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.

[merged small][merged small][ocr errors][merged small]

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.

« PreviousContinue »