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Rivington's Mathematical Series

ELEMENTS OF GEOMETRY

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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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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.

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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 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.

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