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THE

FIRST THREE BOOKS

OF

EUCLID'S ELEMENTS

OF

GEOMETRY,

FROM THE TEXT OF

DR. ROBERT SIMSON,

TOGETHER WITH

VARIOUS USEFUL THEOREMS AND PROBLEMS,
AS GEOMETRICAL EXERCISES ON EACH BOOK.

BY THOMAS TATE,

MATHEMATICAL MASTER OF THE NATIONAL SOCIETY'S
TRAINING COLLEGE, BATTERSEA ;

AUTHOR OF "THE PRINCIPLES OF THE DIFFERENTIAL AND INTEGRAL
CALCULUS," ETC. ETC.

SOLETA
TH-LOW

LONDON:

PRINTED FOR

NUSITIO

BIB

LONGMAN, BROWN, GREEN, AND LONGMANS,

PATERNOSTER-ROW.

LONDON:

SPOTTISWOODES and SHAW, New-street-Square.

ADVERTISEMENT.

THIS edition of Euclid has been published in a cheap form, with the hope that it may tend to advance the mathematical education of this country, and with an especial reference to the instruction of Schoolmasters who may be desirous of obtaining a Government certificate.

EUCLID'S

ELEMENTS OF GEOMETRY.

BOOK I.

DEFINITIONS.

I.

A POINT is that which hath no parts, or which hath no magnitude.

II.

A line is length without breadth.

ni.

The extremities of a line are points.

IV.

A straight line is that which lies evenly between its extreme points.

V.

A superficies is that which hath only length and breadth.

VI.

The extremities of a superficies are lines.

VII.

A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies.

B

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