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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.

BODY

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BIB

LONDON:

PRINTED FOR

LONGMAN, BROWN, GREEN, AND LONGMANS,

PATERNOSTER-ROW.

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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.

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

magnitude.

II.

A line is length without breadth.

III.
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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