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THE

ELEMENTS OF EUCLID

CONTAINING THE FIRST SIX BOOKS

CHIEFLY FROM THE TEXT OF DR SIMSON.

WITH A SELECTION OF

GEOMETRICAL PROBLEMS FOR SOLUTION.

TO WHICH IS ADDED

THE PARTS OF THE ELEVENTH AND TWELFTH BOOKS WHICH ARE

USUALLY READ AT THE UNIVERSITIES.

BY

JAMES MARTIN,

HEAD MASTER OF THE ENDOWED SCHOOL, WEDGWOOD INSTITUTE, BURSLEM.

LONDON: GEORGE PHILIP & SON, 32 FLEET STREET; LIVERPOOL: CAXTON BUILDINGS, SOUTH JOHN STREET, AND 49 & 51 SOUTH CASTLE STREET.

1874.

183. q. 73

PREFACE.

The present edition of Euclid's Elements of Geometry, like most of its contemporaries, is based on the invaluable work of Dr Simson. Its leading characteristics are the following: (a) In all the propositions, a clear line of demar

cation is drawn between the construction and

the proof or demonstration. (6) By a typographical expedient, the several steps

in the reasoning are clearly shown. (c) In describing the figures, those parts which are

given in the enunciation are represented by dark lines, and those which are added in the

course of the demonstration by dotted lines. (d) In all cases, the figure has been repeated,

wherever it was found necessary. With the foregoing aids, the present Euclid cannot fail to be of very great service to every student of Geometry.

JAMES MARTIN.

WEDGWOOD INSTITUTE,

BURSLEM.

CONTENTS.

PAGE

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PREFACE . . .
FIRST BOOK OF THE ELEMENTS
SECOND BOOK
THIRD BOOK
FOURTH Book
FIFTH Book
Sixth BOOK
GEOMETRICAL EXERCISES ON Book I.
ALGEBRAICAL DEMONSTRATIONS OF Book II.
GEOMETRICAL EXERCISES ON Book II.

Book III. .
Book IV.

Book VI. .
ELEVENTH BOOK OF THE ELEMENTS .
TWELFTH BOOK " . .

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EUCLID'S ELEMENTS OF GEOMETRY.

BOOK I.

DEFINITIONS.

1.

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

2. A line is length without breadth.

The extremities of a line are points,

4.

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

A superficies is that which has only length and breadth.

6. The extremities of superficies are lines.

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

A plane angle is the inclination of two lines to each other in a plane, which meet together, but are not in the same straight line.

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