BEING

The First Four Books

OF

EUCLID'S ELEMENTS OF GEOMETRY,

FROM

THE EDITION OF DR. ROBERT SIMSON;

WITH A PECULIAR TYPOGRAPHICAL ARRANGEMENT, BY WHICH IS
EXHIBITED, WITHOUT ABRIDGMENT OF THE TEXT, A
PERSPICUOUS OUTLINE OF EACH DEMONSTRATION,

TO FACILITATE TEACHING IN CLASSES

AND PRIVATE STUDY.

WITH EXERCISES.

BY

SAMUEL A. GOOD,

MEMBER OF THE COLLEGE OF PRECEPTORS, AND MASTER OF THE MATHEMATICAL
SCHOOL IN HER MAJESTY'S DOCKYARD, PEMBROKE.

BODI

LONDON: .

THIS

CHARLES HENRY LAW, 131, FLEET STREET.

MDCCCLIII.

183.c.7.

PREFACE.

In this edition, it is endeavoured, by a new, yet extremely simple, typographical arrangement, to render the text of Euclid more perspicuous than when printed in the ordinary manner, and to make it, as it were, its own interpreter, so as to obviate, as much as possible, the necessity of books of questions, notes, and explanations.

The leading feature of the work is, that the principal steps in every demonstration have the conclusions numbered, and printed in separate lines with a different type from the premises; thus presenting to the eye the substance of the whole in the form of a synopsis which, it is hoped, the teacher will find of no small advantage in the important business of examination.

This plan will, it is believed, give considerable aid to the student, in enabling him not merely to acquire a clear perception of the subject as he proceeds, but to fix in his memory, with comparatively little trouble, the order in which the lines, angles, &c., composing the diagrams are to be considered in the course of demonstration, thereby preventing the confused notion of the whole, by which learners are so commonly embarrassed at the commencement of their geometrical studies.

EUCLID'S

ELEMENTS OF GEOMETRY.

Book I.

DEFINITIONS.

I.

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

A line is length without breadth.

II.

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 has 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.

VIII.

"A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction."