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EUCLID'S ELEMENTS

OF

GEOMETRY

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 T. TATE, F. R. A.S.,

AUTHOR OP

“ THE PRINCIPLES OF THE DIFFERENTIAL CALCULUS," OUTLINES OP

EXPERIMENTAL CHEMISTRY," " THE FIRST PRINCIPLES OF

A RITHMETIC, EXERCISES ON MECHANICS," ETC.

66

LONDON:
LONGMAN, BROWN, GREEN, AND LONGMANS.

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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. III. The extremities of a line are points. IV. A straight line is that which lies evenly be

tween 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. 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.” IX. A plane rectilineal angle is the inclination of

two straight lines to one another, which meet together, but are not in the same straight line.

B

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