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: 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 |