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 137 161 PREFACE . . . Book III. . Book VI. . 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. |