Post 4to., pp. 32, price 2s., TABLES, BY JOHN CHARLES CURTIS, B.A. CONTENTS. In the Battles, the names of the Commanders on LONDON: SIMPKIN, MARSHALL, & CO. THE ELEMENTS OF PLANE GEOMETRY; OR, THE FIRST SIX BOOKS ОР EUCLID. FROM THE TEXT OF ROBERT SIMSON, M.D., Emeritus Professor of Mathematics in the University of Glasgow. EDITED BY WILLIAM DAVIS, B. A. FIRST THOUSAND. LONDON: LONGMAN, GREEN, LONGMAN, ROBERTS, AND GREEN. EDINBURGH ; OLIVER AND BOYD. DUBLIN: J, ROBERTSON AND CO. 1863. 1831. f. 9 EUCLID'S ELEMENTS OF PLANE GEOMETRY. BOOK I. DEFINITIONS. I. II. III. The extremities of a line are points. IV. V. VI. 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. N.B.-When several angles are at one point B, any one of them is expressed by three letters, of which the letter that is at the vertex of thë angle, that is, at the point in which the straight lines that contain the angle meet one another, is put between the other two letters, and one of these two is somewhere upon one of those straight lines, and the other upon the other straight line: B В thus the angle which is contained by the straight lines, A B, CB, is named the angle A B C, or CBA; that which is contained by AB, D'B, is named the angle A B D, or D BA; and that D which is contained by D B, CB, is called the angle D B C, or CBD; but, if there be only one angle at a point, it may be expressed by a letter placed at that point; as the angle at E. X. XI. XII. XIII. XIV. XV. XVI. XVII. A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference. XVIII. A semicircle is the figure contained by a diameter and the part of tho circumference cut off by the diameter. XIX. A segment of a circle is the figure contained by a straight line, and the part of the circumference it cuts off. XX. XXI. XXII. XXIII. Multilateral figures, or polygons, by more than four straight lines. XXIV. Of three-sided figures, an equilateral triangle is that which has three equal sides. |