Post 4to., pp. 32, price 2s., TABLES, CONTENTS. Saxon Periods; Wars with Scotland in the reigns of Edward I., II., and III. ; Wars with France in the reigns of Edward III., Henry V., and VI.; Wars of the Roses; Civil Wars; Battles fought by the Marquess of Montrose in behalf of Charles I. ; Wars in the reign of William III.; War of the Succession in Spain ; the American War; War with France, Spain, and Holland (during the American War); War with France and her Allies (not including the Peninsular War); the Penin- sular War; Battles and Sieges in India ; Battles and Sieges not included in the preceding Tables ; Tables of Treaties and their Terms ; Genealogical Tables of the Anglo-Saxon, Anglo-Danish, English, Scottish, and French Kings; of the Dukes of Normandy; of the principal Members of the Beaufort, the Neville, and the Howard Families ; of the claimants for the French Crown in the time of Edward III., and for the Spanish Crown at the close of the Seventeenth Century; of the Descendants of Louis Philippe ; and of the principal Members of the Napoleon Family. In the Battles, the names of the Commanders on both sides, and the immediate results are given, and in LONDON: SIMPKIN, MARSHALL, & CO. THE ELEMENTS OF PLANE GEOMETRY; OR, THE FIRST SIX BOOKS Or EUCLID. . ROM 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. EUCLID'S ELEMENTS OF PLANE GEOMETRY. BOOK 1. 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 tho angle, that is, at the point in which А 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 tbus 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 A B, D B, is named the angle A BD, 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. A |