WITH EXPLANATORY NOTES, AND A SERIES OF QUESTIONS ON EACH BOOK. BY ROBERT POTTS, M.A., TRINITY COLLEGE; WITH EXAMINATION PAPERS ADDED BY THOMAS KIRKLAND, M.A., CANADIAN COPYRIGHT EDITION. TORONTO: W. J. GAGE & CO., 11 WELLINGTON STREET WEST. ELEMENTS OF GEOMETRY. A FOINT is that which has no parts, or which has 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 between its extreme points V. A superficies is that which has only length and eadth. 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. VIII. A plane angle is the inclination of two lin plane, which meet together, but are not in the sa IX. A plane rectilineal angle is the inclination of one another, which meet together, but are not i ...ies. each other in a direction. o straight lines to same straight line. 1208 25 N.B. 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: but when several angles are at one point B, either of them is expressed by three letters, of which the letter that is at the vertex of the 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 these straight lines, and the other upon the other line. Thus the angle which is contained by the straight lines AB, CB, is named the angle ABC, or CBA; that which is contained by AB, DB, is named the angle ABD), or DBA; and that which is contained by DB, CB, is called the angle DBC, or CBD. X. When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of these angles is called a right angle; and the straight line which stands on the other is called ■ perpendicular to it. XI. An obtuse angle is that which is greater than a right angle. XII. An acute angle is that which is less than a right angle. XIII. A term or woundary 18 the extremity of any thing. XIV. A figure is that which is enclosed by one or more boundaries XV. A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another. XVI. And this point is called the center of the circle. XVII. A diameter of a circle is a straight line drawn through the center, and terminated both ways by the circumference. XVIII. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter. XIX. The center of a semicircle is the same with that of the circle. XX. Rectilineal figures are those which are contained by straight lines. XXI. Trilateral figures, or triangles, by three straight lines. XXII. Quadrilateral, by four straight lines. XXIII. Multilateral figures, or polygons, by more than four straight lines. |