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A B C ABCD altitude base bisect called centre chord circle circumference circumscribed common cone consequently construct contained convex surface cylinder diagonal diameter difference distance divided draw drawn edge equal equal Prop equivalent EXAMPLES extremities faces feet figure formed four frustum given gles greater half hence homologous hypothenuse inches included inscribed intersecting Join length less line A B manner measured meet multiplied opposite parallel parallelogram parallelopipedon pass perimeter perpendicular plane polygon prism PROBLEM Prop PROPOSITION pyramid radii radius ratio rectangle regular remain right angles Scholium segment shown sides similar solidity sphere spherical square straight line tangent THEOREM third triangle triangle ABC twice vertex VIII whole XVIII XXII
Side 59 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Side 52 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Side 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Side 168 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Side 159 - The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let C denote the circumference of one of ^ the circles, R its radius OA, A its area; and let C...
Side 38 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 254 - RULE. — Multiply the base by the altitude, and the product will be the area.
Side 35 - If a side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles ; and the three interior angles of every triangle are together equal to two right angles.