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A B C altitude base bisect called centre chord circle circumference common cone consequently construct contained described diagonal diameter difference distance divided draw drawn edge equal equal Prop equivalent extremities faces feet figure formed four frustum given gles greater height hence homologous hypothenuse inches included inscribed interior angles intersect join length less Let ABCD magnitudes manner mean meet middle multiplied opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportion PROPOSITION pyramid radii radius ratio rectangle regular remain right angles Scholium segment shown side A B sides similar solidity sphere spherical square straight line tangent THEOREM third triangle triangle ABC twice vertex VIII whole XVIII XXII
Page 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.
Page 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.
Page 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 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.
Page 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...
Page 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.
Page 254 - RULE. — Multiply the base by the altitude, and the product will be the area.
Page 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.