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A B C adjacent altitude axis base bisect called centre chord circle circumference coincide common cone construct convex surface cylinder DEFINITIONS denote describe diagonals diameter difference direction distance divided draw drawn equal equally distant equiangular equilateral EXERCISES extremities faces fall feet figure four frustum given given line greater half height Hence homologous hypothesis inscribed intersect isosceles joining lateral length less mean measure meet multiplied oblique parallel parallelogram pass perimeter perpendicular plane polygon portion position prism Prob PROBLEM proportional Prove pyramid quantities QUERIES radii radius ratio rectangle regular polygon right angles segments sides similar sphere spherical triangle square straight line Suppose surface tangent THEOREM third triangle unit vertex vertices VIII volume
Side 18 - if two triangles have two sides of the one equal to two sides of the...
Side 13 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Side 107 - If two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other, each to each, they are equal in all their parts.
Side 24 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 38 - If two sides of a quadrilateral are equal and parallel, the figure is a parallelogram.
Side 42 - If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let bc=ad.
Side 232 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Side 14 - In an isosceles triangle the angles opposite the equal sides are equal.
Side x - AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal.