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ABCDE altitude angle approaches axis base bisector bisects called centre chord circle circular circumference circumscribed coincide common cone construct corresponding curve cylinder denote describe diagonals diameter difference dihedral angles distance divided Draw drawn edges ellipse equal equidistant equilateral equivalent faces fall feet figure Find formed frustum given line given point greater half height Hence homologous inches included increased inscribed intersection isosceles joining lateral legs length less limit locus measured meet middle point opposite parallel parallelogram pass perimeter perpendicular plane polygon prism PROBLEM Proof proportional PROPOSITION prove pyramid quantities radii radius ratio rectangle regular polygon respectively right angle segments sides similar sphere spherical square straight line surface tangent THEOREM third touches triangle vertex vertices volume
Page 44 - If two triangles have two sides of the one equal, respectively, to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 52 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Page 43 - If two angles of a triangle are unequal, the sides opposite are unequal, and the greater side is opposite the greater angle.
Page 193 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.
Page 362 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 171 - In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the altitude upon the third side.
Page 73 - The sum of the perpendiculars dropped from any point within an equilateral triangle to the three sides is constant, and equal to the altitude.
Page 385 - Hence the two last are right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is at right angles to the base, and bisects the vertical angle.