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A B C D AABC ABCD altitude arc A B axis base and altitude bisect centre chord circle circumference circumscribed coincide conical surface COROLLARY cylinder denote diagonals diameter dihedral angle distance divided draw equal respectively equally distant equiangular polygon equilateral equivalent frustum given point greater Hence homologous sides hypotenuse intersection isosceles lateral area lateral edges lateral faces Let A B line A B measured by arc middle point mutually equiangular number of sides parallelogram parallelopiped perimeter perpendicular plane MN prism prove pyramid Q. E. D. PROPOSITION radii radius equal ratio rectangles regular polygon right angles right triangle SCHOLIUM segment sides of equal similar polygons slant height sphere spherical angle spherical polygon spherical triangle square straight line drawn subtend surface symmetrical tangent tetrahedron THEOREM third side trihedral vertex vertices volume
Page 126 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Page 46 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 83 - A straight line perpendicular to a radius at its extremity is a tangent to the circle. Let MB be perpendicular to the radius OA at A.
Page 349 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 146 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 186 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 207 - To construct a parallelogram equivalent to a given square, and having the difference of its base and altitude equal to a given line.
Page 134 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.