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A B C D AABC ABCD altitude arc A B axis base and altitude centre circumference circumscribed coincide conical surface COROLLARY cylinder denote diagonals diameter dihedral angle distance divided Draw equal arcs equal respectively equally distant equilateral equivalent frustum given point greater Hence homologous sides hypotenuse intersection isosceles lateral edges lateral faces Let A B line A B measured by arc middle point number of sides opposite parallel parallelogram parallelopiped perimeter perpendicular plane MN polyhedrons prism prove pyramid Q. E. D. PROPOSITION radii radius equal ratio rectangles regular inscribed 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 50 - ... 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 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 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.
Page 337 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 175 - Any two rectangles are to each other as the products of their bases by their altitudes.
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 188 - 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.