Elements of Geometry and Trigonometry |
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Page 165
... frustum of a pyramid , having parallel bases A and B ; AB will be the mean pro- portional between those bases ; and the solidity of the frustum will be Hx ( A + B + √AB ) . In fine , let P and p represent the solidities of two similar ...
... frustum of a pyramid , having parallel bases A and B ; AB will be the mean pro- portional between those bases ; and the solidity of the frustum will be Hx ( A + B + √AB ) . In fine , let P and p represent the solidities of two similar ...
Page 166
... by a plane parallel to the base , the remaining solid CBHF is called a truncated cone , or the frustum of a cone . We may conceive it to be generated by the revolution .166 GEOMETRY . BOOK VIII The three round bodies,
... by a plane parallel to the base , the remaining solid CBHF is called a truncated cone , or the frustum of a cone . We may conceive it to be generated by the revolution .166 GEOMETRY . BOOK VIII The three round bodies,
Page 167
... frustum , the circles BDC , HFK , are its bases , and BH is its side . 4. Two cylinders , or two cones , are similar , when their axes are to each other as the diameters of their bases . 5. If in the circle ACD , which forms the base of ...
... frustum , the circles BDC , HFK , are its bases , and BH is its side . 4. Two cylinders , or two cones , are similar , when their axes are to each other as the diameters of their bases . 5. If in the circle ACD , which forms the base of ...
Page 171
... frustum of a cone is equal to its side multiplied by half the sum of the circumferences of its two bases . Let BIA - DE be a frustum of a cone BOOK VIII . 171.
... frustum of a cone is equal to its side multiplied by half the sum of the circumferences of its two bases . Let BIA - DE be a frustum of a cone BOOK VIII . 171.
Page 172
... frustum of the cone . The con- vex surface of the frustum of the L E C D K I A pyramid is equal to half the sum of the perimeters of its bases multiplied by the slant height fh ( Book VII . Prop . IV . Cor . ) . Let now the number of ...
... frustum of the cone . The con- vex surface of the frustum of the L E C D K I A pyramid is equal to half the sum of the perimeters of its bases multiplied by the slant height fh ( Book VII . Prop . IV . Cor . ) . Let now the number of ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex