Elements of Geometry and Trigonometry |
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Page 159
... pyramid S - abc will be less than this pyramid . Hence the difference , between the sum of all the exterior prisms and the sum of all the interior ones , must be greater than the difference between the two pyramids them- selves . Now ...
... pyramid S - abc will be less than this pyramid . Hence the difference , between the sum of all the exterior prisms and the sum of all the interior ones , must be greater than the difference between the two pyramids them- selves . Now ...
Page 160
... pyramid , ABC - DEF a triangular prism of the same base and the same altitude ; the pyramid will be equal to a third of the prism . Cut off the pyramid F - ABC from the prism , by the plane FAC ; there will remain the solid F - ACDE ...
... pyramid , ABC - DEF a triangular prism of the same base and the same altitude ; the pyramid will be equal to a third of the prism . Cut off the pyramid F - ABC from the prism , by the plane FAC ; there will remain the solid F - ACDE ...
Page 161
... pyramid is mea- sured by a third part of the product of its base by its altitude . E D C B Cor . 1. Every pyramid is the third part of the prism which has the same base and the same altitude . as the same base a ह Cor . 2. Two pyramids ...
... pyramid is mea- sured by a third part of the product of its base by its altitude . E D C B Cor . 1. Every pyramid is the third part of the prism which has the same base and the same altitude . as the same base a ह Cor . 2. Two pyramids ...
Page 162
... pyramid a section fgh situated at the same distance above the common plane of the bases ; and therefore the section ... pyramid , it will be true of every other . Let FGH - hfg be the frustum of a tri- angular pyramid , having parallel ...
... pyramid a section fgh situated at the same distance above the common plane of the bases ; and therefore the section ... pyramid , it will be true of every other . Let FGH - hfg be the frustum of a tri- angular pyramid , having parallel ...
Page 163
... pyramid K - FƒH may be regarded as having its vertex in f , and thus its altitude will be the same as that of the ... pyramid is equivalent to three pyramids whose common altitude is that of the frustum and whose bases are the lower base ...
... pyramid K - FƒH may be regarded as having its vertex in f , and thus its altitude will be the same as that of the ... pyramid is equivalent to three pyramids whose common altitude is that of the frustum and whose bases are the lower base ...
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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