Elements of Geometry and Trigonometry |
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Page 179
... Prisms are named from the number of sides of their bases ; a triangular prism is one whose bases are triangles ; a pentangular prism is one whose bases are pentagons , & c . 7. A PARALLELO PIPEDON is a prism whose bases are ...
... Prisms are named from the number of sides of their bases ; a triangular prism is one whose bases are triangles ; a pentangular prism is one whose bases are pentagons , & c . 7. A PARALLELO PIPEDON is a prism whose bases are ...
Page 188
... triangular prisms . Let ABCD - H be a parallelopipedon , and let a plane be passed through the edges BF and DH then will the prisms ABD - H and BCD - H be equal in volume . For , through the vertices F and B let planes be passed ...
... triangular prisms . Let ABCD - H be a parallelopipedon , and let a plane be passed through the edges BF and DH then will the prisms ABD - H and BCD - H be equal in volume . For , through the vertices F and B let planes be passed ...
Page 189
... prism ( D. 2 , 4 ) , polyedrons Bad - h and Bcd - h . hence , the poly- as are also the ... prisms are equal in volume . In like manner , it may be shown that the ... triangular prism ABD - H , is equal to half of the parallelopipedon AG ...
... prism ( D. 2 , 4 ) , polyedrons Bad - h and Bcd - h . hence , the poly- as are also the ... prisms are equal in volume . In like manner , it may be shown that the ... triangular prism ABD - H , is equal to half of the parallelopipedon AG ...
Page 190
... prisms AEI - M and the triangular BFK - L , we have the line AE equal and parallel to BF , and EI equal to FK ... prisms are equal ( P. V. ) = If from the polyedron ABKE - H , we take away the prism BFK - L , there will remain the ...
... prisms AEI - M and the triangular BFK - L , we have the line AE equal and parallel to BF , and EI equal to FK ... prisms are equal ( P. V. ) = If from the polyedron ABKE - H , we take away the prism BFK - L , there will remain the ...
Page 197
... triangular prisms . These prisms will all have a common altitude equal to that of the given prism . K Now , the volume of any one of the BOOK 197 VII .
... triangular prisms . These prisms will all have a common altitude equal to that of the given prism . K Now , the volume of any one of the BOOK 197 VII .
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Common terms and phrases
ABCD ACĀ² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence