Elements of Geometry and Trigonometry |
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Page 147
... prism , are equal to the three planes which form the solid angle of another prism , each to each , and are like situated , the two prisms will be equal to each other . Let the base ABCDE be equal to the base abcde , the paral lelogram ...
... prism , are equal to the three planes which form the solid angle of another prism , each to each , and are like situated , the two prisms will be equal to each other . Let the base ABCDE be equal to the base abcde , the paral lelogram ...
Page 148
... prisms will coincide : therefore , the two prisms coinciding throughout are equal ( Ax . 13. ) . Cor . Two right prisms , which have equal bases and equal al- titudes , are equal . For , since the side AB is equal to ab , and the ...
... prisms will coincide : therefore , the two prisms coinciding throughout are equal ( Ax . 13. ) . Cor . Two right prisms , which have equal bases and equal al- titudes , are equal . For , since the side AB is equal to ab , and the ...
Page 149
... THEOREM . The two triangular prisms into which a parallelopipedon is di- vided by a plane passing through its opposite diagonal edges , are equivalent . N * Let the parallelopipedon ABCD - H be divided by the BOOK VII . 149.
... THEOREM . The two triangular prisms into which a parallelopipedon is di- vided by a plane passing through its opposite diagonal edges , are equivalent . N * Let the parallelopipedon ABCD - H be divided by the BOOK VII . 149.
Page 150
... prism ( Def . 6. ) ; and that prism is right , because the side BF is perpendicular to its base . But the right prism Badc - g , is divided by the plane BH into the two right prisms Bad - h , Bcd - h , since they have the same alti ...
... prism ( Def . 6. ) ; and that prism is right , because the side BF is perpendicular to its base . But the right prism Badc - g , is divided by the plane BH into the two right prisms Bad - h , Bcd - h , since they have the same alti ...
Page 151
Adrien Marie Legendre Charles Davies. gular prisms BAD - H , BDC - G , being equivalent to the equal right prisms , are equivalent to each other . Cor . Every triangular prism ABD - HEF is half of the paral- lelopipedon AG described with ...
Adrien Marie Legendre Charles Davies. gular prisms BAD - H , BDC - G , being equivalent to the equal right prisms , are equivalent to each other . Cor . Every triangular prism ABD - HEF is half of the paral- lelopipedon AG described with ...
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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