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 two equal right prisms Bad - h , Bcd - h ; for , the bases Bad , Bcd , of these ...
... 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 two equal right prisms Bad - h , Bcd - h ; for , the bases Bad , Bcd , of these ...
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 altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex