Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 201
... parallelopipedons have a common lower base , and their upper bases between the same parallels , they are equal in volume ... parallelopipedon AL : hence , these parallelo- pipedons are equal in volume ( A. 3 ) ; which was to be proved ...
... parallelopipedons have a common lower base , and their upper bases between the same parallels , they are equal in volume ... parallelopipedon AL : hence , these parallelo- pipedons are equal in volume ( A. 3 ) ; which was to be proved ...
Page 202
... parallels , QG , NF ( P. VIII . ) . For a like reason , this third parallelopipedon will also be equal in volume to the parallelopipedon AL : hence , the two parallelopipedons AG , AL , are equal in volume ; which was to be proved . Cor ...
... parallels , QG , NF ( P. VIII . ) . For a like reason , this third parallelopipedon will also be equal in volume to the parallelopipedon AL : hence , the two parallelopipedons AG , AL , are equal in volume ; which was to be proved . Cor ...
Page 203
... parallelopipedon equal in volume to a right parallelopipedon whose base is any parallelo- gram . Let ABCD - M be a right parallelopipedon , having for its base the parallelogram ABCD . MQ LP K Through the edges Al and BK pass the planes ...
... parallelopipedon equal in volume to a right parallelopipedon whose base is any parallelo- gram . Let ABCD - M be a right parallelopipedon , having for its base the parallelogram ABCD . MQ LP K Through the edges Al and BK pass the planes ...
Page 204
... parallel to ABCD . These planes divide the parallelopipedon AG into 15 parallelopipedons , which have equal bases ( P. II . , C. ) and equal altitudes ; hence , they are equal ( P. X. , Cor .. Now , AG contains 15 , and AL 8 of these ...
... parallel to ABCD . These planes divide the parallelopipedon AG into 15 parallelopipedons , which have equal bases ( P. II . , C. ) and equal altitudes ; hence , they are equal ( P. X. , Cor .. Now , AG contains 15 , and AL 8 of these ...
Page 205
... parallelopipedon , whose base is ABCD , and altitude Am ; since the altitudes AE , Am , are to each other as two ... parallelopipedons are to each other as their altitudes ; which was to be proved . Sch . Any two rectangular ...
... parallelopipedon , whose base is ABCD , and altitude Am ; since the altitudes AE , Am , are to each other as two ... parallelopipedons are to each other as their altitudes ; which was to be proved . Sch . Any two rectangular ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence