Elements of Geometry and Trigonometry |
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Page 190
... parallels , they are equal in volume . mon Let the parallelopipedons AG and AL have the com- lower base ABCD , and their ... parallelopipedon AL : hence , these parallelopipedons are equal in volume ( A. 3 ) ; which was to be proved ...
... parallels , they are equal in volume . mon Let the parallelopipedons AG and AL have the com- lower base ABCD , and their ... parallelopipedon AL : hence , these parallelopipedons are equal in volume ( A. 3 ) ; which was to be proved ...
Page 191
... 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 192
... parallelopipedon , having for its base the parallelogram ABCD . Through the edges AI and BK pass the planes AQ and ... parallelopipedon equal to the given parallelopipedon . It will be a rect- angular parallelopipedon , because all of ...
... parallelopipedon , having for its base the parallelogram ABCD . Through the edges AI and BK pass the planes AQ and ... parallelopipedon equal to the given parallelopipedon . It will be a rect- angular parallelopipedon , because all of ...
Page 193
... parallel to ABCD . divide the parallelopipedon AG into 15 parallelopipedons , which have equal bases ( P. II . C. ) and equal altitudes ; hence , they are equal ( P. X. , Cor . 3 ) . Now , AG contains 15 , and AL 8 of these equal ...
... parallel to ABCD . divide the parallelopipedon AG into 15 parallelopipedons , which have equal bases ( P. II . C. ) and equal altitudes ; hence , they are equal ( P. X. , Cor . 3 ) . Now , AG contains 15 , and AL 8 of these equal ...
Page 195
... parallelopipedon AQ . The parallelopipedons AG and AQ have a common base AH ; they are there- K H fore to each other as their altitudes ( P. XI . ) : hence , we have the proportion , M AB and AO N vol . AG : vol . AQ B P The ...
... parallelopipedon AQ . The parallelopipedons AG and AQ have a common base AH ; they are there- K H fore to each other as their altitudes ( P. XI . ) : hence , we have the proportion , M AB and AO N vol . AG : vol . AQ B P The ...
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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