 The volume of a triangular prism is equal to the product of its base and altitude. Let AE be the altitude of the triangular prism ABC-C'. To prove that volume ABC-C' = ABC x AE. Construct the parallelopiped ABCD-D' having its edges equal and parallel...  The Elements of Geometry - Page 277by Webster Wells - 1886 - 371 pagesFull view - About this book
 | William Guy Peck - Conic sections - 1876 - 376 pages
...the prism into triangular prisms; these will all have the same altitude as the given prism. Now, each triangular prism is equal to the product of its base and altitude ; hence, their sum is equal to the sum of their bases multiplied by their common altitude, that is,... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...diagonal, surface, and volume. 2. The surface of a cube is s ; find its edge, diagonal, and volume. 3. The volume of a triangular prism is equal to the product of the area of a lateral face by one-half the perpendicular from the opposite edge to that face. II. PYRAMIDS.... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...and the volume of this parallelopiped is equal to the product of its base by its altitude ; therefore the volume of a triangular prism is equal to the product of its base by its altitude. 3d. By passing planes through its lateral edges, any prism can be divided into... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...prism is half ft parallelopiped having a double base and the same altitude (2, , f Cor. 1) : hence the volume of a triangular prism is equal to the product of its base by its altitude. (6 Cor.) Any prism, ABCDE-A', may be divided into triangular prisms by passing... | |
 | Charles Scott Venable - 1881 - 380 pages
...triangular prisms are equal when they have their lateral faces equal and arranged in the same manner. 3. The volume of a triangular prism is equal to the product of one of its lateral faces by half the distance from this face to the opposite edge. 4. Every plane which... | |
 | Euclides - 1885 - 340 pages
...AJK-EMN. Hence ABC-EFG = ACD-EGH. Therefore the diagonal plane bisecU the parallelepiped. Cor. 1 . — The volume of a triangular prism is equal to the product of its base and altitude ; because it is half of a parallelepiped, which has a double base and equal altitude. 288 PEOP. IV.—... | |
 | Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...AJK-EMN. Hence ABC-EFG = ACD-EGH. Therefore the diagonal plane biiects the paralklopiped. Cor. 1. — The volume of a triangular prism is equal to the product of its base and altitude ; because it is half of a parallelopiped, which has a double base and equal altitude. 2S8 PEOP. IV.—... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...equal to the product of its base and altitude (PX, C. 1). PROPOSITION XIV. THEOREM. The volume of any prism is equal to the product of its base and altitude. Let ABCDE-K be any prism : then is its volume equal to the product of its base and altitude. For, through... | |
 | William Chauvenet - Geometry - 1887 - 346 pages
...any parallelopiped is equal to the product of the area of its base by its altitude. PROPOSITION XII. The volume of a triangular prism is equal to the product of its base by its altitude. Corollary. The volume of any prism is equal to the product of its base by its... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...Tetraedron. Hexaedron. Dodecaedron. Octaedroa. A V Icosaedron. EXERCISES ON BOOK VII. THEOREMS. 1. THE volume of a triangular prism is equal to the product of the area of a lateral face by one-half the perpendicular distance of that face from the opposite edge.... | |
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