 Two rectangular parallelopipeds are to each other as the products of their bases and their altitudes. Given M and N, two rectangular parallelopipeds, B and B' their bases, and a and a' their altitudes respectively.  Plane and Solid Geometry - Page 364by Arthur Schultze, Frank Louis Sevenoak - 1925 - 480 pagesFull view - About this book
 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...AE x AD, AO x AM, which will give solid AG : solid AZ : : AE x AD x AE : AO X AM X AX. Therefore any two rectangular parallelopipeds are to each other as the products of their bases by their altitudes, or as the products of their three dimensions. 405. Scholium. Hence we may take... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...substitute AB x AD, AO x AM, which will give solid AG : solid AZ::ABx AD x AE : AO x AMx AX. Therefore any two rectangular parallelopipeds are to each other as the products of their bases by their altitudes, or as the products of their three dimensions. 405. Scholium. Hence we may take... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...rectangular parallelopipeds of the same altitude are to each other as their bases. THEOREM. 404. Any two rectangular parallelopipeds are to each other as the products of their bases by their altitudes, or as the products of their three dimensions. Fig. 213. Demonstration. Having placed... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...rectangular parallelopipeds of the same altitude are to each other as their bases. THEOREM. 404. Any two rectangular parallelopipeds are to each other as the products of their bases by their altitudes, or as the products of their three dimensions. Demonstration. Having placed the... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...common, are to each other in the products of the other two dimensions. PROPOSITION X.— THEOREM. 32. Any two rectangular parallelopipeds are to each other as the products of their three dimensions. Let a, b and c be the three dimensions of the rectangular parallelopiped P; m, n... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...to each other in the products of the other two dimensions. PROPOSITION X.—THEOREM. A /) Q 32. Any two rectangular parallelopipeds are to each other as the products of their three dimensions. Let a, b and c be the three dimensions of the rectangular parallelopiped P; m, n... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...their altitudes, and those of the same altitudes are to each other as their bases. And, in general, parallelopipeds are to each other as the products of their bases and altitudes. PROPOSITION XL OF PRISMS AND CYLINDERS. DEM. — 1st. Let E.ABD be a triangular prism. Complete... | |
 | David Munn - 1873 - 160 pages
...Two rectangular parallelopipeds having equal altitudes, are to each other as their bases So III. Any two rectangular parallelopipeds are to each other as the products of their dimensions 80 IV. Volume of rectangular parallelopiped Si EXERCISES (8) 83 V. Volume of a prism 84.... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...to each other as the products of the other two dimensions. PRISMS. PROPOSITION IX. THEOREM. 537. Any two rectangular parallelopipeds are to each other as the products of their three dimensions. V Let а, b,с, and a,' /'', c', be the three dimensions respectively of the two... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...the area of the base EB, and BIXBN of the base ED; therefore GEOMETRY OF SPACE. THEOREM IX. •{ I . Rectangular parallelopipeds are to each other as the products of their bases by their altitudes. Let AB, CD, be rectangular parallelopipeds, then Produce the edge EA to G making... | |
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