 | George Washington Hull - Geometry - 1807 - 408 pages
...are to each other as the products of their other two dimensions. PROPOSITION X. THEOREM. 457. Any two rectangular parallelepipeds are to each, other as the products of their three dimensions. Given — P and Q two rectangular parallelepipeds ; the dimensions of P are a, b, c, and those of Q... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...dimensions. / / Q e PI / e / P e Ill /, • in n i a 4 PRISMS. PROPOSITION IX. THEOREM. 537. Any two rectangular parallelepipeds are to each other as the products of their three dimensions. \ Let a, b, c, and a,' b', d, be the three dimensions respectively of the two rectangular parallelopipeds... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...rectangular parallelepipeds having equal altitudes are to each other as their bases. PROPOSITION IX. Any two rectangular parallelepipeds are to each other as the products of their three dimensions. PROPOSITION X. The volume of a rectangular parallelepiped is equal to tne product of its three dimensions,... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...of a rectangular parallelopiped whose edges are 1, 4, and 8. Proposition 1O. Theorem. 605. Any two rectangular parallelepipeds are to each other as the products of their three dimensions. Hyp. Let P and Q be two rectangular parallelopipeds whose dimensions are a, b, c, and a', V, c', respectively.... | |
 | William Chauvenet - Geometry - 1891 - 344 pages
...to each other as the products of the other two dimensions. PROPOSITION IX.— THEOREM. 28. Any two rectangular parallelepipeds are to each other as the products of their three dimensions. Q Let a, b, and c be the three dimensions of the rectangular parallelepiped P; m, n, and p those of... | |
 | George Albert Wentworth - Geometry - 1892 - 468 pages
...dimensions). The product of these two equalities is P ^ aXb P a'xb' QED PROPOSITION IX. THEOREM. 574. Two rectangular parallelepipeds are to each other as the products of their three dimensions. Let a, b, c, and a', b', c?, be the three dimensions respectively of the two rectangular parallelepipeds... | |
 | Webster Wells - 1894 - 172 pages
...in common, are to each other as the products of their other two PROPOSITION X. THEOREM. 499. Any two rectangular parallelepipeds are to each other as the products of their three dimensions. Let P and Q be two rectangular parallelopipeds, having the dimensions a, b, c, and a', b', d ', respectively.... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...parallelepipeds having equal altitudes are to each other as their bases. PROPOSITION X. THEOREM 666. A ny two rectangular parallelepipeds are to each other as the products of their three dimensions. GIVEN — the rectangular parallelepipeds P and P', whose dimensions are a, b, c and a', b', c' respectively.... | |
 | Harvard University - Geometry - 1899 - 39 pages
...parallelepiped divides it into two equivalent triangular prisms. THEOREM VI. 20 THEOREM VII. The volumes of two rectangular parallelepipeds are to each other as the products of their three dimensions. THEOREM VIII. The volume of a rectangular parallelepiped is equal to the product of its three dimensions.... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...corresponding members of these two equalities give PP< a X b a'Xb'' QED PROPOSITION IX. THEOREM. 621. Two rectangular parallelepipeds are to each other as the products of their three dimensions. Let a, b, c, and a', b', c', be the three dimensions, respectively, of the two rectangular parallelopipeds... | |
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Two rectangular parallelepipeds are to each other as the products of their three dimensions. 
