 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...the same base, or equivalent bases, are to each other as their altitudes. 491. Cor. 4. Pyramids are to each other as the products of their bases by their altitudes. 492. Scholium. The solidity of any polyedron may be found by dividing it into pyramids, by passing... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...the same base, or equivalent bases, are to each other as their altitudes. 491. Cor. 4. Pyramids are to each other as the products of their bases by their altitudes. 492. Scholium. The solidity of 'any polyedron may be found by dividing it into pyramids, by passing... | |
 | Benjamin Greenleaf - 1863 - 338 pages
...57. 5. If a -f- x : a — x : : 11 : 7, what is the ratio of a to x '! Ans. 9 : 2. 6. Triangles are to each other as the products of their bases by their altitudes. The bases of two triangles are to each other as 17 to 18, and their altitudes as 21 to 23 ; required... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...the same base, or equivalent bases, are to each other as their altitudes. 491. Cor. 4. Pyramids are to each other as the products of their bases by their altitudes. 492. Scholium. The solidity of any polyedron may be found by dividing it into pyramids, by passing... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...bases ; triangles having equal bases are to each other as their altitudes ; and any two triangles are to each other as the products of their bases by their altitudes. PROPOSITION VI.— THEOREM. 17. The area of a trapezoid is equal to the produet of its altitude by... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...are to each other as their altitudes ; of equal altitudes, as their bases ; and in general they are to each other as the products of their bases by their altitudes. PROPOSITION VII. 325. TJieorem. — The area of a trapezoid is equal to the product of its altitude... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...are to each other as their altitudes ; of equal altitudes, as their bases ; and in general they are to each other as the products of their bases by their altitudes. PROPOSITION TII. 325. Theorem. — The area of a trapezoid is equal to the product of its altitude... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...cutting a pyramid are as the squares of their distances from the vertex. (39 ; II. 31.) 75. Pyramids are to each other as the products of their bases by their altitudes. (51.) 76. Pyramids with equivalent bases are as their altitudes ; with equal altitudes, as their bases.... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...parallelograms having equal bases are to each other as their altitudes; and any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V.—THEOREM. 13. The area of a triangle is equal to half the product of its bate and altitude.... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...dimensions. 71. In a cube the square of a diagonal is three times the square of an edge. 72. Prisms are to each other as the products of their bases by their altitudes. (25.) 74. Polygons formed by parallel planes cutting a pyramid are as the squares of their distances... | |
| |
Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions. 
