| William Frothingham Bradbury - Geometry - 1872 - 238 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.... | |
| Edward Olney - Geometry - 1872 - 566 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... | |
| 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... | |
| 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.... | |
| David Munn - 1873
...their bases ; triangles having equal bases are toeach other as their altitudes, and two triangles are **to each other as the products of their bases by their altitudes.** PROP. IV. — To find the area of a triangle, -when the three sides are given. In the triangle ABC,... | |
| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...parallelograms having equal altitudes are to each other as their bases ; and, in general, parallelograms are **to each other as the products of their bases by their altitudes.** THEOREM VI. 189. The area of any triangle is equal to the product of its base by half its altitude.... | |
| Adrien Marie Legendre - Geometry - 1874 - 512 pages
...proved. ,< -i \ «.' \ \K \L \ E "i A D A \ I M °\ : : AB : . i J t AO. PROPOSITION XHI. THEOREM. **Any two rectangular parallelopipedons are to each other as the products of their bases** and altitudes ; that is, as the products of their three dimensions. Let AZ and AG be any two rectangular... | |
| Benjamin Greenleaf - Geometry - 1874 - 206 pages
...parallelograms having equal altitudes are to each other as their bases; and, in general, parallelograms are **to each other as the products of their bases by their altitudes.** THEOREM VI. 189. The area of any triangle is equal to the product of its base by half its altitude.... | |
| 1875 - 164 pages
...cases. 2. To make a square which is to a given square in a given ratio. 3. Prove that two rectangles are **to each other as the products of their bases by their altitudes.** What follows if we suppose one of the rectangles to be the unit of surface ? 4. Prove that two similar... | |
| Elias Loomis - Geometry - 1877 - 458 pages
...bases ; pyramids having equivalent bases are to each other as their altitudes; and any two pyramids are **to each other as the products of their bases by their altitudes.** Cor. 3. Similar pyramids are to each other as the cubes of their homologous edges. • Scholium. The... | |
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