| Benjamin Greenleaf - Geometry - 1862 - 520 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.** PROPOSITION VI. — THEOREM. 227. Tlie area of any triangle is equal to the product of its base by... | |
| Benjamin Greenleaf - Geometry - 1861 - 628 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... | |
| Adrien Marie Legendre - Geometry - 1863 - 464 pages
...be proved. V \L ^ \ F \Q f* \ \ * 0\ A D \ I ^ \ ] 3 C : : AB : . AO. 196 PROPOSITION XIII. THEOBEM. **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 - 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... | |
| C. Davies - 1867 - 342 pages
...any two rectangular parallelopipedons are to each other as the product of their three dimensionsSck **We are consequently authorized to assume, as the measure...a rectangular parallelopipedon, the product of its** three dimensionsIn order to comprehend the nature of this measurement, it Of Parallelopipedonasolid... | |
| Benjamin Greenleaf - 1868 - 338 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... | |
| Charles Davies - Geometry - 1870 - 319 pages
...two rectangular parallelopipedons are to each other as the product of their three dimensions. Sch. **We are consequently authorized to assume, as the measure...a rectangular parallelopipedon, the product of its** three dimensions. In order to comprehend the nature of this measurement, it is necessary to reflect,... | |
| 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... | |
| Charles Davies - Geometry - 1872 - 464 pages
...bases; which was to be proved. \ • w A i \L \ \ A 3 : : AB : E D I \ 3 1. AO. PROPOSITION THEOPvEM. **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... | |
| 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... | |
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