| John Dougall - 1810 - 554 pages
...altitude of the triangle. Corollary. Triangles on the same base are to each other as their altitudes ; and **triangles of the same altitude are to each other as their bases.** PROP. XVI. fig. SO. The area or surface of a trapezoid, that is, of an irregular quadrilateral, of... | |
| Charles Hutton - Mathematics - 1816 - 610 pages
...tude ; and the two triangles ADE, CDE, on the bases AE, EC, have also the same altitude ; and because **triangles of the same altitude are to each other as their bases,** therefore the triangle ADE = BDE : '• AD : DB, jj g and triangle ADE : CDE : : *E : EC. Bui BDE is... | |
| Adrien Marie Legendre - Geometry - 1819 - 574 pages
...parallelogram = BC x AD (174) ; therefore the area of the triangle = | BC X AD, or BCx^AD. 177. Corollary. **Two. triangles of the same altitude are to each other as their** hases, and two triangles of the same base are to each other as their altitudes. THEOREM. X 178. The... | |
| Dugald Stewart - Psychology - 1821 - 706 pages
...circumference on the same base, we ascertain a relation between two quantities. When we demonstrate, that **triangles of the same altitude are to each other as their bases,** we ascertain a connexion between two relations. It is obvious, how much the mathematical sciences mu... | |
| Adrien Marie Legendre - Geometry - 1822 - 394 pages
...finally, the solidity of a cylinder is equal to the product of its base by its altitude. Cor. 1. Cylinders **of the same altitude are to each other as their bases ; and** cylinders of the same base are to each other as their altitudes. Cor. 9,. Similar cylinders are to... | |
| Charles Hutton - Mathematics - 1822 - 616 pages
...fade ; and the two triangles ADE, CDE, on the bases AE, EC, have also the same altitude , and because **triangles of the same altitude are to each other as their bases,** therefore the triangle ADE : BDE : : AD : on, and triangle ADE : CDE : : AE : EC. But BDE is =CDE ratio... | |
| Adrien Marie Legendre - 1825 - 570 pages
...parallelogram = BCx AD (174); therefore the area of the triangle = £ BC x AD, or BC x £ AD. 177. Corollary. **Two triangles of the same altitude are to each other...the same base are to each other as their altitudes.** THEOREM. 178. The area of a trapezoid ABCD (fig. 105) is equal to tfie Fig. 105. product of its altitude... | |
| Adrien Marie Legendre - Geometry - 1825 - 276 pages
...Every pyramid is a third of a prism of the same base and same altitude. 418. Corollary n. Two pyramids **of the same altitude are to each other as their bases, and two** pyramids of the same base are to each other as their altitudes. 419. Scholium. The solidity of any... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...solidity of a cylinder is equal to the product of its base by its altitude. 517. Corollary i. Cylinders **of the same altitude are to each other as their bases, and** cylinders of the same base are to each other as their altitudes. 518. Corollary n. Similar cylinders... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...solidity of a cylinder is equal to the product of its base by its altitude. 517. Corollary i. Cylinders **of the same altitude are to each other as their bases, and** cylinders of the same base are to each other as their altitudes. 518. Corollary n. Similar cylinders... | |
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