 | John Dougall - 1810 - 734 Seiten
...the same altitude, AE and CF. hoth equal 10 BG, the 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. 30. The area or surface of a... | |
 | John Dougall - 1810 - 554 Seiten
...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 - 1816 - 610 Seiten
...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 - 1819 - 574 Seiten
...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 - 1821 - 706 Seiten
...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... | |
 | Charles Hutton - 1822 - 616 Seiten
...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 Seiten
...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 - 1825 - 276 Seiten
...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 - 1825 - 294 Seiten
...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 - 1825 - 280 Seiten
...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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Two triangles of the same altitude are to each other as their bases, and two triangles of the same base are to each other as their altitudes. And triangles generally, are to each other, as the products of their bases and altitudes. 
