 | 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 - 1812 - 620 pages
...triangles ADE, CDE, on the bases AE, EC, have also the same altitude ; and because triangles of tlic •same altitude are to each other as their bases, therefore the triangle ADE : BDK : : AD : DB, and triangle ADE : CDE : : AE : EC. But BDE is = CDE ; and equals must have to equals... | |
 | Charles Hutton - Mathematics - 1816 - 610 pages
...DE, BC (th. 25). But the two triangles ADE, BDE, flnthe bases AD, DB, have the same altitude; tude ; and the two triangles ADE, CDE, on the bases AE, EC,...bases, therefore the triangle ADE = BDE : '• AD : DB, jj g and triangle ADE : CDE : : *E : EC. Bui BDE is = CDE i and equals must have to equals the same... | |
 | Charles Hutton - Arithmetic - 1818 - 646 pages
...triangles AUE, BDE, on the bases AD, DB, have the same altitude ; tude ; and the two triangles ABE, CDE. on the bases AE, EC, have also the same altitude...triangles of the same altitude are to each other as their bates, therefore the triangle ADE : BDE : : AD : DB, and triangle ADE : CDE : : AE : EC. But BDE is... | |
 | 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... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...(th. 25). But the two triangles ADE, BDE, on the bases AD, DB, have the same altitude ; 328 fade ; and the two triangles ADE, CDE, on the bases AE, EC,...their bases, therefore the triangle ADE : BDE : : AD : on, and triangle ADE : CDE : : AE : EC. But BDE is =CDE ratio ; therefore AD and equals must have... | |
 | Charles Hutton - Mathematics - 1825 - 608 pages
...DB, have the same altitude ; tude ; and the two triangles ADE, CDE, on the banes AE. EC, have al*o the same altitude ; and because triangles of the same...each other as their bases, therefore the triangle ADE : BBE : : AD : DB, and triangle ADE : CDE : : AB : EC. B But BDE is — CDE ; and equals must have... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 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 as their bases, and two triangles of the same base are to each other as their altitudes. THEOREM. 48 Elements of Geometry.... | |
 | Adrien Marie Legendre - 1825 - 570 pages
...= 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 as their bases, and two triangles of the same base are to each other as their altitudes. THEOREM. 178. The area of... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...parallelogram = BC x AD (174); therefore the area of the triangle = \ BC x AD, or BC xi AD. 177. Corollary. 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. . / i THEOREM. 178. The area... | |
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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, and triangle ADE : CDE : : AE : EC. 
