 | John Radford Young - 1827 - 246 sider
...proportional lines are proportional, ABC : DEF : : BC2 : EF2 : : AB2 : DE1 : : AC2 : DF2. Cor. Since triangles of the same altitude are to each other as their bases, it follows (Prop. XIV.) that in a right angled triangle the squares of the sides are to each other... | |
 | Adrien Marie Legendre - 1828 - 346 sider
...parallelogram (174.) -£ is equal to BC x AD ; hence that of the triangle must be iBCx AD, or BCxJAD. 177. Cor. Two triangles of the same altitude are to each other...same base are to each other as their altitudes. And triangles generally, are to each other, as the products of their bases and altitudes. THEOREM. 178.... | |
 | Timothy Walker - 1829 - 138 sider
...half of B N. But GB is the altitude of AC B, and BP is the altitude of AM B. Accordingly, since „ triangles of the same base are to each other as their altitudes, and since GB is greater than BP, the triangle AC B is greater than AMB, which was to be demonstrated. 120.... | |
 | Dugald Stewart - 1829 - 482 sider
...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 must... | |
 | John Playfair - 1835 - 336 sider
...proportional to M, N ; draw the line AD, and the triangle ABC will be divided as required. For, since the triangles of the same altitude are to each other as their bases, we have ABD : ADC : : BD : DC : : B. D 0 M:N. SCHOLIUM. A triangle may evidently be divided into any... | |
 | Benjamin Peirce - 1837 - 216 sider
...its altitude. 252. Corollary. Triangles of the same base are to each other as their altitudes, and triangles of the same altitude are to each other as their bases. 253. Theorem. The area of a trapezoid is half the product of its altitude by the sum of its parallel... | |
 | John Playfair - 1837 - 332 sider
...proportional to M, N ; draw the line AD, and the triangle ABC will be divided as required. For, since the triangles of the same altitude are to each other as their bases, we have ABD : ADC : : BD : DC : : M: N. SCHOLIUM. PROP. Q. PROS. To divide a triangle intn two parts... | |
 | Adrien Marie Legendre - 1841 - 288 sider
...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... | |
 | John Playfair - 1842 - 332 sider
...tional to M, N ; draw the line AD, and the triangle ABC will be divided as required. For, since the triangles of the same altitude are to each other as their bases, we have ABD : ADC : : BD : DC : : B 3> C M:N. SCHOLIUM. A triangle may evidently be divided into any... | |
 | Nathan Scholfield - 1845 - 894 sider
...proper-" A tional to M, N ; draw the line AD, and the triangle ABC will be divided as required. For since triangles of the same altitude are to each other as their bases, we have ABD : ADC: :BD : DC: :M : N. Scholium. A triangle may evidently be divided into any number... | |
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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. 
