 | Euclid, John Playfair - 1846 - 334 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. To divide a so that PROP. Q. PROS. triangle... | |
 | Charles William Hackley - 1847 - 248 sider
...BA ; and the two triangles ADE, CDE, on the bases AE, EC, have also a common 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. But BDE is = CDE... | |
 | Benjamin Peirce - 1847 - 204 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. Area of the Trap 253. Theorem. The area o! product of its altitude by the sui Proof. Draw the diagonal... | |
 | George Roberts Perkins - 1847 - 326 sider
...altitude ; and the two triangles ADF, CDF, on. the bases AF, FC, have also the same altitude ; and because triangles of the same altitude are to each other as their bases, therefore ADF : BDF -. : AD : DB ; ADF : CDF : : AF : FC. But BDF = CDF ; consequently, by equality... | |
 | Elias Loomis - 1849 - 252 sider
...AD its altitude ; the area of the triangle ABC is measured by half the product of BC by AD. Cor. 1. Triangles of the same altitude are to each other as their bases, and triangles of the same base are to each oth.,r as their altitudes. equal altitudes; and equivalent triangles,... | |
 | Charles Davies - 1849 - 372 sider
...therefore 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. 2. Similar cylinders are to each... | |
 | Charles Davies - 1850 - 238 sider
...area of the triangle is equal to half this product : that is, to half the product of AB x CD. Cor. Two triangles of the same altitude are to each other...are to each other as the products of their bases and altitudes. THEOREM X. The area of a trapezoid is equal to half the product of its altitude multiplied... | |
 | Charles Davies - 1850 - 218 sider
...the area of the triangle is equal to half this product : that is, to half the product ofABxCD. Cor. Two triangles of the same altitude are to each other...are to each other as the products of their bases and altitudes. THEOREM X. The area of a trapezoid is equal to half the product of its altitude by the sum... | |
 | George Roberts Perkins - 1850 - 332 sider
...altitude ; and the two triangles ADF, CDF, on the bases AF, FC, have also the same altitude ; and because triangles of the same altitude are to each other as their bases, (B. IV, Prop, iv, Cor.) therefore, ADF : BDF : : AD : DB; ADF : CDF : : AF : FC. But BDF = CDF; consequently,... | |
 | 1851 - 716 sider
...two legs half the diagonals of the rhombus (fig. 51). The areas of two parallelograms as well as of two triangles of the same base, are to each other as their altitudes ; of the same altitude, as their bases ; and generally, parallelograms are to each other as the products... | |
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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. 
