 | Adrien Marie Legendre - Geometry - 1841 - 288 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... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...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... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...of the (5. 4 ;) hence the area of the triangle must be JBC x AD, orBCx^AD. Therefore, The area, fyc. Cor. Two triangles of the same altitude, are to each...the same base, are to each other as their altitudes. PROPOSITION VII. THEOREM. The area of the trapezium ABCD, is equal to its altitude CE, multiplied by... | |
 | Nathan Scholfield - 1845 - 894 pages
...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... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...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... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...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 - Geometry - 1847 - 326 pages
...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... | |
 | Charles William Hackley - Geometry - 1847 - 248 pages
...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... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...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 - Trigonometry - 1849 - 372 pages
...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... | |
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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. 
