 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...It •. AD •. •. JIE . AC, wbich is the case when the line DC is parallel to HE. THEOREM. 218. Two similar triangles are to each other as the squares of their homologous sides. Demonstration. Let the angle A = D (Jig. 122), and the an-Fie. 122. gle B — E, then, by the preceding... | |
 | Peter Nicholson - Architecture - 1823 - 210 pages
...triangle ABC : AB x AC. : AB x AC : AD x AE. THEOREM 64. 162. Similar triangles are to one another as the squares of their homologous sides. Let the angle A be equal to the angle D, and A the angle B equal to E. Then AB : DE •: AC : DF (155) and AB:DE ::AB:DE. therefore,... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...: AD X AE. AB : AD : : AE : AC, which is the case when the line DC is parallel to BE. THEOREM. 218. Two similar triangles are to each other as the squares of their homologous sides. Demonstration. Let the angle A — D (fig'. 122), and the an- Fig. 122. gle B = E, then, by the preceding... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...: AD x AE. AB : AD : : AE : AC, which is the case when the line DC is parallel to BE. THEOREM. 218. Two similar triangles are to each other as the squares of their homologous sides. Demonstration. Let the angle A = D (fig. 122), and the an- Fig. 12£ gle B — E, then, by the preceding... | |
 | John Radford Young - Euclid's Elements - 1827 - 228 pages
...angles, which the student will not find much difficulty in demonstrating. PROPOSITION XVII. THEOREM. Similar triangles are to each other as the squares of their homologous sides. Let the triangles ABC, DEF be similar, and let BC, EF be homologous sides ; that is, let the angles B, C be... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...art. 181, HP : PI= EF : FG, whence, on account of the common ratio HP : PI, — EF : FG. 266. Theorem. Similar triangles are to each other as the squares of their homologous sides. Demonstration. In the similar triangles ABC, A'B'C (fig. 109), we have, by art. 199, CE : CE' = AB... | |
 | Adrien Marie Legendre - Geometry - 1839 - 372 pages
...the two triangles would be equivalent, if .the rectangle AB.AC were equal to the rectangle AD. AE, or if we had AB : AD : : AE : AC ; which would happen...similar triangles are to each other as the squares described on their homologous sides. Let ABC, DEF, be tw,o similar triangles, having the angle A equal... | |
 | Joseph Denison - Euclid's Elements - 1840 - 96 pages
...fc k But ab and ed are any two right lines ; wherefore, &c.— QED PROPOSITION XXXVI. — THEOREM. Similar triangles are to each other as the squares of their homologous sides. Let abe and ade be two similar triangles ; then will the triangle abe be to the triangle ade, as the square... | |
 | Benjamin Peirce - Geometry - 1841 - 186 pages
...by § 251, the area of ABC: the area of A'B'C'=ABZ : A'B'\ 267. Corollary. Hence, by § 197 & 198, similar triangles are to each other as the squares of their homologous altitudes, and as the squares of their perimeters. 268. Theorem. Similar polygons are to each other... | |
 | Charles Waterhouse - Arithmetic - 1842 - 180 pages
...in the other, are to each other as the rectangles of the sides, which contain the equal angles. 21. Two similar triangles are to each other as the squares of their homologous sides. 22. Two similar polygons are composed of the same number of triangles, which are similar to each other,... | |
| |
Similar triangles are to each other as the squares of their homologous sides. 
