| Adrien Marie Legendre - Geometry - 1819 - 208 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 - 596 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 - Geometry - 1825 - 224 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 - Geometry - 1825 - 224 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 - 208 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 - 159 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 - 269 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 - 84 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 - 166 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,... | |
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