 | Adrien Marie Legendre - 1819 - 574 sider
...•. 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... | |
 | Adrien Marie Legendre - 1822 - 394 sider
...AB : AD : : AE : AC ; which would happen if. DC were parallel to BE. PROPOSITION XXV. THEOREM. Two similar triangles are to each other as the squares of their homologous sides. Let the angle A be equal to D, and the A. angle B=E. Then, first, by reason of the equal angles A and D, according... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 280 sider
...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... | |
 | Adrien Marie Legendre - 1825 - 276 sider
...or if 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. i«; gle B = E, then, by the preceding... | |
 | John Radford Young - 1827 - 228 sider
...two right angles, which the student will not find much difficulty in demonstrating. PROPOSITION XVII. THEOREM. Similar triangles are to each other as the...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 respectively equal... | |
 | Benjamin Peirce - 1837 - 216 sider
...But, by 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... | |
 | Joseph Denison - 1840 - 96 sider
...Supplement) ; 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 - 1841 - 186 sider
...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 - 1842 - 178 sider
...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,... | |
 | Nicholas Tillinghast - 1844 - 108 sider
...and consequent (B. IV. Prop. 8), we shall have ABC : DEC : : AC.CB : DC.CE. PROP. XX. THEOREM. Two similar triangles are to each other as the squares of their homologous sides. Let ABC, DEF, be the similar triangles, having the angles A, B, C, respec- Fig- 77. lively equal to D,... | |
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Similar triangles are to each other as the squares of their homologous sides. 
