 | Adrien Marie Legendre - 1819 - 574 σελίδες
...•. 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... | |
 | Adrien Marie Legendre - 1822 - 394 σελίδες
...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... | |
 | Adrien Marie Legendre - 1825 - 276 σελίδες
...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... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 280 σελίδες
...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... | |
 | John Radford Young - 1827 - 228 σελίδες
...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... | |
 | Benjamin Peirce - 1837 - 216 σελίδες
...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'... | |
 | Joseph Denison - 1840 - 96 σελίδες
...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,... | |
 | Benjamin Peirce - 1841 - 186 σελίδες
...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 as the squares... | |
 | Charles Waterhouse - 1842 - 178 σελίδες
...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... | |
 | Nicholas Tillinghast - 1844 - 108 σελίδες
...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... | |
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Since similar triangles are to each other as the squares of their homologous sides, ABC : DBE : : AB' : BD3 ; whence BD = AB J ^5| ~ AB A/— ^ — . j A150 f in -f- n The construction of Fig. 
