| Adrien Marie Legendre - Geometry - 1819 - 576 pages
...•. 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 - Geometry - 1822 - 394 pages
...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 - Geometry - 1825 - 280 pages
...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 - Geometry - 1825 - 276 pages
...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. iĞ; gle B = E, then, by the preceding... | |
| John Radford Young - Euclid's Elements - 1827 - 228 pages
...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 - Geometry - 1837 - 216 pages
...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 - Euclid's Elements - 1840 - 96 pages
...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 - 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 - 178 pages
...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 - Geometry, Plane - 1844 - 108 pages
...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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