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Similar triangles are to each other as the squares of their homologous sides.
Elements of Geometry and Trigonometry - Page 123
by Adrien Marie Legendre - 1863 - 455 pages

## Elements of Geometry

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...

## Elements of Geometry and Trigonometry: With Notes

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...

## Elements of Geometry...: Translated from the French for the Use of the ...

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...

## Elements of Geometry

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...

## Elements of Geometry: With Notes

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...

## An Elementary Treatise on Plane and Solid Geometry

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...

## A new supplement to Euclid's Elements of geometry, by the author of 'A new ...

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...

## An Elementary Treatise on Plane and Solid Geometry

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...