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" Similar triangles are to each other as the squares of their homologous sides. "
Elements of Geometry and Trigonometry: With Notes - Page 62
by Adrien Marie Legendre - 1822 - 367 pages
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Elements of Geometry

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...
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The new practical builder, and workman's companion, Volume 2

Peter Nicholson - Building - 1823
...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,...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 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...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 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...
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Elements of geometry: with notes

John Radford Young - Geometry, Plane - 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...
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An Elementary Treatise on Plane and Solid Geometry

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...
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Elements of geometry and trigonometry

Adrien Marie Legendre - Geometry - 1839 - 359 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...
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A new supplement to Euclid's Elements of geometry, by the author of 'A new ...

Joseph Denison - 1840
...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...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1841 - 150 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...
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Arithmetical Spyglass and Teacher's Assistant: Intended as a Key and ...

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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