 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...its consequent FGH (Prop. XI. Bk. II.), or as A Ba is to F Ga ; hence the areas of similar polygons are to each other as the squares described on their homologous sides. 278. Cor. 1. The perimeters of similar polygons are also to each other as their corresponding diagonals.... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...its consequent FGH (Prop. XI. Bk. П.), or as A B2 is to F Ga ; hence the areas of similar polygons are to each other as the squares described on their homologous sides. 278. Cor. 1. The perimeters of similar polygons are also to each other as their corresponding diagonals.... | |
 | Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...mean proportional between the parts of the hypotenuse (Def. 2, Sec. X). THEOREM VIII. The areas of similar triangles are to each other as the squares...homologous sides. Let ABC, DEF, be two similar triangles of which the angles A and B are respectively equal to the angles D and E. It may be shown that their... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...to its consequent FGH (Prop. XI. Bk. II.), or as AB is to FG ; hence the areas of similar polygons are to each other as the squares described on their homologous sides. 278. Cor. 1. The perimeters of similar polygons are also to each other as their corresponding diagonals.... | |
 | Benjamin Greenleaf - Geometry - 1866 - 328 pages
...equivalent, the triangles would be equivalent. BCE proportional F (Art. PROPOSITION XXIX. — THEOREM. 274. Similar triangles are to each other as the squares...homologous sides. Let ABC, DEF be two similar triangles, and let AC, DF be homologous sides; then the triangle ABC will be to the triangle DEF as the square... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...to its consequent FGH (Prop. XI. Bk. II.), or as AB is to FG ; hence the areas of similar polygons are to each other as the squares described on their homologous sides. 278. Cor. 1. The perimeters of similar polygons are also to each other as their corresponding diagonals.... | |
 | Benjamin Greenleaf - 1869 - 516 pages
...term ABE, we have (Prop. XIII. Bk. II.), ABC:ADE::ABXAC:ADXAE. PROPOSITION XXIX. — THEOREM. 274. Similar triangles are to each other as the squares...their homologous sides. Let ABC, DEF be two similar A triangles, and let AC, DF be homologous sides; then the triangle l) ABC will be to the triangle DEF... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...each other as tne rectangles of the sides which contain the equal angles. PROPOSITION XXIV. THEOREM. Similar triangles are to each other as the squares...similar triangles, having the angle A equal to D, the angle B equal to E, and C equal to F ; then the triangle ABC is to the triangle DEF as the square... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...out the demonstration.] AREAS OF SIMILAR FIGURES. PROPOSITION TIII. 362. Theorem. — Tlie areas of similar triangles are to each other as the squares described on their homologous sides. DEM. — Let ABC and DEF be any two similar triangles ; then is area ABC : area DEF : : CB" : F? :... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...out the demonstration.] AREAS OF SIMILAR FIGURES. PROPOSITION VIIL 362. Theorem. — T/ie areas of similar triangles are to each other as the squares described on their homologous sides. DEM.— Let ABC and DEF be any two similar triangles ; then is area ABO : area DEF : : C§' : FT :... | |
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Two similar triangles are to each other as the squares described on their homologous sides. Let ABC, DEF, be two similar triangles, having the angle A equal to D, and The angle B=E. 
