 | Edward Brooks - Geometry - 1868 - 284 pages
...the first proportion, we have, ABC:ADE::AB*:AD\ THEOREM XVII. Similar polygons may be divided into the same number of triangles, similar each to each, and similarly situated. ~LetABCDE and FGHIK\}& two similar polygons, having the angle A equal to the angle F, B to G, CtoH,... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...DE X DF (Prop. XXVIII.) ; consequently (Prop. X. Bk. II.), ABC : DEF : : AC? : DF2. Therefore, the two similar triangles ABC, DEF are to each other as the squares described on the homologous sides AC, DF, or as the squares described on any other two homologous sides.... | |
 | Benjamin Greenleaf - 1869 - 516 pages
...AC istoDEXDP (Prop. XXVIII.) ; consequently (Prop. X. Bk. II.), ABC: DEF:: AC2: DF*. Therefore, the two similar triangles ABC, DEF are to each other as the squares described on the homologous sides AC, DF, or as the squares described on any other two homologous sides.... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...passes through O. In the same way, Dd is shown to pass through O. PROPOSITION X.— THEOREM. 38. If two polygons are composed of the same number of triangles similar each to each and similarly placed, the polygons are similar. Let the polygon AB CD, etc., be composed of the triangles ABC, A... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...ac But, from the hypothesis [1J, we have by (12), AB AC ab ac PROPOSITION X.—THEOREM. 38. If two polygons are composed of the same number of triangles similar each to each and similarly placed, the polygons are similar. Let the polygon ABCD, etc., be composed of the triangles ABC, ACD,... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...isto DE X DF (Theo. XVIII.) ; consequently (Theo. IX. Bk. II.), ABC: DBF: : AC* : DF*. Therefore, the two similar triangles ABC, DEF are to each other as the squares described on the homologous sides AC, DF, or as the squares described on any other two homologous sides.... | |
 | L J V. Gerard - 1874 - 428 pages
...each to each, to the remaining triangles of the polygon A' B' C' D' E' F' G' H' ; that is, the two polygons are composed of the same number of triangles similar each to each and similarly placed : therefore they are similar to each other [42], WWTBD THEOREM 44. Two parallelograms about... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...DEX DF (Theo. XVIII.) ; consequently (Theo. IX. Bk. II.), .1 BC: DBF: : AC~ : ~D~F*. Therefore, the two similar triangles ABC, DEF are to each other as the squares described on the homologous sides AC, DF, or as the squares described on any other two homologous sides.... | |
 | Benjamin Greenleaf - Geometry - 1875 - 204 pages
...triangle FIK similar to AD E. The polygon FG HIK will be similar to ABCDE, as required. For these two polygons are composed of the same number of triangles, similar each to each, and similarly situated (Theo. XX. Cor., Bk. IV.). PROBLEM VII. To inscribe a square in a given circle. Draw two diameters,... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...number of triangles, which are similar each to each, and similarly situated. Cor. Conversely, if two polygons are composed of the same number of triangles, similar each to each, and similarly situated, the polygons are similar. For, because the triangles are similar, the angle ABC is equal to FGH ; and... | |
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Two similar polygons are composed of the same number of triangles, similar each to each, and similarly situated. 
