 | Adrien Marie Legendre - Geometry - 1838 - 372 pages
...homologous sides AC, DF, or as the squares of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar polygons are composed of the same number...triangles, similar each to each, and similarly situated. Let ABCDE, FGHIK, be two similar polygons. From any angle A, in the polygon ABCDE, ^- „ draw diagonals... | |
 | Adrien Marie Legendre - Geometry - 1839 - 372 pages
...sides AC, DF, or as the squares of any other two homologous sides. PROPOSITION XXVI. THEOREM. Tico similar polygons are composed of the same number of...triangles, similar each to each, and similarly situated. Let ABCDE, FGHIK, be two similar polygons. From any angle A, in the polygon ABCDE, draw diagonals AC,... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...proportion, AC : DF : : AC : DF, we shall have AB X AC : DE X DF : : TC : DF. Hence ABC : DEF ::TC:DF. Therefore two similar triangles ABC, DEF, are to each...polygons are composed of the same number of triangles, which are similar to each other, and similarly disposed. Demonstration. In the polygon ABCDE (fig.... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...are to each other as the rectangles of the sides which contain that angle. PROPOSITION XXV. THEOREM. Two similar triangles, ABC, DEF, are to each other as the squares of their homologous sides, AC, DF. D Let the angle A be equal to D, and the angle B = E. Then, by reason... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...: AC : DF, there will result AB.AC : DE.DF : : AC 2 : DP. Consequently, ABC : DEF : : AC" : DF 2 . Therefore, two similar triangles ABC, DEF, are to each other as the squares described on their homologous sides AC, DF, or as the squares of any other two homologous sides. PROPOSITION... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...the opposite side, and then taking two-thirds of this line from the vertex. PROPOSITION XIX. THEOREM. Two similar polygons are composed of the same number...triangles similar each to each, and similarly situated. Let ABCDF, GHKLM be two similar polygons. From any angle A in the polygon ABCDF, draw the diagonals... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...triangle FIK similar to AD E. The polygon FGHIK 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 (Prop. XXX. Cor., Bk. IV.). PROBLEM XXXVI. 341. Tioo similar polygons being given, to construct a similar... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...to DE X DP (Prop. XXVIII.) ; consequently (Prop. X. Bk. II.), ABC: DEF: : AC9 : DF8. 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 - 1862 - 518 pages
...to DE X DF (Prop. XXVIII.) ; consequently (Prop. X. Bk. II.), ABC: DEF: : AC2 : DFa. 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 - 1863 - 504 pages
...toDEX DP (Prop. XXVIII.) ; consequently (Prop. X. Bk. II.), ABC : DEF : : A~C2 : D"F2. ' 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.... | |
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Two similar polygons are composed of the same number of triangles, similar each to each, and similarly situated. 
