 | Adrien Marie Legendre - 1822 - 394 σελίδες
...AC, DF, or as the squares of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar polygons are composed of the same number of triangles similar each to each, and similarly situated. From any angle A, in the polygon ABCDE, draw diagonals AC, AD to the other angles. From the... | |
 | John Radford Young - 1827 - 246 σελίδες
...number of triangles, similar each to each, and similarly situated ; and, conversely, polygons which are composed of the same number of triangles, similar each to each, and similarly situated, are themselves similar. ELEMENTS OP GEOMETRY. while the sides containing these angles are... | |
 | Adrien Marie Legendre - 1836 - 394 σελίδες
...die squares of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar polygons tire 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... | |
 | Adrien Marie Legendre - 1838 - 372 σελίδες
...AC, DF, or as the squares of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two 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, ^- „... | |
 | Charles Davies - 1849 - 372 σελίδες
...AC, DF, or as the squares of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar polygons are composed of the same number of triangles, similar each to each, and similarly situated.' From any angle A, in c Let ABCDE, FGHIK. be two similar polygons. the polygon ABCDE, B^--^\... | |
 | George Roberts Perkins - 1850 - 332 σελίδες
...side, and then taking two-thirds of this line from the vertex. PROPOSITION XIX. THEOREM. Two similar polygons are composed of the same number of 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... | |
 | Adrien Marie Legendre - 1852 - 436 σελίδες
...any other two homologous sides. PROPOSITION XXVI. THEOEEM. Two similar polygons may be divided into the same number of triangles, similar each to each, and similarly placed. Let AEDCB, FKIHG, be two similar polygons. From any angle A, in the polygon AEDCB, draw diagonals,... | |
 | Charles Davies - 1854 - 436 σελίδες
...any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar polygons may be div1ded into the same number of triangles, similar each to each, and similarly placed. Let AEDCB, FKIHG, be two similar polygons. From the vertex of any angle A, in the poly• C gon AEDCB,... | |
 | Benjamin Greenleaf - 1862 - 518 σελίδες
...the 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. Two similar polygons being' given, to construct... | |
 | Benjamin Greenleaf - 1862 - 532 σελίδες
...triangle FIK similar to AD E. The polygon FGHIK will he similar to А В С DE, 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 XXXYI. 341. Two similar polygons being- given, to construct... | |
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If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 
