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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. "
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... - Σελίδα 107
των William Chauvenet - 1872 - 368 σελίδες
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 1822 - 367 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...

Elements of Geometry: With Notes

John Radford Young - 1827 - 208 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...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1836 - 359 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...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1838 - 359 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, ^- „...

Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - 1849 - 359 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^--^\...

Elements of Geometry: With, Practical Applications

George Roberts Perkins - 1850 - 320 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...

ELEMENTS OF GEOMETRY AND TRIGONOMETRY

A. M. LEGENDRE - 1852
...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,...

Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1854 - 432 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,...

Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 490 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...

Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 490 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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