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Books Books 1 - 10 of 163 on If two polygons are composed of the same number of triangles, similar each to each....  
" If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. "
Plane Geometry - Page 179
by John Wesley Young, Albert John Schwartz - 1915 - 223 pages
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 pages
...triangles similar and similarly situated. Scholium. The converse of the proposition is equally true : If two polygons are composed of the same number of triangles similar and similarly situated, those two polygons will be similar. For, the similarity of the respective triangles...
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Elements of geometry with notes

John Radford Young - 1827
...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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair, James Ryan - Euclid's Elements - 1835 - 316 pages
...similar rectilineal figures are to one another as the squares of their homologous sides. SCHOLIUM. If two polygons are composed of the same number of triangles similar, and similarly situated, those two polygons will be similar. For the similarity of the two triangles...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...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...
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Elements of geometry and trigonometry

Adrien Marie Legendre - Geometry - 1837 - 359 pages
...triangles, similar, and similarly situated. Scholium. The converse of the proposition is equally true : If two polygons are composed of the same number of triangles similar and similarly situated, those two polygons will be similar. For, the similarity of the respective triangles...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 359 pages
...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, ^- ...
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Elements of geometry: containing the first six books of Euclid, with a ...

John Playfair - Mathematics - 1842 - 317 pages
...similar rectilineal figures are to one another as the squares of their homologous sides. SCHOLIUM. If two polygons are composed of the same number of triangles similar, and similarly situated, those two polygons will be similar. For the similarity of the two triangles...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845
...triangles, similar and similarly situated. Scholium. 1. The converse of the proposition is equally true : If two polygons are composed of the same number of triangles similar and similarly situated, those two polygons will be similar. For, the similarity of the respective triangles...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 317 pages
...upon the first, to a similar, and similarly described rectilineal figure upon the second. SCHOLIUM. If two polygons are composed of the same number of triangles similar, and similarly situated, those two polygons will be similar. For the similarity of the two triangles...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies, Sir David Brewster, Adrien Marie Legendre - Trigonometry - 1849 - 359 pages
...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^--^\...
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