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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. "
Plane Geometry - Page 170
by Webster Wells, Walter Wilson Hart - 1915 - 309 pages
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 394 pages
...when they have two angles in each respectivety equal. Second. Two polygons are similar, when both may be divided into the same number of triangles, similar each to each, and similarly placed. But to prevent this latter definition itself from including any superfluous conditions, ftie number...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 228 pages
...proved to be similar, and so on in every pair of corresponding triangles ; hence, similar polygons may be divided into the same number of triangles, similar each to each, and similarly situated. Conversely. Let the polygons be composed of the Same number of similar triangles similarly...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1830 - 344 pages
...two angles in each respectively equal. Second. Two polygons are similar when both may be divided info the same number of triangles, similar each to each, and similarly placed. But to prevent this latter definition itself from including any superfluous conditions, the number...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...squares described on 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,...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...described on 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,...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...described on any other two homologous sides. PROPOSITION XXX. — THEOREM. 275. Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. ELEMENTS OF GEOMETRY. Let ABCDE, FGHIK be two similar polygons ; they may be divided into...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...described on any other two homologous sides. PROPOSITION XXX. — THEOREM. 275. Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. A 0 .' D? ; т d I Oií Let ABODE, FG IJ I К be two ^^f\ . H similar polygons ; they may...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...proportion (B. II, P. IV.), we have, ABC : DEF : : AC2 : DF\ PROPOSITION XXVI. THEOREM. Similar polygons may be divided into the same number of triangles, similar, each to each, and similarly placed. Let ABCDE and FGHIK be two similar polygons, the angle A being equal to the angle F, B to Gr, C to...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...PROPOSITION XXX. — THEOREM. LLEMfcNTS OF UEOMETRY. H Let ABCDE, FGHIK be two similar polygons; they may be divided into the same number of triangles similar each to each, and similarly situated. From the homologous angles A and F, draw the diagonals AC, AD and FH, F I. The two polygons...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 340 pages
...PROPOSITION XXX. • — THEOREM. ELEMENTS OP GEOMETRY. H Let ABCDE, FGHIK be two similar polygons ; they may be divided into the same number of triangles similar each to each, and similarly situated. From the homologous angles A and F, draw the diagonals AC, AD and FH, FI. The two polygons...
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