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" FIK are similar ; hence the similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. "
New Elementary Geometry: With Practical Applications : a Shorter Course Upon ... - Page 88
by Benjamin Greenleaf - 1874 - 176 pages
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...remaining triangles are similar, whatever be the number of sides in the polygons proposed: therefore, two similar polygons may be divided into the same number of triangles, similar, and similarly placed. Scholium. The converse of the proposition is equally true: If two polygons are...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1857 - 226 pages
...&c. PROPOSITION XXV. THEOREM. Two similar polygons may be divided into the fame numoet of trianglet, similar each to each, and similarly situated. Let...polygons ; they may be divided into the same number of similar triangles. Join AC, AD, FH, FI. Because the polygon ABCDE is similar to the polygon FGHIK,...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1857 - 444 pages
...remaining triangles are similar, whatever be the number of sides in the polygons proposed: therefore, two similar polygons may be divided into the same number of triangles, similar, and similarly placed. Scholium. The converse of the proposition is equally true: If two polygons are...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...similar triangles, &c. PROPOSITION XXV. THEOREM. Two similar polygons may be divided into the same numoet of triangles, similar each to each, and similarly...polygons ; they may be divided into the same number of similar triangles. Join AC, AD, FH, FI. Because the polygon ABCDE is similar to the E polygon FGHIK,...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1861 - 244 pages
...divided into the same numbei of triangles, similar each to each, and similarly situated. Let ABODE, FGHIK be two similar polygons ; they may be divided into the same number of similar triangles. Join AC, AD, FH, FI. Because the polygon ABCDE is similar to the polygon FGHIK,...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 514 pages
...the same manner, it may be shown that the corresponding triangles ADE, FIK are similar ; hence the similar polygons may be divided into the same number...triangles similar each to each, and similarly situated. 276. Cor. Conversely, if two polygons are composed of the same number of similar triangles, -and similarly...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 pages
...the same manner, it may be shown that the corresponding triangles ADE, FIK are similar ; hence the similar polygons may be divided into the same number...triangles similar each to each, and similarly situated. of the same number of similar triangles, and similarly situated, the two polygons are similar. For...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 320 pages
...the same manner, it may be shown that the corresponding triangles AD E, FIK are similar ; hence the similar polygons may be divided into the same number...triangles similar each to each, and similarly situated. of the same number of similar triangles, and similarly situated, the two polygons are similar. For...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...with the first 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,...
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Elements of Geometry and Trigonometry;: With Practical Applications

Benjamin Greenleaf - Geometry - 1863 - 502 pages
...AC, DF, or as the squares described on any other two homologous sides. PROPOSITION XXX.—THEOREM. 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 P, draw the diagonals AC, AD and FH, F I....
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