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" 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 - 1873 - 176 pages
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 340 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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The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

Edward Brooks - Geometry - 1868 - 284 pages
...X AF : :AB * :IS\ Comparing this with the first proportion, we have, ABC:ADE::AB*:AD\ THEOREM XVII. Similar polygons may be divided into the same number...triangles, similar each to each, and similarly situated. ~LetABCDE and FGHIK\}& two similar polygons, having the angle A equal to the angle F, B to G, CtoH,...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...PROPOSITION XXX. — THEOREM. ELEMENTS OF GEOMETRY. K 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 being similar,...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...PROPOSITION XXV. THEOREM. Two similar polygons may be divided into the same numtiei of triangles, simila: each to each, and similarly situated. Let ABCDE, FGHIK...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 K polygon FGHIK,...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...similarity (24). PROPOSITION XI.— THEOREM. 39. Conversely, two similar polygons may be decomposed into the same number of triangles similar each to each and similarly placed. Let ABCD, etc., A'B'C'D', etc., be two similar polygons. From two homologous vertices, A and...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...the first proportion (B. II., P. IV.), we have, ABC : DEF : : AC* : 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 poly gone, the angle A being equal to the angle F, B to...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...of similarity (24). PROPOSITION XI—THEOREM. 39. Conversely, two similar polygons may be decomposed into the same number of triangles similar each to each and similarly placed. Let AB CD, etc., A'B'C'D', etc., be two similar polygons. From two homologous vertices, A and...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 pages
...other as the squares of AB and DE, or of BC and EF ; which was to be proved. PROPOSITION XXVI. THEOREM. Similar polygons may be divided into the same number...of triangles, similar, each to each, and similarly placed. let ABODE and FGIIIK be two similar polygons, the angle A being equal to the angle F, B to...
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The elements of geometry, in eight books; or, First step in applied logic

L J V. Gerard - 1874 - 428 pages
...similarly placed : therefore they are equal to each other [39], WWTBD THEOREM 41. (Eucl. VI. 20.) Two similar polygons may be divided into the same number of triangles similar each to each. Let ABCDEFG and A' B' C' D' E' F' G' be two similar polygons. If the two polygons be of the same magnitude,...
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Elements of Euclid Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...polygons are to one another in the duplicate ratio of their homologous sides. M Let ABODE and OPQKS be two similar polygons; they may be divided into the same number of similar triangles, and they have to one another a ratio duplicate of that of the homologous sides....
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