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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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The elements of geometry, in eight books; or, First step in applied logic

L J V. Gerard - 1874
...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 [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874 - 234 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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Euclid simplified. Compiled from the most important French works, approved ...

John Reynell Morell - 1875 - 220 pages
...the base BC is divided at the points F, G, H. THEOREM XII. Two similar polygons can fee decomposed into the same number of triangles, similar each to each, and similarly placed. Let there be two similar polygons ABCDE, A' B' C' ' D' E'. From their homologous summits draw...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 458 pages
...are similar each to each, and similarly situated. Cor. Conversely, if two polygons are composed of the same number of triangles, similar each to each, and similarly situated, the polygons are similar. For, because the triangles are similar, the angle ABC is equal to FGH ; and...
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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - Geometry - 1878 - 236 pages
...other as AB is to ab. Hence, also, ABC : abc = AD- : ad2. SIMILAR POLYGONS. XXVII. • Theorem. Two similar polygons may be divided into the same number of triangles similar each to each. HYPOTII. ABODE and abode are similar polygons, divided into triangles by diagonals drawn from the vertices...
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A Geometry for Beginners

George Anthony Hill - Geometry - 1880 - 332 pages
...angles of a polygon = 180 X the number of bides less two. 4. Two polygons are equal, if they can be divided into the same number of triangles, similar each to each, and similarly placed. 5. A polygon is equilateral, if its sides are equal ; equiangular, if its angles are equal...
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...Likewise we can prove that A DB С is similar to A KGS. QED 279. COR. — Two similar polygons can be divided into the same number of triangles similar each to each and similarly placed, by drawing lines to their vertices from any two homologous points. ELEMENTS OF PLANE GEOMETRY....
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Essentials of Geometry

Alfred Hix Welsh - Geometry - 1883 - 326 pages
...the area of the first than that of the second? An*. 2$. THEOREM IX. Similar polygons may be resolved into the same number of triangles, similar, each to each, and similarly placed. Let P and P' be two similar polygons; then, can they be resolved into the same number of similar...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1885 - 540 pages
...the first proportion (B. II., P. IV.), we have, ABC : DEF : : ^C* : DF2. 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 G,...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1885 - 389 pages
...line can be cut only at a single point into external segments having a given ratio.) 516. COROLLARY. Similar polygons may be divided into the same number of triangles similar and similarly placed. For if, with their corresponding sides parallel, one of the polygons were placed...
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