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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. In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB, EEC, CED be similar, respectively, to the triangles A'E'B',... "
Elements of Geometry and Trigonometry: With Notes - Page 73
by Adrien Marie Legendre - 1828 - 316 pages
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826
...lines be cut by parallel lines, they are cut in the same ratio. 2. If, on two bases, there be placed the same number of triangles, similar each to each, and similarly situated, the polygons formed by joining the vertices of the triangles will be similar. 3. A straight line, drawn...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 208 pages
...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 proportional...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 208 pages
...that is, the triangles are similar. PROPOSITION XIX. THEOREM. Similar polygons may be divided into the same 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,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...remaining triangles are similar, whatever be the number of sides in the polygons proposed : . therefore two similar polygons are composed of the same number of triangles, similar, and similarly situated. Scholium. The converse of the proposition is equally true : If two polygons...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 359 pages
...homologous sides AC, DF, or as the squares of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar polygons are composed of the same number...triangles, similar each to each, and similarly situated. Let ABCDE, FGHIK, be two similar polygons. From any angle A, in the polygon ABCDE, ^- „ draw diagonals...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1839 - 269 pages
...sides AC, DF, or as the squares of any other two homologous sides. PROPOSITION XXVI. THEOREM. Tico 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, draw diagonals AC,...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845
...were parallel to BE. • PROPOSITION XXIII. THEOREM. 104 Let ABCDE, FGHIK, be two similar polygons. From any angle A. in the polygon ABCDE, draw diagonals AC, AD, to the other angles. From A the homologous angle F, in the other polygon FGHIK, draw diagonals FH, FI, to the other angles. These...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 pages
...remaining triangles are similar, whatever be the number of sides in the polygons proposed : therefore two similar polygons are composed of the same number of triangles, similar, and similarly situated. FH, Fl to the other angles. For, the similarity of the respective triangles...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...the opposite side, and then taking two-thirds of this line from the vertex. PROPOSITION XIX. THEOREM. Two similar polygons are composed of the same number...triangles similar each to each, and similarly situated. Let ABCDF, GHKLM be two similar polygons. From any angle A in the polygon ABCDF, draw the diagonals...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 628 pages
...triangle FIK similar to AD E. The polygon FGHIK will be similar to ABCDE, as required. For these two polygons .are composed of the same number of triangles, similar each to each, and similarly situated (Prop. XXX. Cor., Bk. IV.). PROBLEM XXXVI. 341. Tioo similar polygons being given, to construct a similar...
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