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 Βιβλία Βιβλία 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 - Σελίδα 75
των Adrien Marie Legendre - 1828 - 316 σελίδες
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο ## The Elements of Geometry

Henry W. Keigwin - 1897 - 227 σελίδες
.../_K—£D, etc., and the homologous sides are in the ratio of similtude AB : HI. 271. THEOREM. If two polygons are composed of the same number of triangles similar each to each and similarly placed, the polygons are similar. 272. THEOREM. If two polygons are similar, they may be resolved into... ## Elements of Geometry

George Washington Hull - 1897 - 398 σελίδες
...DF* =CM*iFN* = AM1 : DN*. § 128 PROPOSITION XXVI. THEOREM. 271. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. Given—A .4-BC similar to AFC ' //, A^CD to &FHK, and &ADE to &FKL. To Prove—EB similar... ## Entrance Examinations in Mathematics, 1884 to 1898 [with Supplements to 1900]

Yale University - 1898
...center, the nearer is the greater. 3. Define similar polygons, similar sectors, similar segments. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 4. The areas of similar segments have the same ratio as the squares... ## Yale University Entrance Examinations in Mathematics: 1884 to 1898

1898 - 208 σελίδες
...center, the nearer is the greater. 3. Define similar polygons, similar sectors, similar segments. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 4. The areas of similar segments have the same ratio as the squares... ## Plane and Solid Geometry

James Howard Gore - 1898 - 210 σελίδες
...of their sides is a parallelogram. PROPOSITION XV. THEOREM. 224. Two polygons are similar when they are composed of the same number of triangles, similar each to each and similarly placed. A Let ABCDE and A'B'C'D'E' be two polygons composed of the same number of similar triangles... ## The Essentials of Geometry (plane)

Webster Wells - 1898 - 242 σελίδες
...homologous base of a similar triangle is PROI-. XX. THEOREM. 266. Tiro polygons are similar irhen the;/ are composed of the same number of triangles, similar each to each, and similarly placed. Given, in polygons AC and A'C", A ABE similar to A A'B'E', A BCE to AB'C'E', and A CDE to A... ## Bulletin

1901
...point are equal, and make equal angles with the line ; the point to the center. 3 Prove that if two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. 4 Complete and demonstrate the following : the area of a trapezoid... ## Plane and Solid Geometry

George Albert Wentworth - 1899 - 473 σελίδες
...E'C'D' are similar. §351 § 351 Ax. 1 §357 QED PROPOSITION XXVI. THEOREM. 366. CONVERSELY : 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,... ## Plane Geometry

George Albert Wentworth - 1899 - 256 σελίδες
...§351 Ax. 1 § 357 QEO BOOK III. PLANE GEOMETRY. PROPOSITION XXVI. THEOREM. 366. CONVERSELY : 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,... ## The Elements of Plane Geometry

Charles Austin Hobbs - 1899 - 240 σελίδες
...triangle similarly situated in , Proposition 142. Theorem. 176. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. Since the homologous A are either homologous A of similar A, or else the sums of such A, the...