 | Benjamin Greenleaf - 1875 - 204 σελίδες
...the triangle FIK similar to AD E. The polygon FG HIK 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 (Theo. XX. Cor., Bk. IV.). PROBLEM VII. To inscribe a square in a given circle. Draw two diameters,... | |
 | John Reynell Morell - 1875 - 220 σελίδες
...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 the homologous... | |
 | Elias Loomis - 1877 - 458 σελίδες
...same number of triangles, which 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... | |
 | William Henry Harrison Phillips - 1878 - 236 σελίδες
...be shown that the remaining triangles are similar each to each. XXVIII. Theorem. Conversely, if tu'o polygons are composed of the same number of triangles similar each to each, and similarly situated, the polygons are similar. . HYPOTII. In the two polygons, ABCDE and abcde, A ABC ~ abc, ACD... | |
 | George Anthony Hill - 1880 - 348 σελίδες
...polygon = 180° X the number of sides less tw0. 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 ; regular,... | |
 | Charles Scott Venable - 1881 - 380 σελίδες
...AC, DF, or as the squares of any other two homologous sides. PROPOSITION XXVIII. THEOREM. Two similar polygons are composed of the same number of triangles, similar, each to each, and similarly situated. From any angle, A, in the polygon ABCDE, draw the diagonals AC, AD, to the other angles.... | |
 | Franklin Ibach - 1882 - 208 σελίδες
...:: HK : FG :: CK : CG ELEMENTS OF PLANE GEOMETRY. THEOREM XX. 277. Two polygons are similar if they are composed of the same number of triangles similar each to each and similarly placed. Let the As ABE, EBD, and DBC, of which the polygon ABСDE is composed, be respectively similar to the... | |
 | Franklin Ibach - 1882 - 208 σελίδες
...similar. (237) QED ELEMENTS OF PLANE GEOMETRY. THEOREM XXI. 278. Two similar polygons can be divided into the same number of triangles similar each to each and similarly placed. Let the polygon ABCDE be similar to the polygon FGHKM, and let diagonals be drawn from the vertices... | |
 | Alfred Hix Welsh - 1883 - 326 σελίδες
...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 triangles,... | |
 | Charles Davies, Adrien Marie Legendre - 1885 - 538 σελίδες
...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, C to H,... | |
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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. 
