 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...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 G, C to... | |
 | Benjamin Greenleaf - Geometry - 1875 - 204 pages
...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 pages
...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 - Conic sections - 1877 - 458 pages
...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 - Geometry - 1878 - 236 pages
...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 - Geometry - 1880 - 348 pages
...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 pages
...the same number of tetraedrons, similar each to each and similarly situated, their surfaces are also composed of the same number of triangles, similar each to each and similarly grouped. Moreover, the inclination of two adjacent triangles of the first surface is equal to the inclination... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...similar to As CDF, CFG, and CGE. ' (269) ... AH : DF :: CH : CF :: HK : FG :: CK : CG THEOREM XX. 277. Two polygons are similar if they are composed of the...triangles similar each to each and similarly placed. Let the As ABE, EBD, and DBC, of which the polygon ABODE is composed, be respectively similar to the... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...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 - Geometry - 1885 - 538 pages
...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. 
