| 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,... | |
| 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.... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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.... | |
| 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... | |
| 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,... | |
| 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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