| John Playfair - 1806 - 311 sider
...described triangle upon the second. For, BC : BG : : triangle ABC : triangle DEF. PROP. XX. THEOR. SIMILAR **polygons may be divided into the same number of similar...another that the polygons have ; and the polygons** have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL... | |
| Euclid, Robert Simson - 1806 - 518 sider
...the first to a similar, and similarly described triangle upon the second. PROP. XX. THEOR. SIMILAR **polygons may be divided into the same number of similar...another that the polygons have ; and the polygons** have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL... | |
| John Mason Good - 1813
...triangles are to one another in the duplicate ratio of their homologous sides. Prop. XX. Theor. Similar **polygons may be divided into the same number of similar...another that the polygons have ; and the polygons** hare to one another the duplicate ratio of that which their homo, logons sides have. Prop. XXI. Theor.... | |
| Euclides - 1814
...upon the first to a similar and similarly described triangle upon the second. PROP. XX. THEOR. SIMILAR **polygons may be divided into the same number of similar...triangles, having the same ratio to one another that** thepolygons have; and the polygons have to one another the duplicate ratio of that which their homologous... | |
| Euclides - 1816 - 528 sider
...similar and similarly described triangle upon the second, PROP. XX. THEOR. SIMILAR polygons may he **divided into the same number of similar triangles,...another that the polygons have ; and the polygons** have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL... | |
| John Playfair - 1819 - 317 sider
...the first to a similar, and similarly described triangle upon the second, PROP. XX. THEOR. Similar **polygons may be divided into the same number of similar...another that the polygons have ; and the polygons** have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL... | |
| Adrien Marie Legendre - 1819 - 208 sider
...antecedent ABC is to its consequent FGH, or as . .'// is to FG (219). Therefore the surfaces of similar **polygons are to each other, as the squares of their homologous sides.** 222. Corollary. If three similar figures be constructed whose homologous sides are equal to the three... | |
| James Mitchell - 1823 - 576 sider
...similar triangles, have their homologous sides proportional. AH similar triangles, rectangles, and **polygons, are to each other as the squares of their homologous sides.** HORARY Circles, hour lines or circles, marking the hours on globes, dials, &c. HORARY Motion, the motion... | |
| Peter Nicholson - 1825 - 372 sider
...first to a similar, and similarly described triangle upon, the second. » PROP, XX. THEOR. Similar **polygons may be divided into the same number of similar triangles, having the** tame ratio to one another that the polygon« have ; and the polygons have to one another the duplicate... | |
| Adrien Marie Legendre, John Farrar - 1825 - 224 sider
...antecedent ABC is to its consequent FGH, or as AB is to FG (219). Therefore the surfaces of similar **polygons are to each other, as the squares of their homologous sides.** • 222. Corollary. If three similar figures be constructed whose homologous sides are equal to the... | |
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