 | John Playfair - 1806 - 320 σελίδες
...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... | |
 | Robert Simson - 1806 - 546 σελίδες
...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 - 714 σελίδες
...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 - 560 σελίδες
...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 - 588 σελίδες
...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 - 354 σελίδες
...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 - 574 σελίδες
...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 - 666 σελίδες
...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 - 1046 σελίδες
...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 - 280 σελίδες
...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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Similar polygons may be divided into the same number of similar triangles, having the same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. 
