| John Playfair - 1806 - 311 sider
...COR. 1. In like manner it may be proved that similar four sided figures, or of any number of sides, **are to one another in the duplicate ratio of their homologous sides** ; and it has already been proved in triangles. Therefore, universally, similar rectilineal figures... | |
| Robert Simson - 1806 - 518 sider
...sides, and it has already been proved in triangles. Therefore, universally, similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides.** COR. 2. And if to AB, FG, two of the homologous sides, a h 10. iU t'. third proportional M be taken,... | |
| John Mason Good - 1813
...rectilineal figure similar, and similarly situated to a given rectilineal figure. Prop. XIX. Tbeor. **Similar 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 triangles, having... | |
| Euclides - 1814
...upon a given straight line similar to one given, and so on. Which was to be done. PROP. XIX. THEOR. **SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF** he similar triangles, having the angle B equal to the angle E, and let AB be to BC, as DE to EF, so... | |
| 1814
...though he should have met it before. The demonstration of the 19tb Prop, of Euclid's 6th book, ie " **Similar triangles are to one another in the duplicate ratio of their homologous sides,"** requires the previous or the syn hro nous establishment of Props, vi. 11, v. 16, v. 11, vi. 15., and... | |
| Euclides - 1816 - 528 sider
...sides, and it has already been proved in triangles. Therefore, universally, similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides.** COR. 2. And if to AB, FG, two of the homologous sides, k 10 Def. 5. a third proportional M be taken,... | |
| John Playfair - 1819 - 317 sider
...upon a given straight line similar Co one given, and so on. Which was to be done. ^ PROP. XIX. THEOR. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** D Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC,... | |
| John Playfair - 1819 - 333 sider
...upon a given straight line similar to one given, and so^ou. Which was to be done. PROP. XIX. THEOR. **Similar triangles are to one another in the duplicate ratio of their** homOlogousjides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let... | |
| Euclid, Robert Simson - 1821 - 516 sider
...upon a given straight line similar to one given, and so on. Which was to be done. PROP. XIX. THEOR. **SIMILAR triangles are to one another in the duplicate...ratio of their homologous, sides. Let ABC, DEF be** similartriangles, having theangle B equal to the angle E, and let AB be to BC, as DE to EF, so that... | |
| Euclides - 1821
...aquo, from the proportionality of the sides about 'the «£^.s composing them. 52 PROP. XIX. THEOR. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Assume on the greater base from either extremity a third proportional to that base and the homologous... | |
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