| Robert Simson - Trigonometry - 1762 - 466 pages
...given ftraight line fimilar to one given, and fo on. Which was to tx? done. PROP. XIX. THE OR. xiiLAR **triangles are to one another in the duplicate ratio of their homologous** fides. Let ABC, DEF be fimilar triangles having the angle B equal to the angle E, and let AB be to... | |
| Euclid - Geometry - 1765 - 464 pages
...all equilateral and equiangular figures are alike deferred upon any right lines. PROP. XIX. THE OR, **Similar triangles are to one another in the duplicate ratio of their homologous** fides. Let the trianges A B. c, DEF be fimilar, having the angle B equal to the angled ; and let AB... | |
| Robert Simson - Trigonometry - 1775 - 520 pages
...a given ftraight line li« milar to one given, and- fo on. Which was to be done. PROP. XIX. THEO R. **SIMILAR triangles are to one another in the duplicate ratio of their homologous** ftdes. Let ABC, DEF be fimilar triangles having the angle B equal to the angle E, and let AB be to... | |
| Euclid - 1781 - 520 pages
...upon a given ftraight line ;.milar to one given, and fo ou. Which was to be doue. PROP. XIX. THEO R. **SIMILAR triangles are to one another in the duplicate ratio of their homologous** fides. Let ABC, DEF be fimilar triangles, having the angle B equal to the angle E, and let AB he to... | |
| John Playfair - Euclid's Elements - 1795 - 400 pages
...given ftraight line fimilar tct one given, and fo on. Which was to be done. S PROP. XIX. THEO R. IMILAR **triangles are to one another in the duplicate ratio of their homologous** fides. Let ABC, DEF be fimilar triangles, having the nngle B equal to the angle E, and let AB be to... | |
| Alexander Ingram - Trigonometry - 1799 - 351 pages
...fimilar to CDKFE : and fo on. Which was to be done. PROP. BooK V|. PROP. XIX. THEOR. V>rv-vJ IMILAR **triangles are to one another in the duplicate ratio of their homologous** fides. Let ABC, DEF be fimilar triangles, having the angle B equal to the angle E, and let AB be to... | |
| Robert Simson - Trigonometry - 1806 - 518 pages
...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 similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
| John Playfair - Euclid's Elements - 1806 - 311 pages
...described upon a given straight line similar to one given. 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 two similar triangles, having the angle B equal to the angle E ; and let AB be to BC,... | |
| Euclides - 1814
...third, so is any triangle upon the first to a similar and similarly described triangle upon the second. **PROP. XX. THEOR. SIMILAR polygons may be divided into...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... | |
| 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... | |
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