| Robert Simson - Trigonometry - 1762 - 488 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 - 492 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 - 534 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 - 552 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... | |
| Euclid, John Playfair - Euclid's Elements - 1795 - 462 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 - 374 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 - 546 pages
...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 Playfair - Mathematics - 1806 - 320 pages
...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... | |
| John Mason Good - 1813 - 714 pages
...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... | |
| 1814 - 760 pages
...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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