| Euclid, John Keill - Geometry - 1733 - 444 pages
...Similar "Triangles are in the duplicate Ft ofortion of their homologous Sides. LET ABC, DEF, be fimilar **Triangles, having the Angle B equal to the Angle E ; and let AB** be to BC as DE is to EF, fo that BC be the Side homologous to £ F. I fay, the Triangle ABC, to the... | |
| 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
...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
...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
...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 Keill - Geometry - 1782 - 476 pages
...Similar Triangles are in the duplicate Proportion of their homologous Sides. LET ABC, DEF, be fimilar **Triangles" having the Angle B equal to the Angle E ; and let AB** be to BC, as DE is to EF, fo that BC he the Side homologous to E F. I fay, the Triangle ABC, to the... | |
| 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... | |
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