 | Euclid, John Keill - 1733 - 444 σελίδες
...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 - 1762 - 488 σελίδες
...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 - 1765 - 492 σελίδες
...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 - 1775 - 534 σελίδες
...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 σελίδες
...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 - 1782 - 476 σελίδες
...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 - 1795 - 462 σελίδες
...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 - 1799 - 374 σελίδες
...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 - 1806 - 546 σελίδες
...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 - 1806 - 320 σελίδες
...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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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
