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AN EXAMINATION of various Solutions of KEPLER'S Problem^ 

 and a Jhort pradical Solution of that Problem pointed out. By the 

 Rev. J. BRINKLEY, A. M. M. R. I. A. Andrews Profeffor of 

 AJironomy in the Univerfity c/" DUBLIN. — Read Nov. i/?, 1802. 



»»ei-4t'te««»»— 



JTROM the time when Kepler difcovered by the obfervations of Tycho 

 Brahe, that the motions of the planets were performed in elliptical orbits, 

 aftronomers and mathematicians have been continually propofing different 

 methods of obtaining the true from the mean place of a planet. A direft me- 

 thod of folution was long unknown, and even after the improved flate of the 

 analytical art furniflaed a direft folution, or more ftriftly fpeaking, a 

 direft approximation, it was found that indireft folutions are the readieft 

 for praftice. Many indireft folutions have been given, and I cannot but 

 think that an examination of the principal of them, and a comparifon 

 of their different degrees of accuracy, will be confidered both as curipus 

 and ufeful. It is certainly an objeft for curiofity to compare togethei* 

 folutions, feme of which brought to their refpeftive authors, in their 

 day, no fmall credit, and fome of which have fmce been very inaccu- 

 rately appreciated by different writers ; and it is alfo both curious and 

 ufeful to contemplate the prefent ftafe of the analytical art which now 

 fo readily furnilhcs methods of making a comparifon. I know not 

 that this comparifon has before been made, and I have been the 



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