IX. yi New and Universal Solution of KepLer's Pro- 

 blem. By James lyoRT, Efq. Communicated by John 

 FlayfaIR^ Profejfor of Mathematics and F. R, S. Edin, 



[Read July 7. 1800.] 



I. XT' EPLER, having difcovered the laws that regulate the 

 A\. motion of a planet in its orbit, propofed the following 



problem, for determining the 



true place of a planet at any M 



given time : " To draw a yf^*^ f ^*""N^ 



" ftraight line DE, from an 



^' eccentric point D in the 



*' diameter of a femiciixle 



" AEB, fo that the whole fe- 



" micircle may be to the 



" fedlor ADE, in a given 

 " ratio." 



In refolving this problem, we are to take the qvfadrature o^ 

 the circle for granted ; and therefore, if C be the centre of the 

 circle, and if the fedlor AGM be taken, fuch, that the whole fe- 

 micircle is to the fedlor ACM in the required given ratio, the 

 problem may be otherwife enunciated : " To draw a ftraight 

 " line DE from an eccentric point D, to cut off a fedlor ADE, 

 " that fliall be equal to the given fedlor ACM." 



The given arch AM, or the given angle ACM, is ufually 

 called the mean anomaly ; and the arch AE, or the angle ACE, 

 the anomaly of the eccentric : the problem, therefore, is redu- 

 ced 



