IX. A New and Universal Solution of Kepler's Pro- 

 blem* By James Ivory, Efq. Communicated by John 

 PLAfFMR, Profeffbr of Mathematics and F> R, S. Edin* 



[Read July >] . 1800.] 



1. T7" EPLER, having difcovered the laws that regulate the 

 JLjL. 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 



" ftraight line DE, from an 

 eccentric point D in the 



" diameter of a femicircle 



" AEB> fo that the whole fe- 



" micircle may be to the 



" fector ADE, in a given 



B 



" ratio." 



In refolving this problem, we are to take the quadrature of 

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

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

 micircle is to the feclor 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 feclor ADE, 

 " that fhall be equal to the given feclor 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 



