Of KEPLER'S PROBLEM. 



223 



are fufficient, in all cafes whatever, for computing the eccentric 

 anomaly, when the mean anomaly is given. They embrace 

 the problem in its fulled extent, and, in point of univerfality, 

 nothing more is to be wifhed for. 



Thus, then, we have a general and direct method of deter- 

 mining the motion of a body defcribing an- elliptic orbit r whe- 

 ther the eccentricity of the orbit be fmall or great. The me- 

 thod is fo extenfive, as even to comprehend the cafe, when the 

 elliptic orbit, having become indefinitely flattened, the motion 

 of the body is no longer in a curve, but in a flraight line, tend- 

 ing to the centre of forces. (Vide Prin. Math. lib. 1. feci. 7. 

 prop. 32. et 36. J 



13. In order to illuftrate the method of computation required 

 in the rules that have been inveftigated, I fhall now fubjoin two 

 examples. I have felected, for this purpofe, two problems re- 

 lating to the circle, taken from a work of M. Euler, (Int. in 

 Analyf. Inf. lib', xi. cap. 22. prob. 4. et 5.) where they are refolved 

 by the method of trial and error* 



Example t. Prob. To draw a chord, AC, from, the extremity 

 of the diameter of a femieircle, that fhall divide the femicircle 

 into two equal parts. 



Take D, the centre of the 

 circle, and draw DE perpen- 

 dicular to AB : It is mani- 

 feft, that the fedor BDE will 

 be equal to the fe£or BAC ; 

 and that BE, being the mean 

 anomaly, BG will be the ano- 

 maly of the eccentric. We 

 have here, then, ni z± 90° 

 and e == 1 : and we muft compute by the rule in Art. to. 



F f 2 - 1. To 



