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 fulleft extent, and, in point of univerfality, 

 nothing more is to be wiflied for. 



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

 mining the motion of a body defcribing an- elliptic orbit, 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 longef in a curve, but in a ftraight line, tend- 

 ing to the centre of ;fprces_. (l^ide Prin. Math. lib.i./eB.j. 

 prop. 32. et 36. J _ ^'^'- "■- 



1 3. In order to Illuftrate the method of computation required 

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

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

 lating to the circle, taken from a work of M. Euler, (I/it. in 

 Analyf. Inf. lib', xl. cap. 22. prob. 4. et ^.) 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 femieirck, that fliall divide the femicircle 

 into two equal parts. 



Take D, the ceiiffe of the 

 circle, and draw I>E perpen- 

 dicular to AB : It is mani- 

 feft, that the fedor BDE will 

 be equal to the fedlor BAG ; 

 and that BE, being the mean 

 anomaly, BC will be the afto- 

 maly of the eccentric. We 

 have here, then, wz" rz go"^ 

 and 6=1: and we muft compute by die rule in Art. to. 



F f 2 ' I. To 



