APPENDIX. 437 



solution of this less difficult problem &quot; will find difficulties 

 almost as insurmountable as in the great fundamental 

 problem of astronomy ; &quot; and adds that, after making many 

 fruitless attempts, he had at last been led to a solution by 

 the accident of an error into which he had fallen in his in 

 vestigation. What he proposes is to find the cases in which 

 the curve is algebraical ; there being, according to the con 

 ditions, an infinite variety, most of them transcendental. 

 He considers, however, that if this case of two bodies in 

 fixed centres, and in the same plane with the body at 

 tracted, should be incapable of solution, the general pro 

 blem must prove still more so. Nothing can exceed the 

 clearness of his investigation ; and the ingenious subtlety 

 of the contrivances by which he facilitates the reduction 

 of his differential equations to those of a lower degree. 

 Of this Lagrange expresses great admiration, who, in 

 giving a solution of the case in some respects more ex 

 tended, but in others less, became fully sensible of the 

 difficulties of the process, and whose investigation is less 

 luminous than his great predecessor s. Euler reduces his 

 investigation to the integration of the equation 



IL d x v d y 



V x H- x* *Jy + y* 



and obtaining the relation between the angles made by the 

 two radii vectores with the axis. It is clear that La- 

 grange s solution is obtained by another course altogether. 



No. V. LEIBNITZ S DYNAMICAL TRACTS. 



EARLY in 1689, about a year and a half after the pub 

 lication of the Principia, there appeared in the Acta Eru- 

 ditorum, of Leipsic, two papers of Leibnitz, entitled, 

 &quot; G. G. L. Schediasma de Resistentia Medii et Motu pro- 

 jectorum gravium in medio resistente,&quot; and &quot; Tentamen 



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