AEQVATIONIS DIFFEREMTIALIS. 231 



a'ddy-{g-VVdydx^gkaydx'-dx\^f~^ -f 



R 



{f — e){j—i} 



} 



U—e){i~J) 



a'ddy-~(i ■^k)d^dydx-\-i kaydx^zzdx-(r—^ 1 ^?^ - - 



) 



a'ddy-{f-^g)a'dydx^fgaydx-dx\^-^-^-\~ —-. 



a(f — e) 



T 



e){e — i) 

 ' a{i — e)' 



et fi haec operatio vlteriiis continuetur, inuenietur 

 denique 



a V — jS^ _(.f— .p-.f)R _^ V 



^ {e-j){e.i)^ ^j-ey-{f^i)i a{j~e)(j—.iy 



_ (^i -.e— /)T j Y • 



(r_e)^(z_/)3 ' a(z_eXi— j)3 J 



ratio autem inueniendi V et Y, , patet ex §. §. 6 

 et p. Sinniliter fi propofita fit aequatio difFerentia- 

 lis fexti gradus , in qua ipfi m hi valores corape- 

 tunt , c^eJ^J^k et affiimcum fit f-g^ i~k nec non 



cx -cx 



P— N^CF+yN" X^Ji')erit huius aequationis in- 

 tegrale completum 



^y — l . 1 Q^ ^ R(-(/-cy/ -e) -H(/-c)f /- J4-f/-e)( f-f)) 



H/ - {c.e){c~fy(c~i)^^(e-c)(e-fy(e.iy {f-cy(jJ7)Tj^T' 



a^ . I T(;(z— c)(i — e ) _|_ (? — c )( z —j>i^ 'i^e)(i—f )) 



~ a\g-c)(g-e)(g~i)'' (i — oy{i — ey{i—j)3- 



, Y ^ 



nr a(i—c)(i—eyo —j)^' 



Denique fi aequatio difFerentialis cuius quaeritur 

 integrale , fit (exti gradus eiusque indolis , mx. valo- 

 xes ipfiu tn fint iidem ac in cafu proxime praece- 

 denti , eo tantum cum difcrimine, quod iam pona- 

 tur i — k~Cf obtinebitur per integrationem ayzr. 

 A^Q.-4-B'R-i-CT + D^V-i-E/Y + F^Y" in qua 



aequa- 



