i§S DE /A'F;A7T75 CrRFlS 



Qiio fiirto erit acqiutio modularis hnec : kmnz—{hm 



-{-kn-\-i}in)u-\-ik-{-in-i-n)t — sz:zo. 



§. 30. Sit porro r: — 7'( P -+- Q_)* ^.v , vbi P iit fmi- 



(flio n dimenrioniim , Q vero tunclio ;;/ dimenlionnm 



iplarnm a et .v. Qirando igitiir clt fl^Pzi: A^.v-f- JW« 



et d Q_~Q d X -\-T) d a ^ erit ;; P — A .v -H B « et 



m Qziz C .r -f- D a. Diflfcrcntiale antem ipfuis ( P-H Q_ )* 



polito X conftante dinifum per da ert fc(B-4-D)(P-hQ/'~'' 



Hanc ob rem erit dz-[V-{-(lf dx -\- ^ /( P -f- Q)''""' 



( B tf -H D ^ ) «'.r. Cum autcm fit B ^ — « P - A .v et D ^ 



rr:;«Q— C.r, et Adx—d? et Cdx—dQ^ ob a in 



hac integratione conftans , crit dzzz{?-\- Q/ dx-\~ ^ 



J V-\-(^f-^{n?dx-\-mQjlx-xd?-xdq),ku dzzz 



[l±_^naclx_-jaa) d_a p^Q^),_. ^(„^_^ , ^ 



a a 



^ . . ^ adz-i?-\Of(adx-xda)-zda 

 ?dx-\-{mk-\- 1 )Q^.v;. Ponatur ^ , 



— t{ erit «=r/(;zPr/.v-|-;;/Q^.v)(P-f-Q'=— . Quare 

 fi integrale /( n ? dx -f- w Qrt^.v ){?-\-Q^f— pendet ab 

 intcgrali /(P-hQV.v liabebitur aequatio modularis dif- 

 ferentialis gradus primi ^ fm mirius dif!creiitiatio e(t con- 

 tinuanda. Fit autem du— {n?dx-\-mQdx ) (P-hQ)*-' 

 -\- f - ?(«P-4-wQ)(P-hQ)*-.v-h'?/ hr- ?^dx-h{^~k 

 m n -\-7f-^ m n -\- nr) ? Q^dx -\- k ;«'Q^.v)/(P -+- Q^f-'. 

 adu-uda- {n?-\-mQ) i P-j-Q)*^— ' {adx - xda) 

 Et pofito tzz Ya 



eri t t — / ikn^?- dx-\-i^kmn-\- ?i~ - ci ;;; n-\-?n-) ? Q_dx 

 ^knf-Q^dx){?-\-Q^f-\ 



§■ 31- 



