EIVSDEM CENERIS, 183 



dt 



ieda conftante l-—ffzpf' ^t fi propofita fit aequatio 

 71 xdz-\- dx y ( x^ -4- J2* ) m «> fiet P — ^- ^ '\^~^ ^" ^ , po- 

 fitoque z=:tx, erit T := '^^ idcoque / ^ -/T^Tii^i^^^^^fjy 

 fiiit V,x-^U)=zt-\-s erit /=:■=" et ^f — =-^;t££>. 



Qiuire erit /^ —j (-;i:;:7jiz.(H:=:7)^ — S^ /i 4- ^r^, /(^( n-i) 

 s-—n — i). 



§. 41. Qiio tamen vfus calculi §.36' in cafu fpe- 

 ciali app.ueat, fit aequutio propofita dz-{-pzdx — qdx 

 znOy in qua p et q vtcunque in ^ ct .v dantur. Qiiae 

 aequatio cum illa generali dz~{-?dxz=o collata dat 

 ?=pz-q, ex quo fiet B—p, et IR—Jpdx feu R 

 — f-^^'*^. Cum igitur fpdx per quadraturas poflit af- 

 fignari, cognitus ell: vaior ipfius R, idcoque aequatio 

 propofita per e^^'^^ multipHcata fit integrabilis : erit igi- 

 tur ef^^^dz-^-e^^^^^^pzdx-e^^^^^^qdx — O huiusque in- 

 tegralis e^^'^'' zz=:fe^^^'' qdx feu z—e-^P^^^^fe^P^^qdx. 

 DifFerentiari itaque debet £>— /f"^^/^/? -^-^ q ^x pofitis et a - 

 et X variabilibus, et difFerentiale ipfi dz aequale poni, 

 quo fado habebitur aequatio modularis. Pofitis igitur 

 dp—fdx-\-gdactdq — hdx-\-ida prodibit ifta ae^ 

 quatio modular is dz zz: - e~^P^^ {pdx-h d afg dx )fe^P^* 

 q dx -h q dx -\- e-^f''='dafe^'f'^'= ( i dx -j- q dxfg dx ) , feu 

 pofito breuitatis gratia/5'-'f''*</^,v=rT erit dz — — e~^^^* 

 Tpdx-\-q dx -\- ^--^? •'^ dafe^^^^ i dx - e-^^'^'' dafTg dx. 

 Ex qua operatione intelligi potefl;, nd aequationem 

 modularem inueniendam id maxime effe efficiendum , 

 vt in aequatione propofita indeterminatae a fe inui- 

 cem feparentiir. 

 Tom. Fli. Bb AD- 



