DE CALCULO INTEGRALI, i6i 



-^MR^S-V-RS</M. Hoc cft 3 ^^ dx-^^^xdx^g^j^ xxdx 



^qqx'^ dx—^qx^^dx:^ (--i^qdx-^-xdx^iA-Ar^qq-xx) ^M. 



Quare fi fiat M—A-^-ViX-^-Qxx-^-^Dx ' «quatio cano- 



nica mutabitur in 



'^q'' dx—q^xdx--{-gq'^ xxdx—qqx"^ dx--6qx^dx 



zr:—jqAdx-\-Axdx~-^qCxxdx—Cx^dx—2Dx'^dx. ^ 



-^qq^ -|^B H-3^^D -|^D 



~\-2qqC 



Ex collatione terminorum homologorum eliciuntiir 



seftimationes coefiicientum, quales fequuntur. D—^^, 



C—O) Bii:3^^ & Azi:<7. Quare invenitur 



3 

 «=(3^'-r-|-3</j' ) : V (^'-H^^vV-^Arx— .v' ). 



Exempla proxime antecedentia 5, 6, & 7'*"*. niu- 

 tuo fumfi ex Neivtom tradatudej2«^r/r^/^«r/j,quibus Ce- 

 leberr. Audor fcriem fuam Tiieoremate III. pro qua- 

 draturis cxhibitam, illuftravit. Sed quid vetat , quomi- 

 nus hanc feriem ipfiim ex primo noftro theoremate de- 

 rivemus ? Eftergo 



Exemplum S. 



Sint Rir^-t-ys^-l-^si^^^-H^s^^-H &c. dein 2=« 

 -H^5:^-4-fs-«-f-^2^«-H&c. & du-=Sl-'Zz^-'dz. In- 

 venire integralem huius formulae. 



Eft itaque^K— Zs'"'''^^, Xrz:/-i, & per theor.i. 

 acquatio canonica ^«'""Vsizi/M^R-f-R^M. Ponamus 

 iuxta prxcedentia M^Az"* H-Bsj^^^-hCs"^^^^ 

 D2™^3 9_^&c.-f-N, eritque 



Ii/M-?»fAs'^Vz-h(w-H^).fBs'^^-V5j4-(w-f-2^)fCa"^=«-V«4-&c.R//N 



H-w/A ^_(w-H^)/B 



/].^R= H-/^As'"-^«-'^2:-t-2|:/^A3'^2«"V5:-h&c.-f-/N^ 



1 X Ergo 



