Hoc igitiir modo has iiitcgrationcs Quovsqiic libiicrit coii- 

 tiniiare iicct , duin ex bmis quibtibquc (equcns ope huius 

 rcgulae fdrmatiir , ira vt omni;i h>icc integr.iHa vel a lo- 

 garithiTiis vcl ab arcubus circuianbus pendeant, pronti 

 cotfiidcns c fucrit vei pofitiuus vcl ncgitiuu». Maniferium 

 antem c(\ irtos volores afli^nari non poire, nifi cxponens « 

 fucrit numcrus intcger politiuus. 



§. lo. F,x forma infcrnli modo inuenta, fi pod 

 integrationem fiatuiuur jc - -^^^ *^~'""^' , vnde fit j-o, erit 



■^ V{aa—2 0x-i-c-xx) ^ ^ -^ V [a a—2 b x-i-c xx) 



^ ^ x^-^^dx 



"^ ' -^ V \^aa—2.bx-^exx) ^ 



vnde fi breuitatis gratia ponamus 



x""-' d X _ jc" dx 



J V [aa- ^b x-\-c X x) ~ ' -^ V [aa— 2 b x -^^ cx x) ^' 



.v^-^Va- j^ .y^-^-^ ^A- _ 



•/ V (d « - 2 Z» A-hf jf 7) "~ y(aa-2Z;;f + c xlv) = ^' ^^<^ 



hae quantitatcs P, Q, R, S ita a fe inuicem pendent 

 vt fit 



«flaP = C2«-f- I jZ^Q-^w-f-OcR; 



(?7-|-iVflQ=;(2?j-f-3)^R-(«H-2)<rS; 

 in-\-2)aaK-{2n-^S)l>S~{n-i- 3)cT] 

 {n-{-^)aa S - ( 2 ;;-h 7>T-(«-f-4) fU; 



■ (« + 4)«^T=:(2«-t-9)^U- (n-j-5jc-W; 

 etc, etc, 



I a Ex 



