52 METH. INTEG FORM. DIFFERENT. RATION. 



fridor = 1-^ px -^ qxx realis , qui fit prodinfliim cx 

 his imagin:irii5 ( i -f- r.v) ( i -+-J.v) , cxilkntc r-\-s = 

 p ct rs — q. His ad paragr. 41. rcnocatis crit R rr 



( — i)**:— 2n(— J.)"'i:z — in fiibfidinm vocatis 



qiiac §.28. fiint tnidita. Simili modo cft Srz— i-^^ — j 



vndc cx fadlore i-H p.v-f-^-V-V orictur ilVa intcgralis pars 

 ( f_r )'":;:; f-jr-") dx-\-rs ((-r)'''-"':^i-.0'^'-"'-').v</.v 

 J zn[i-\-px-\-qxx) 



cft Tero r - t±m:^ et i ^f^^ 

 Formetiir hinc fcrics , ciiius tcrminus gcncralis fitrr(-r)* 

 ►l-(-j)'', ciusque tcrmini ita progrcdicntur 

 1^3 4 



ponatur huius lcriei tcrminus, cuius indcx cll zn — jn—i 

 — M ct tcrminus fcqucns cuius indcx cft ~ 2 « — ;/; fit 

 n: N , habcbitiuquc iltud intcgralc 



— NV.v-+-M<7.v</.v 



Jzn[i-\-px-\-qxx) 

 qnod pcr logarithmos ct arcus circulares dat : 



->-?,/(. +p.v + ?.v.v) - siS A «"S '-^'^? . 

 at ex natura lcricrum rccurrcntium M ct N ita a lc in- 

 \iccm pcndcnt , vt fit N'-hMNp-i- Ar^=: 

 -^"-'"-r/)/)-4^)fcuN = -";-f(4^-p/))(<7=''-'^'-'^' ) 

 Cum crgo fit 2 N -f- M/)— y( 4*7 -/)/))( 4^'"-"'-'- M') crit 



intcgralc formulac J~y^,^^^% = 



cft.]uc f^\ — ±l tti::^-:^) ) -f- ( t:!^p±.al ) 



vbi 



