Ybi fcillcet finguli fadores tam niimeratoris , qiiam deno- 

 minatoris continuo eadem quantitate n augentur. Hic 

 autem probe tendendum efl, yeritatem iftius lemmatis fub- 

 fiftere non poffe , nifi fingulae litterae m, «, p et q deno- 

 tent nnmeros pofitiuos , quos tamen femper tanqnam iu- 

 tegros fpedare licet. 



§. 13. Circa has duas formulas integrales, a termino 

 X ~ o vsque ad Jf — i extenfas , duo cafus imprimis feor- 

 fim notari merentur , quibus integratio adu fuccedit , ve- 

 rusque valor abfolute alTignari potefl:. Prior cafus locnni 

 habet, fi fuerit p — n, ira vt formula fit /X x'^^' dx. Po- 



771 rt 



fito enim x^^—j fiet X — ( i — ^ } "■ et x"^"' dx — \dy 



flcque ifia formula euadet n/dj(i—j) " , pariter a ter- 

 mino j' zz: o vsque ad / — i extendenda, quae porro po- 



fito 1 — j — z abit in hanc formulam —'j,/z "■ d z tl 

 termino z—i vsque ad sz: o cxtendendam; eius ergo inte- 



771 



grale manifefto eft — ^ z" -f- ^i ^nde fado z — o valor 

 erit — ,\. Confequenter pro cafu pznn habebimus 



/Xx^-'dx[f,l^:]-^ 



ficque fi fuerit vel p — « vcl q — n , integrale abfolute 

 innotefcit. 



§. 14. Alter cafus notatu dignus eft quoprrw-wr, 

 ita vt formula integranda fit y X j^-""'""' </a-; tum enim, fi 



ponatur .v ( i ~ x'^)"- fiue ■ r— J'? pcfirox— ofiet 



(i - jr^f 

 ^'iiio, at pofito x—i fiet j — cv); tum autem erit 



„n — 77) 



-,71-771 ■y „71— 77» 



•/ 71 — 771 ■'»■ ♦* 



(l_J,«j — 



B a vnde 



