ALOYSII CASIXELLI 



NOVA METHODUS EVEHENDI AD POTENTLOI QUA-MCUMQUE, 

 QUANTITATES POLYNOMIAS. 



X olynomium quodcumque 



ad potestateni quamcuniqne m esiniam evehendnm sit. 

 Principio Canhesii circa series poiialur 



(1 -^a iX-^2x''-\-u^x^-\-a iX^-^-a ■jX^-{-a(^x^-\- ec. m) 



=1 +A ,a:-l-A2x2-4-A3a:3-t-A4x '-t-Aja: s+Aex^-i- etc. 



et sumptis logarithmis habebimus 



m log. (l-f-ajx-t-flix^-f-asx^+a 4x^+0 sx^-i-fljx*-!- etc.) 



=iog. {^+^^x-^-^2x'^-hA^x^-{-\^x*-^-AiX^-i-A.(iX^-^- etc.). 



Differenlialione hujus aequationis, erit, ejeclo comniuni la- 

 clore dsc 



1 -^aiX-^a2x'-~\~a3X'^-^-axX*-i-a^x^-{-a,^x'^-i- eic. 



A,H-2A.,x-f-3A.(.r*4-lA,x''.4-5A5xi4.6Acx5-t-7A7x6+stc. 



1-l-A,x-t-A2X-4-A3x3-J-A,a'-+-A^x^-t-Acx«-+-etc. 



Disponalur haec acqualio secundum poiestates variabilis x, 

 habebimus 



m«|-4-2 ma-2X -4- 3 /«a3 x^ +4r7ia4 X'* -4- 5 m njx' -|-6niag x^-^- etc. 



4-''»A|aiX-f-2mA|a2X--4-3mA|a3x3-(-4mA|aix<-+-5niA,<j5xi-j-cic. 



•+• mA2«|X*-4-2mA2a-2^^-t-3mA203x'-+-4njA2a4x*-H »tc. 



-+- mA3aiX''-H2mA3a2^'+3"»A3rt3x'-f- etc. 



-I- mA4aix*-H2mA,n2J?^-t-eic. 



-y- mAjflix'-f- f'c. 



