Dell' Accademia . 8p 



T H E O R E M A. 



B 



n 



y^p t^p n i^p — I 



Inomii ( <if ■♦- « ) evolutio dat <? -h (//>).<? x+. 



n n 



2-3 



a jc' -t- ^-^^ — ^-^ — '-^ —a x^ 



o 



2- 3- 4 



DEMONSTRATIO I. 



P 



JL Onatur (/?4-x) = ,A-^-Bx +.Cx'- +.D x^ -ì-Ex* +• 



F x^ +. &c. , refque eo reda£ta erit, ut coefficlentium in- 

 determinatorum ^, -S, C, &c. valores aequales often- 

 dantur valoribus termi norurn refpondentium in propofi- 

 ta formula .• id vero ita aflequi licet . Evanefcente x in 



ifla aequatione oritur i°. ^ =^ a . Sumatur porro 

 aquationis ejufdem differentlale j prodibit aquatio (f/) 



n 

 « l^p—l 



iyp)' dx (^a-t-x) ~ Bdx j- iC xdx ^ ^Hx^dx ^ 



4Ex^ d X ^ ^ F x'^ d X -t-6ic.j qua divifa per dx^ fado- 



il t^p I 



que3(;=o, prodit 2°. B = (/p). a . Caplatur rur- 



fus differentiaJe aquationis (C/), aflumpto dx conftanti; 



» 



obtinebitur2equatio(X) C^^/^). (//'— i). dx* (^a^x) = 



iCdx^ 4- g. 2. Dxdx- 4- 4- 3. E x"- d x^ +- 5. 4. 



fa:' </.->:* 4- &c. , qucG fi dividatur per dx"- , ac deinde 



M affa- 



