5+ = 

 ( l -h X -h X X ■+■ X 



* a 



I 



I -4- 2x-f-3 xx-4-4-x'-^- 33: -»- 2x''-+-x 



i-H3X-t-<5xx-+-iox^-+-i2X*-+-i^x'-i- iox*-+-<5j?'-*-3x*-f-x' 

 41 i-f-4X-t-icxx-«-2cx*-+-3i xV4Cx'-t-44X* +-4C x'-»-3i X*-+ ctc. 



i-t-5x+-i 5XX+-35x' +-'^5x*-t-ioix'-^-i3';x*-t-i 5 sx^-f-zssr"-» etc. 

 i-t-6x-4-2ixx-i-5<Jr^-t-i*or*-<--i<5x'-t- etc. 

 etc. etc. 



§. 15. Niinc formuLim propofitam fub h,ac binoniiali : 

 [ r -{-X ' i -h X -}- X X ) ]" rcfeiamiis , eiusquc evoluLio nobis 

 praebet hanc feriem : 



H-Ci/[x( I -f-x^xx)]-^(^)'x*(r-47X-fxx)*-f-etc. 

 cuius teriniiius generalis eft (,^)' x' ( i -4- X -1- x x)". Nunc 

 vero, quid ( i -h X -h X x)"* eft poteftas Irinomialis, erit 



( 1+ X -+- X X )" = I -f- ( ? )' X -4- (^ )=• x X -+- r i )' x^ -h elc. 

 cuius ileruni terminus gencralis eft (j-Y x'^; luidf fi propo- 

 natur potcftas x\ c:^iftenle X — a -h (3, ex hoc mcmbro orie- 

 tur pro hac potcftatc (^)^(-^)'x\ 



5. 16. Cum igitur in evolutionr qnarfita potcftatis 

 3:^ coifllciens fit (~y, cius valor repcrictur, fi, obXra-+j?, 

 omnes valorcs formulae (-J)'(y)' i" unam fummam colli- 

 gantur; quo faflo crit 



(J/zz(^)*(^/-t-(j^,y(^')'-^(;^,)'(^:-=)* 



Sic- 



