C ) 
Theorem for finding the C .inii.] Kions ani. * ^ ^ 
of ID things takcd n and n univerfally : i.e. vVncci. .1 
confiftof things all diCrent ornot, and whether n be 
^qual to, or lefs than m. 
If n be exprefs'd, according to all the different Forms 
of Combi nation which the things exposed are capable of, 
f p = the higheft Index r = the number of "Jin erery 
and )^ "^^^ liigheft y ^ the numberof q^C form of 
|r = the next higheft ^> = the number of rf Conbi. 
f = the next higheft t / = the number of b jnatlon. 
'A = the number of all Indices not lefs than pi Which are 
)B ^ the number of alllndices not lefs than qf in the 
|C = the number of all Indices not lefs than rf things 
I> the number ot all Indices not lefs than f j Exposed 
&(^. 
and b = c==b + >, d=c+J», cJx 
I fay the number of the Combinations of ra things ta- 
ken n and n, in any one Form of Combination, (hall be 
A X A— I X A— 2; , ^ B -fic- i C — b X C— b— I 
«^x<fc~ 1 xn - 2 i3x/3— .1 ^ y ^ y — I 
n Cfc ^ ^"^ ^ (^c. Continued to fo many Terms ^ 
as there are different Indices in the form of Co mbination ^ 
and each Term to *, jg; &c> places rcfpeftivdy, and i 
this . number multiplyVl into 
X n— I X n— 2 H n x —4. ^ 0-4. x "-.5 x n-^fr ggc. cont^nue<^ to n p'o"ces« 
p-Ji^— SfC'l* X q x q- X X iJc.; 1^ x . x _i ^ Scc.csch Seriei centinucJ to p,q?» » 
(C^^tr. places refpeftively, (hall be the number of their Alter- 
naiions- 
B«it the fum of all rhc: Combinations and Afternii^Gns ^ 
wivich are in every Form ac fh^iil b^- Vm whoie number 
of Combinations- and ; AUernatiou^ ot .m ihings,fakit'^^^^ 
and J2. 
