( 19^^ ) 
- Firfl:, Then 'tis evident, rbar cuofe Combinations, w4iich 
are in differenC forqnis, differ from each other. 
Again, Tis evident that the Conbinations of m things, 
as a^' b d? e'^ f'l g'J h^ i^, &c. (the Indices fimply confi- 
der'd) taken n and n, in a form wherein are p« q^and f, 
(liallbe equal to the number of the Combinations ot the p'* 
which are in the things exposci, taken .tand multiply'd 
into the number of the Combinacions of the q» taken /3 and d 
multiply 'd into the number cf-the 'Combinations of the r* 
taken y md y, 
Butbecaufe p and all leflcr Indices are comprehended in 
every Index which is greater than rhemfelves 5 therefore, is 
A to the number ot p« vvhich are in the things exposy, 
andior the fame* reafon, would B — the number of the 
q', ^ and C the number of r' ; But the number of the p*, 
which are in every form of Combination, is = « 5 there- 
fore is B ^ to the number of q^ 3 alfo becaufe the 
number of p and q^ t6gether, which are in every form of 
Combination, . wherein there are q% is = <t -t- ^ = b • 
therefore is G — b = to the number of r% and fo on, how 
many foever were the different uidices in any form of' Com- 
bination. * ^ 
But (by Lem. 5thJ the number of the Combinations of 
the p', which are ia the things expos'd, whofe number is 
A, taken ^ and a,is - VTTZTTTTir^ contina'd to 
replaces, and the number of the Combinations of the q\ 
whofe number is B--<*, taken ^ and^, is ^ —T'^J — "^TTi 
X 2 continued JO /2 places, and the number 
of the Combinations of t|ie p, whole number is C — b> 
taken > and is '^9 ^ ^ ''^^^:^_i zz l continued tp y 
places Q;E*D. But 
