11. T%e 1)oBrme of Comhinations and Altermtlons^ Im* 
proVd and Compleatedy hy Major Edward Thorny^ 
croft. 
IN order to und^rftand what follows, it muft be obfer- 
ved, 
ift. That as ia the notation of Powers, a a a a b b b c c 
is defignd by a* b^ c% and univerfally p times the poticK^ti 
of a, q times the pofition of b, r times thepoficion of c, 
by ap b^ c% fo in things exposfd likewife : ( unlefs where 
'tis propos'd they fhould he all different) which Indices, 
as they have here no relation to Powers, but exprefs only 
the Occurrences of thofe things to which they refpe^tively 
belong 5 I therefore call Indices of Occurrences. 
2dly, That as often as I (hall hereafter mention the 
Combinations or Alternations of the p' qs r* or s% (which 
confider'd by themfelves are capable of no variatioL) I 
mean of thofe things whofe Indices they are. 
gdly, That m is generally put for the whole number of 
things expos'd, whether all different or not, /. e. equal to 
the fum of their Indices 5 and n, for fuch a number of 
them, as each Combination and Alternation muft confift of; 
(unlejs prefuppofed equal) which explains what is hereaf- 
ter meant hy the Combinations and Alternations of m things 
taken n and n 5 or of m things taken m and m^ and the 
like Expreffion, by whatever Symbols the number ot things 
out of which the Combinations and Alternations are to 
be made, or of which they are to confift, may be de- 
Jign!d. 
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