ALGORITHMl SINGVLARIS. 57 



riis etc. combinationibus , quae nullum implicant indi- 

 cem communem j vnde ratio coropofitionis iam fit 

 perfpicua. 



9. Ex hac euolutione iam manifeftum eft , fi 

 indices ordine retrogrado difponantur , eosdem plane 

 prodire numeros inde formatos. Erir fcilicet 



(*, b) =r (b, a) 



(a, b, c) —fe b, a) 



(«, b, c, d) = (</, c, b, a) 



(a, b } c, d, e) = (e, d, c\ b, a). 

 Dummodo ergo ordo indicum detur , fiue fit direclus , 

 fiue retrogradus, perinde eft- vtroque cnim modo idem 

 numerus inde formatus obtinetur. 



10. Hinc ergo fequitur , fore formulas §. 7 hoc 

 modo inuertendo : 



(a, b) z= a (b) -H 1 



(a, b, c) = a (b, c) -f- (c) 



(a,b,c f d) = a(b,c, d)-±-(c % d) 

 (a, b c,d e) — a (b, c, 4, e) -+- (c 7 d> e) 

 atque in genere eiit pro quotcunque indicibus : 

 (a, b, c\ d, etc.) — a (b, c, d, etc ) -+- (c, d s etc.) 



11. Si ergo ponatur : 

 (a % b, c, d, e, etc) zzz A 

 (£, c, d, e y etc.) =: B 

 (c\ d, e, etc.) zz C 

 (d y e, etc.) zz D 

 (e, etc.) = E 



Tom. IX. Nou. Comm. H habe- 



