[ 33° ] 



The Oxford editor hath annexed to his table, to 



explain the ufe of it, fome detached paflages, which 

 he hath felecled from the text of Nicomachus,- and 

 from a comment upon Nicomachus afcribed to 

 Joannes Grammaticus. In thefe paffages the dif- 

 ference between Prime and Compofite numbers is 

 explained, in many words indeed, but not with 

 the greateft accuracy; and it is propofed to frame 

 a kind of Table of all the odd numfciers,, from 3 to 

 any given limit, in which the Compofite numbers 

 fhould be diftinguifhed by certain marks*. The 

 Primes would confequently be charadterifed, as far 

 as the table mould be carried, by being unmarked. 

 But, upon what principles, or. by what rule, fuch a 

 table is to be conftructed, is not at all explained. It 

 is obvious that, in order to mark the Compofite 

 numbers, it is neceflary to know which are fucho 

 And, without fome rule to diftinguifh which. num- 

 bers are. Prime, and which are Compofite, inde- 

 pendent of any table in which they fhall be diftin— 

 guifhed by marks, it is impoffible to judge, whe- 

 ther the table be true, as far as it goes* or to extend: 

 it, if requifite, to a further limit. Now it was. 

 the Rule by which, the Prime numbers and the 

 Compofite might be diftinguifhed, not aTable con- 

 ft rucked we know not how, that was the inven- 

 tion of Eratofthenes, to. which from its ufe, as, 

 well as from the nature of the operation, which 



*■ Nicomachus and Joannes Grammaticus propofe that thefe 

 marks mould be fuch, as mould not only diftinguilh. the com- 

 pofite numbers, butlilcewife ferve to exprefs all the divifors of 

 every fuch number. It will be fhewn, in a. proper place, that 

 this was no part of the original contrivance of the Sieve. 



£ proceeds 



