[ 53* 1 



Secaufe it is the moft fimple that the theory feems 

 to afford, 1 fcruple not to adopt as the original' 

 Operation of the Sieve, though nothing like it is 

 to be found in Nieomachus ; though, on the con- 

 trary, Nichomachus, and all hi& Commentators, 

 would fugged: an operation very different from it, 

 and far more laborious. For the fat-isfaction of ; 

 the curious and the learned, I have annexed. 

 a copy of £o much of Nicomacrms's treatife, 

 as relates to this fubjecl:, with fuch corrections 

 of the text, as it ftands in the edition of Wiche- 

 lius, printed at Paris ann. 1538, as the fenfe hath 

 fuggefled tome, or I have thought proper to adopt, 

 upon the authority of a manufcnpt preferved; 

 among thofe of Archbifhop Laud, in the Bodleian- 

 Library ; which, in this part, I have carefully col- 

 lated. By comparing this with the account which. 

 I fubjoin, every one will be able to judge how 

 far I have done juftice to the invention I have un- 

 dertaken to explains 



P R OFLE M. 

 'to find all the Prime 'Numbers, 



The number 2 is a Prime number ; but, except 2, 

 no even number is Prime, becaufe every even numr 

 ber,. except 2, is divifible by 2,. and is therefore 

 Compofite. Hence, it follows, that all the Prime 

 numbers, except the number 2, are included in 

 the feries of the odd numbers, in their natural or- 

 der, infinitely extended • that is, in the feries 



3 



• 5- 



7- 



9- '■ 



[i. i 



E 3- 



*5- 



17. 



19. 



21. 23. 



25. 27,. 



29. 



&> 



33 



>U> 



■37- 



39- 



41, 



,43. 



45. 



47. 49- 



51. &c» 

 Every 



