[ S3* } 
becaufe it is the mold fimple that the theory Teems 
to afford, I fcruple not to adopt as the original 
Operation of the Sieve, though nothing like it is 
to be found in Nicomachus; though, on the con- 
trary, Nichomachus, and all his Commentators, 
would fuggeft an operation very different from it, 
and far more laborious. For the fatisfadtion of 
the curious and the learned, I have annexed 
a copy of fo much of Nicomachus’s treatife, 
as relates to this fubjedt, with fuch corrections 
of the text, as it ftands in the edition of Wiche- 
lius, printed at Paris ann. 1 538, as the lenfe hath 
fuggefted to me, or I have thought proper to adopt, 
upon the authority of a manufcript prelerved 
among thofe of Archbifhop Laud, in the Bodleian 
Library j which, in this part, 1 have carefully col- 
lated. By comparing this with the account which 
I fubjoin r every one will be able to judge how 
far I have done juftice to the invention I have un- 
dertaken to explain. 
PROBLEM. 
l T j find all the Prime Numbers. 
The number 2 is a Prime number ; but, except 2, 
no even number is Prime, becaufe every even num- 
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. 11. 13. 15. 17. 19. 2J. 23. 25. 27. 
39 - 3 1, 33 - 35 - 37 - 39 - 43 * 45 - 47 * 49 - 5 r - &c » 
Every 
