[ 33 1 ] 
proceeds (as will be {hewn) by a gradual extermi- 
nation of the compofite numbers from the arith- 
metical feries 3. 5. 7. 9. 1 1. &c. infinitely conti- 
nued, its author gave the name of the Sieve. I 
have thought it necelfary topremife thefe remarks, 
to remove a prejudice, which I apprehend many 
may have conceived, as this beautiful and valuable 
edition of Aratusis in every ones hands, that this 
ill-contrived table, the ufelefs work of fome monk 
in a barbarous age, was the whole of the invention 
of the great Eratofthenes, and in jullice to my- 
felf, that I might not be fufpe&ed of attempting 
to reap another’s harveft. 
I now proceed, to give a true account of this 
excellent invention ; which, for its ufefulnefs, as 
well as for its limplicity, I cannot but confider as 
one of the moft precious remnants of Ancient Arith- 
metic. I {frail venture to reprefent it according to 
my own ideas, not obliging myfelf to conform, in 
every particular, to the account of Nicomachus, 
which 1 am perfuaded is in many circumftances 
erroneous. In Eating the principles upon which 
the Operation of the Sieve was founded, he hath 
added obfervations upon certain relations of the 
odd numbers to one another, which are certainly 
his own, becaufe they are of no importance in 
themfelves, and are quite foreign to the purpofe. 
Every thing of this kind I omit: and having Hated 
what I take to have been the genuine Theory of 
Eratofthenes’s method, cleared from the adul- 
terations of Nicomachus, I deduce from it an ope- 
ration of great limplicity, which folves the Pro- 
blem in queftion with wonderful eafe, and which, 
U u 2 becaufe 
