[ 33i ] 



proceeds (as will be flievvn) by a gradual extermi- 

 nation of the compofite numbers from the arith- 

 metical feries 3. 5. 7.9. 11. &c. infinitely conti- 

 nued, its -author gave the name of the Sieve. I 

 have thought it neceffary to premife 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 fable, the ufelefs work of fome monk 

 in a barbarous age, was the whole of the invention 

 of the great Eratofthenes, and in juftice to my- 

 felf, that I might not be iufpe&ed of attempting 

 to reap another's harvefL 



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 coniider as 

 oneof the moil: precious remnants of Ancient Arith- 

 metic. I mail venture to reprefent it according to 

 my own ideas, not obliging myfelf to conform, m 

 every particular, to the account of Nicomachus, 

 which I am perfuaded is in many circumftances 

 erroneous. In ftating 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 ftated 

 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 fimplicity, which folves the Pro- 

 blem in queftion with wonderful eafe, and which, 

 U u 2 becaufe 



