C 337 ] 
the method of the Sieve. And he could not mean, 
to apply this method to a problem, to which ano- 
ther was better adapted. 
Ladly, Eratofthenes could not mean, that the 
method of the Sieve fhould be applied to the find- 
ing of all the poflible divifors of any Compofite 
number propofed, becaufe he could not be unac- 
quainted with a more ready way of doing this, 
founded upon two obvious Theorems, which could 
not be unknown to him. 
The Theorems I mean are thefe, 
i ft. If two Prime numbers multiply each other » 
the number produced hath no divifors but the two 
prime fadlors. 
2 d. If a Prime number multiply a Compofte num- 
ber , and likewife multiply all the divifors of that 
compofite fever ally, the numbers produced by the mul- 
tiplications cf thefe divifors will be divifors of the 
number produced by the fir f multiplication : And the 
number produced by the fir (l multiplication will have 
no divifors , but the two fadlors , the divifors of the 
Compofite fadior, and the numbers made by the multi- 
plication of thefe divifors by the Prime fadior fever ally. 
The method of finding all the divifors of any 
Compofite number, delivered by Sir Ifaac New- 
ton in the Arithmetica Uni verbal is, and by Mr. 
Maclaurin in his Treatife of Algebra, may be 
deduced from thefe propofitions, as every ma- 
thematician will eafily perceive. This method 
requires indeed that the lead prime divifor fhould 
be previoufiy found ; and, if the lead prime di- 
vifor fhould happen to be a large number, as it 
is not affignable by any general method, the 
v ol. LXIJ, X x itwe < 
