[ 33 ° ] 
The Oxford editor hath annexed to his table, to 
explain the ufe of it, fome detached paflages, which 
he hath feledted from the text of Nicomachus, and 
from a comment upon Nicomachus afcribed to 
Joannes Grammaticus. In thefe paflages the dif- 
ference between Prime and Compofite numbers is 
explained, in many words indeed, but not with 
the greateft accuracy; and it is propofed to frame 
a kind of Table of all the odd numbers, from 3 to 
any given limit, in which the Compofite numbers 
fhould be diftinguifhed by certain marks *. The 
Primes would confequently be charafterifed, as far 
as the table fhould be carried, by being unmarked. 
But, upon what principles, or by what rule, fuch a 
table is to be conftrudted, is not at all explained. It 
is obvious that, in order to mark the Compofite 
numbers, it is neceffary to know which are fuch. 
And, without fome rule to diftinguifh which num- 
bers are Prime, and which are Compofite, inde- 
pendent of any table in which they fhall be diftiti- 
guifhed by marks, it is impofiible to judge, whe- 
ther the table be true, as far as it goes, or to extend 
it, if requifite, to a further limit. Now it was 
the Rule by which the Prime numbers and the 
Compofite might be diftinguifhed, not aTable con- 
ftrufted we know not how, that was the inven- 
tion of Eratofthenes,.. to which from its ufe, as 
well as from the nature of the operation, which 
* Nicomachus and Joannes Grammaticus propofe that thefe 
marks fhould be fuch, as fhould not only diftinguifh the com- 
pofite numbers, butlikewife ferve to exprefs all the divifors of 
every fuch number. It will be fhewn, in a proper place, that 
this wai no part of the original contrivance of the Sieve. 
5 proceeds 
