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book of the Elements, and is to be found in many 
common treatii’es of Arithmetic and Algebra. But 
to determine, concerning any number propofed, 
whether it be absolutely Prime or Compolite, is a 
Problem of much greater difficulty. It fee ms in- 
deed incapable of a diredt folution, by any general 
method ; becaufe the lucceffive formation of the 
prime numbers doth not feem reducible to any ge- 
neral law. And for the fame reafon, no diredt 
method hath hitherto been hit upon, for conftrudt- 
ing a Table of all the prime numbers to any given 
limit. Eratofthenes, whole Ikill in every branch 
of the philofophy and literature of his times, ren- 
dered his name lo famous among the Sages of the 
Alexandrian School, was the inventor of an indi- 
rect method, by which fuch a table might be con- 
itrufted, and carried to a great length, in a ffiort 
time, and with little labour. This extraordinary 
and ufeful invention is at prefent, I believe, little, 
if at all, known ; being deferibed only by two 
writers, who are l'eldom read, and by them but 
obfcurely ; by Nicomachus Gerafinus, a lhallow 
writer of the 3d or 4th century, who feemsto have 
been led into mathematical {peculations, not lo 
much by any genius for them, as by a fondnels for 
the myfleries of the Pythagorean and Platonic phi- 
lofophy ; and by Boethius, whole treatife upon 
numbers is but an abridgment of the wretched per- 
formance of Nieliomachus I flatter myfelf 
therefore, that a fuccindl account of it will not be 
unacceptable to this learned Society. 
* There are more pieces than one of this Nichomachus 
•extant. That which I refer to is intitled Eta-afuf/i Ap^r^.n. 
I But 
