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hook of the Elements, and is to be found in many 

 common treatifes of Arithmetic and Algebra. But 

 to determine, concerning any number propofed, 

 whether it be absolutely Prime or Compoiite, is a 

 Probleoi of much greater difficulty. It feems in- 

 = deed incapable of a direct folution, by any general 

 method ; becaufe the fucceffive formation of the 

 prime numbers cloth not feem reducible to any -ge- 

 neral Jaw. And for the fame reafon, no direct 

 method hath hitherto been hit upon, for conftruct- 

 ing a Table of all the prime numbers to any given 

 limit. Eratofthenes, whofe ikill in every branch 

 of the philofophy and literature of his times, ren- 

 dered his name fo famous among the Sages of the 

 Alexandrian School, was the inventor of an indi- 

 rect method, by which fuch a table might be con- 

 itructed, and carried to a great length, in a fhort 

 time, and with little labour. This extraordinary 

 and ufeful invention is at prefent, I believe, little, 

 if at all, known ; being defcribed only by two 

 writers, who are feldom read, and by them but 

 obfcurely ; by Nicomachus Gerafiims, a (hallow 

 writer of the 3d or 4th century, who feems to have 

 been led into mathematical fpeculations, not fo 

 much by any genius for them, as by a fondnefs for 

 the myfteries of the Pythagorean and Platonic phi- 

 lofophy ; and by Boethius, whofe treatile upon 

 numbers is but an abridgment of the wretched per- 

 formance of Nichomachus *! I flatter my felt" 

 therefore, that a fuccincl account of it will not be 

 unacceptable to tills learned Society. 



* There are more pieces than one of this Niehomachus 

 .errant. That which I refer to is intitled Eto-«Jo>J>j Apt!^^ 



i But 



