[ 33 6 3 



more Com polite numbers were Prime or Compofite 

 with refpecl: to each other. I have many reafons 

 to think, that this was not the cafe. I mall as 

 briefly as poffible point out fome of the chief, for 

 the matter is not fo important, as to juftify my 

 troubling the Society with a minute detail of them, 

 Firft then, in the natural feries of odd numbers, 

 3. $.7. &c. every number is a divifor of lome fuc- 

 ceeding number. Therefore if we are to have 

 ■marks for all the different divifors of every Com- 

 polite number, we muft have a different mark for 

 every odd number. Therefore we mull: have as 

 many marks, or fyftems of marks, as numbers; 

 and I do not fee, that it would be poffible, to find 

 any more compendious marks, than the common 

 numeral .characters. This being the cafe, it would 

 be impracticable to carry fuch a table as Nicoma- 

 chus propoies, and his commentators have iketched, 

 to a lufficient length to be of ufe, on account of 

 the multiplicity of the divifors of many numbers, 

 and the confufion which this circumftance would 

 create*. It is hardly to be fuppofed, that Era- 

 toflhenes could overlook this obvious difficulty, 

 though Nicomachus hath not attended to it. Era- 

 toflhenes therefore could not intend the conftruo 

 tion of fuch a table. 



In the next place, fuch a table not being had, 

 Eratofthenes could not but perceive, that, the 

 determining whether two or more numbers be 

 Prime or Compofite with refpecl: to one an- 

 other, is in all cafes to be done more eafily, 

 by the direct method given by Euclid, than by 



* The number 3465 hath no lef? than 22 different divifors. 



the 



