t 33 6 ] 
more Compofite numbers were Prime orCompofite 
with refpeCt to each other. I have many reafons 
to think, that this was not the cafe. I fhall as 
briefly as poflible point out fome of the chief, for 
the matter is not fo important, as to juflify my 
troubling the Society with a minute detail of them. 
Firft then, in the natural feries of odd numbers, 
3. 5.7. &c. every number is a divil'or of lome fuc- 
ceeding number. Therefore if we are to have 
marks for all the different divifors of every Com- 
pofite number, we muff have a ditferent mark for 
every odd number. Therefore we muft have as 
many marks, or fyftems of marks, as numbers; 
and I do not fee, that it would be poflible, 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 fketched, 
to a fufficient 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 beTuppofed, that Era- 
toflhenes could overlook this obvious difficulty, 
though Nicomachus hath not attended to it. Era- 
tolfhenes therefore could not intend the conftruc- 
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 
o 
Prime or Compofite with refpeCl to one an- 
other, is in all cafes to be done more eatily, 
by the direCt method given by Euclid, than by 
* The number 3465 hath no lef? than 22 different divifors. 
the 
