203 



The particular method of Newtou will be easily under- 

 stood, after the general rules which have been delivered above. 

 I shall conclude this Essay with transcribing the rules for find- 

 ins; divisors, which he has >riven in his " Universal Arithmetic." 

 His method, in the first of the following passages, will be 

 applicable, as we have seen, to the rational divisors of one 

 dimension ; that in the second, will extend to the rational 

 quadratic divisors, or divisors of two dimensions; the third 

 of those passages gives us a general view of the method of 

 finding divisors of n dimensions, the demonstration of which 

 has been given in the former Chapter of this Essay; the con- 

 cluding paragraph will appear from the observations which I 

 have made in the foregoing page. I shall state all those 

 passages in the original Latin, which is clearer, perhaps, than 

 any English translation could be, on the subject. 



Si quantitas postquam divisa est per omnes simplices di- 

 visores manet composita, & suspicio est eam compositum ali- 

 quem divisorem habere, dispone eam secundum dimensiones 

 literte alicujus quae in e^ est, & pro litera ilia substitue sigil- 

 latim tres vel plures terminos hujus progressionis arithmeticas 

 3, 2, ], 0, — 1, — 2, ac teriainos totidem resultantes una 

 cum omnibus eorum divisoribus statue e regione correspon- 

 dentium terminorum progressionis, posicis divisorum signis 

 tam affirmativis quam negativis. Dein e regione etiam statue 

 progressiones arithmeticas qua^ per omnium numerorum divi- 

 sores percurrunt pergentes a majoribus terminis ad minores 



eodem 



1 



