E S SAYS 



ON 



POWERS AND THEIR DIFFERENCES. 



BY FRANCIS BURKE, Esq. iCc. Sic. 



THE THIRD ALGEBRAICAL ESSAY. 



On finding Divisors ofEquatiojJS. 



INTRODUCTION. 



Sir I. NEWTON has given no proof of the method of 

 finding divisors, which he has deUvered in his " Universal 

 Arithmetic." But, in his second example for finding a bino- 



mial divisor, the proposed is 6t/ — y — 2li/ + 3y + 20, and the 

 quantity with which the division is to be tried, is y + i, or, 

 which he says is the same thing, 3y + 4. And here Saunderson 



supposed, that the expression of the general {oTmx+- was 



adopted by Newton, lest the divisor /r + e should admit a 

 simple divisor, or its terms admit a common measure. But 

 this supposition cannot hold when the rule has set out with 

 supposing the given quantity to have been previously divided 

 VOL. XI, 2 c bj 



