458 ESSAY ON THE 



coefficients of the terms of any power of a Binom ^?i^s 



also mentioned by Viet A, in his Angulares Se6ti ^^nd^ 



before him, pretty fully treated of by Stifel '^ rithmeti^c... 



Integra, fol. 44 andseq. ; where he inferts and makes tbe liJkeJLife ol fuch 

 a table of figurate numbers, in extracting tl . ..; ^;. ^jwers 



whatever. But it was perhaps known much ear ''-^^ - >^,ears 1— -'-- 

 treatifeon figurate numbers by Nicomachus, (fee Malcolm's Hatory^ 

 p. XVIII.) Though indeed, Cardan feems tc 'bribe this difcovery 

 to Stifelius. See his Opus Novum de Propo. .loiiibas Numerorum, 

 where he quotes it, and extrafts the table and its ufe from Stifel's book. 

 Cardan, in p. 135, &c. of the fame work, makes ufe of a like table to 

 find the number of variations or conjugations, as he calls them. Stevi- 

 8VUS, too, makes ufe of the fame coefficient and method of roots as Stife- 

 iius, (See his Arith. p. 25.) And even Lucas be Burgo extra6ls the 

 cube root by the fame coefficients, about the year 1470. But he does 

 not go to any higher roots. And this is the firH mention I have feen 

 of this law of the coefficients of the powers of a Binomial, commonFy 

 called Sir J. Newton*s Binomial Theorem; although it is very evidenfe 

 that Sir Isaac was not the first inventor of it. The part of it prope'-'f 

 belonging to him, feems to be, only the extending it to fractional ind: 

 which was indeed an immediate effect of the general method of d<r:i:o.^ 

 ting all roots hke powers with fra£lional exponents, the Theorem bebg 

 not at all altered. However, it appears, that our author Briggsw^s 

 *V ^*"st who taught the rule for generating the coefficients of .ae 

 , fucceffively one from another, of any powers of a Binotr''-' 

 4iAcis,^endent of thofe of any other power. For having fhe wn, in 



