46o ESSAY ON THE 



2sit'^*'^^ asid directly as the afcending nui^-^bers fn^ mr-^i , m-'-i. 

 m— 3, e... 1, in the firft column A; and tb^it xoulequenHy fchoiV' 

 coefficients are found by the continual multiplicstiou of thefe fradion': 



T» ~2~» ^r'» ~^""> p ^^1^" ^s ^^^ very 1 ^^orem as u ftanas is 



this day, and as applied by Newton to roots <■. iractional exponents, 

 as it had before hten ufed for integral power This Xheojem then 

 being thus plainly taught by Br. i cos about the year i6oo, it is Curpiifing 

 how a man of such general reading as Dr. Wa lli s was, coul^ poiTibl? be 

 ignorant of it, as he plainly appears to be by the ^ ^ . -i: of hi,. ... 



gebra, where he fully afcribcs the invention to Newton, and<ldds, that 

 he himfeif had formerly fought for fuch a rule but without fuccefs : or 

 how Mr. John Bernouilli, not half a century fince, could himfeif 

 lirfi: difpute the invention with Newton, and then give the discovery of 

 it to M. Pascal, who was not born till long after it had been taught by 

 Briggs, ■ See Bernouilli's works, vol. 4. pa. 173. But I do not won- 

 der that Briggs*s remark was unknown to Newton, who owed almofl 

 every thing to genius and deep meditation^ but very little to reading i 

 and I have no doubt that he made the difcovery himfeif, without 

 any light from Briggs, and that he thought it was new for all powers 

 in generals, as it was indeed for roots and quantities with fractional and 

 irrational exponents^" ' 



Thus far Dr. Hutton. Mr. Reuben Burrows in the lid volume 

 of the Asiatic Refearches, Appendix No. V. fufpe61;s that this rule was 

 known to the Hindus. I am now about to fiiow, that it v/as alfo known 

 to the Arabians, It is to be found in two of their Arithmetical books 



