

BINOMIAL THEOREM. 457 



lor/ Ci Aig<;feF^ 5age 319 and 331, that the learned Sir Isaac 



I^'^r.iv,:* ?^ad difcoVir^d it long before: which the doctor fets down 

 i.: this manne 



Let m -be the e;""or-5nt of the power; 



■Then I i X ~ X "3- X -T ^ "T" *'" 



will be the foies of «he UncicB required ; but he doth not tell us how 

 tl- V bund out, nor have I met with the leaft hint of 



it in any author/' 



Thomas Sim SON, alfo, in the 6th se£lion of his Algebra, attributes 

 it without any hefitation to Sir Isaac Newton. At laft, the late Dr. 

 HuTTON, in the 77th page of the Introdu6lion to his excellent Mathema- 

 tical Tables, edition lYth, Ihowed that this Theorem, as far as relates to 

 integers, was known before the time of Sir Isaac, and that his merit con- 

 iifted in the extenfion of it to fradions. The palTage is not very long, 

 and will fave the trouble of a reference, and bring the whole fubjeCl: at 

 once before the reader ; I (hall therefore tranfcribe it, 



** For alfigningthe coefficients of the terms in the multiple cxpreflions, 

 our author (Briggs) here delivers the conftruflion of figurate or poly- 

 gonal numbers, inserts a large table of them, and teaches their several 

 ufes; one of which is, that every other number, taken in the diagonal 

 lines, furnishes the coefRcients of the terms of the general equation by 

 which the fines and chords of multiple arcs are exprefied, which he aiu^ 

 ply illuflrates; and another, that the fame diagonal numbers conftitute the 



3X 



