TEXT-BOOKS, ly 7,6-1741 157 



both sides of the equation Xfo-]-fXo = èo by 0. 

 However, in the exposition given on p. 50 he is 

 more careful and divides by while is an incre- 

 ment, and obtd.ìns f±-\-±y-\-J^:i;o = v. Then he says : 

 " Imagine the Quantity to be infinitely dimin- 

 ished, or, which is the same thing, the Quantity 

 xy to return back again into its arising State ; then 

 the Quantity ±yo, in this Case, into which is multi- 

 pHed, will vanish ; whence we shall have xy-\-yji'=v 

 for the Fluxion of the Quantity proposed. " Hodgson 

 foUows Newton closely and permits the variable to 

 reach its limit. 



Thomas Bayes, 1736 



153. An anonymous pamphlet of 50 pages, on 

 the Doctrine of Fluxions,^ has been ascribed to Rev. 

 Thomas Bayes. This author contributed in 1763 to 

 the Philosophical Transactions a meritorious article 

 on the doctrine of chances. 



The pamphlet of 1736 represents a careful effort 

 to present an unobjectionable foundation of fluxions. 

 *'The fluxion of a flowing quantity is its rate or 

 swiftness of increase or decrease. " Let «, b,x^ and 

 y be flowing quantities, let A and B be permanent 

 quantities \\{ a\ b = h.'^x : B=Fjj/, during any time T, 

 and at the end of that Time, a^ b, x^ y ali vanish ; 

 then . . . the ratio of A to B is the last ratio of the 

 vanishing quantities a and b (p. 13). This definition 

 is *' in efifect the same" as that given by Newton. 



^ Introduction to Doctrine of Fluxions and Defence of the Mathe- 

 maticiaus agaitist . . . t/ie Ana/j'st, 1736. 



