PRINTED BOOKS, ETC, BEFORE 1734 39 



by De Morgan, it may have been Craig's manu- 

 script that suggested to Newton the need of making 

 bis own fluxions accessible to the public. At any 

 rate, in 1693 there appeared the account of fluxions 

 in Wallis's Algebra. [See Addenda, p. 289.] 



55. Abraham De Moivre, a French mathemati- 

 cian who in 1688, after the revocation of the Edict 

 of Nantes, carne to London, contributed in 1695 to 

 No. 216 of the Philosophical Transactions (London) 

 an article in which he uses x, j>, x, y, and lets both 

 ''fluxion" and "moment" stand for things infin- 

 itely small. In the same number of the Transac- 

 tions, the astronomer Edmund Halley has an article 

 on logarithms in which he uses infinitely small 

 ratiunculce and differentiolce, but neither the nota- 

 tion of Leibniz nor that of Newton. In 1697, David 

 Gregory used in No. 231 of the Transactions x ^nd 

 speaks of " fluxio fluxionis " without, however, ex- 

 plaining bis terms. 



56. Patio de Duillier, a Swiss by birth, who had 

 settled in London and become member of the 

 Royal Society, wrote in 1699 a treatise, Lincee 

 brevissimi dcscensus investigatio geometrica, uses 

 fluxions as infinitely small quantities. This publi- 

 cation is noted as containing a statement which 

 started the Newton-Leibniz controversy on the 

 invention of the Calculus. 



57. It is remarkable that Roger Cotes, in 1701, 

 when an undergraduate at Trinity College, Cam- 

 bridge [Newton's own College], wrote a letter on 

 mathematica! subjccts, in which x is used as 



