TEXT-BOOKS, 1736 1741 175 



efifect figured in a controversy carried on against 

 Simpson. 



As regards the lemma given above, we shall see 

 that the same idea is elaborated in detail by 

 Maclaurin in his work and that a short and even 

 more convincing statement than the one given here 

 is found in the later, revised, text of John Rowe. 



From the above lemma, the derivation of the 

 fluxion of xy becomes easy by considering the rect- 

 angle ABCG as made up of two parts AHCB and 

 AHCG, and applying the lemma to each part. 



John Rowe, 1741, 1757, 1767 



159. The first edition (1741) of John Rowe's 

 Doctrine of Fluxions ^ appeared anonymously. A 

 copy in the British Museum has the following added 

 by band after the preface : " This is the first edition 

 of John Rowe's Fluxions. The second came out 

 withhis name in 1757 with alterations and additions, 

 and the third came out in 1767 much improved. " 



In the first edition Rowc begins by stating his pro- 

 gramme: ''To render the Doctrine of Fluxions plain 

 and easy" by explaining their nature *'as deliver'd 

 both by Sir Isaac Newton and by Leibniz." Accord- 

 ing to Newton, ** Pluxion is the same as velocity." 



''Definition II [Foreigners Definition], Quantities 

 are here suppos'd to be generated by a continuai In- 

 crease, as before; and the indefinitely small Particles 



^ An Introdudion to the Doctrine of Fluxions. Revised by several 

 Gentlemen well skiird in the Mathematics. Felicibus inde Ingeniis 

 aperitur IXar—Claiidian. London, M.DCC.XLI, 



