TEXT-BOOKS, 1736-1741 171 



in the definition of fluxion. Newton makes it a 

 velocity, Simpson makes it a finite distance. On 

 the necessity and wisdom of this change there can 

 readily be difference of opinion. But there can be 

 no denying that Simpson developed his theory of 

 fluxions in a manner almost, though not entirely, 

 free from the objections against fluxions that had 

 been advanced by Berkeley ; infinitely small quan- 

 tities are nowhere used. A short but appreciative 

 review of this text appeared in The Works of the 

 Learned for July, 1737. 



Benjamin AI art in, 1739, 1759 



157. Benjamin Martin was a mathematician, an 

 optical instrument maker, and a general compiler. 

 He was a self-educated man, and at one time taught 

 reading, writing, and arithmetic. His exposition of 

 fluxions, as found in his Eleinents of ali Geonietry ^ 

 and in a later work, is below the standard usually 

 reached by him in mathematica! writing. 



This book, intended as an introduction to modem 

 mathematics, contains in an Appendix an epitome 

 of the doctrine of fluxions. '* Since Fluxions are 

 the very small Increnients and Decrenients of the 

 Flowing Ouantities, or the Velocities of the Motions 

 whereby they increase or decrease, 'tis plain that 

 those Fluxions, or Velocities, themselves may be 

 consider'd as Flowing Quantities, and their Fluxions 

 are call'd Second Fluxions ..." It would seem 



1 nANrEi2METPIA ; or ihe Elements of ali Ceometry. By B. Martin, 

 London, M.DCC.XXXIX. 



