1/2 LIMITS AND FLUXIONS 



that in this statement a fluxion is " very small " and 

 at the same time a *'velocity." A little later the 

 author refers to fluxions as ''in the first Ratio of 

 Augmenta nascentia, " Evidently, in this Appendix, 

 covering twelve pages, the author has not succeeded 

 in presenting a consistent theory of fluxions. 



A fuller exposition was given twenty years later 

 in the System of Mathcmatical InstitutionSy agrecable 

 to the Present State of the Newtonian Mathesis^ 

 by Benjamin Martin, voi. i, London, MDCCLIX. 

 The theory is stili confusing. " Indefinitely small 

 Spaces " (p. 362) are represented by x and j>, which 

 are called the fluxions oi x andjj^, and said to repre- 

 sent the velocities of moving points. Newton is 

 reported to have at first delivered the idea of what 

 Martin calls a fluxion, under the name of momentum^ 

 " a Term used in Mechanics to denote the Quantity 

 of Motion generated by a given Quantity of Matter 

 (A), and the Velocity {a) with which it moved con- 

 jointly. This Momentum therefore was properly 

 represented by (A^). . . . But instead of this 

 mechanical Notation, we now use xx and yy for the 

 Momenta^ or Fluxions. ..." It is seldom that 

 one encounters a more grotesque conglomeration of 

 unrelated ideas than is presented here. Martin 

 gives John Rowe's mode of deriving the fluxions 

 of xy and xyz. 



An Anonynious Text, 1741 



I 58. An Explanation of Fluxions in a Short Essay 

 on the Theo7y. London: Printed for W. Innys, at the 



