ATTEMPTS AT ARITHMETISATION 231 



Parts," designateci as x, etc. '* Such Things as an 

 Instant, a Point, a Fluxion, she [arithmetic] has 

 nothing to do with. ... 1 have joined Fluxion with 

 Point and Instant, because Fluxion seems to be to 

 Motion, as an Instant is to Time ; which I suppose 

 to be as a Point is to a Line. Motion cannot be 

 conceived without Time and Space ; and when the 

 former runs into an Instant, and the latter into a 

 Point, then it is (as I understand it) that Motion 

 becomes Fluxion. ... In this Sense Fluxion is 

 no more a Part of Motion than a Point is a Part of 

 a Line." His " parts " are finite increments. The 

 part oi xyìsxy -\-yx -\-xy. * ' This Doctrine of Wholes 

 and Parts proceeds upwards from Parts to Wholes, 

 as well as downwards from Wholes to Parts uni- 

 versally " (p. 159). "The Ordinate therefore being 

 x'"y when x"'x expresses the Fluxion of it, the only 

 Meaning I have for x is, that it is the Proportion of 

 a Point to an Instant. And to my Apprehension, 

 a Point may as well be called a last Line, as this 

 called a Velocity." ''I have lately deduced some 

 arithmetical Theorems from arithmetical Principles, 

 which other Mathematicians have drawn from 

 Fluxions of PTuxions, etc. , and these Theorems fell 

 in with my Design." Just how these deductions 

 were made is not explained by the author. 



[ohn LandeUy 1758 



202. John Landen was a self-educated mathe- 

 matician of real mathematical power. Had he had 

 the benefits of University training he might have 



