192 LIMITS AND FLUXIONS 



which is capable of being determined." This 

 matter, says Stewart, has been so clearly explained 

 by Newton, *'that the great Dust which has been 

 raised of late about the Whole of this Doctrine, 

 must be owing to Weakness, or some worse 

 Principle " (p. 40). 



William Emerson, 1743 (?), 1757, 1768 



171. William Emerson was a self-taught mathe- 

 matician ; he wrote many mathematical texts which 

 indicate a good grasp of existing knowledge, but not 

 great originality. His Doctrine of Fluxions appeared 

 at London in 1743 (?). We bave before us the third 

 edition, 1768. From it we quote as follows : 



'*The Velocity of the Increase of any generated 

 Ouantity, or the Degree of Quickness (or Slowness) 

 wherewith the new Parts of it continually arise, is 

 called its Fluxion. " 



"The indefinitely small Portions of the Pluent 

 which are generated in any indefinitely small Por- 

 tions of Time are called Moments or Increments." 



**. . . The Moments and Fluxions ought not to 

 be confounded together, since the Moments (being 

 generated by Fluxions) are as difìferent from the 

 Fluxions, as any Effect is different from its Cause." 



The following is given as an axiom : 



" Ouantities, which in any finite Time continually 

 converge to Equality, and before the P^nd of that 

 Time, approach nearer to one another than by any 

 given Difference, do at last become equal." 



" If any should think this not clear enough to 



