i68 LIMITS AND FLUXIONS 



last Ratio, or the Ratio they nihilesce with, is 

 Nothìng. For B^ / E^ is neither B/; nor E^, nor 

 B^ and E^, but a Mark or Expression of their 

 Ratio, which may be expressed as well by any 

 other Character. . . . The Increments are indeed 

 annihilated and gone, but their last Ratio remains, 

 and is as real as any Ratio they ever had " ; . . . 

 they have as real a Ratio at the last Instant of 

 their Existence ; that is, when they are ceasing to 

 be Something, and commencing to be Nothing, as 

 they had at any instant preceding the last Instant 

 of their Existence." . . . ''There is, sometimes, 

 something very strange in the Nature of these 

 evanescing Augments, and it is literally true of 

 them, what Juvenal figuratively says of Man. 



— Mors sola fatetur^ 

 Quantula sunt honiinum corpuscula — 



We know nothing of them till they be dead and 

 gone." 



Of Part III, in which Smith '* demonstrates " 

 Newton's Method of Fluxions, we quote only the 

 last sentence : *' I have made use of infinitely little 

 Quantities, and of a second Point as being next to 

 a first Point ; but this was only for Illustration sake. 

 There is not the least Occasion for any of these 

 Notions in the Demonstration. " 



In the last part of Smith's hook, Berkeley's con- 

 tention, '* No just Conclusion can be drawn from 

 two contrary Suppositions," is answered by the 

 statement, ''This is certainly true, Ì7i sensu com- 

 posito^ but in sensu diviso is intirely false." 



