fURIN V. ROBINS AND PEMBERTON 125 



pression something similar to this. Surely here no 

 one vvill pretend, that an infinite number of terms 

 can in strict propriety of speech, and without a 

 figure, be said to be capable of being actually 

 summed up and added together. " Robins makes 

 the only direct reference that was niade in this 

 debate to Zeno's paradoxes. He mentions Achilles 

 and the Tortoise, but in a manner devoid of interest. 

 Referring to the line which Jurin supposes traced in 

 one hour, Robins says : " Perhaps it may be easiest 

 understood by comparing the present point with 

 the old argument against motion from Achilles and 

 the Tortoise. It is impossible to pursue in the 

 imagination their motion by the means proposed 

 in that argument to the point of their meeting, 

 because the motion of each is described by the 

 terms of an infinite progression." Robins does 

 not seem fully to realise that Achilles and the 

 Tortoise present a case in which a variable reaches 

 its limit. 



135. The editor of the Republick of Letters 

 permitted the two disputants to continue their 

 wranglings in an Appendix to the September issue.^ 



Philalethes's attempt to represent to the imagina- 

 tion the actual equality at which the inscribed and 

 circumscribed figures will arrive with each other, and 

 with the curvilinear figure, is criticised by Robins 



^ Ali Appendix to the Present State of the Republick of Letters for 

 the Moìith of September y 1736. Being Remarks on the Remainder of 

 the Considerations relating to Fluxions, etc.^ that was piiblished by 

 Philalcthes Cantabrigiensis in the Republick of Letters for the last 

 Month. To which is added by Dr. Pemberton a Postscript occasioned by 

 a passage in the said Considerations. London, 1736. 



