of Infinitesimals in England. 329 



manner which would lead any one to suppose that he had never 

 held it. In the new preface, wi'itten about 1704, he says, Quan- 

 titates Mathematicas non ut ex partibiis quam minimis constantes, 

 sed ut motu continito descriptas hie considero : and again, Errores 

 quam minimi in rebus mathematicis non sunt contemnendi. So far 

 we have nothing more than vei'ba de prascnti : not so, however, 

 in incidi paulatim Annis 1665 et 1666 in Methodum Fluxionum 

 qua hie usus sum in Quadratura Curvarum. And yet there is 

 something like a recognition of some one having used infinitely 

 small quantities in Fluxions, contained in the following words : 

 volui ostendere quod in Methodo Fluxionum non opus sit figwas 

 infinite parvus in Geometriam introducere : nothing is wanted 

 except an avowal that the so7ne one was Newton himself. The 

 want of this avowal was afterwards a rock of offence. Berkeley, 

 in the Analyst, could not or would* not see that Newton of 

 1687 and Newton of 1704 were of two different modes of thought. 

 He arrays the infinitely small moments of the Principia, and 

 their rejection in comparison of finite quantities, against the de- 

 claration of the Quadratura Curvarum, that the smallest possible 

 errors must not be neglected. The defenders of Newton got 

 over this palpable contradiction in cveiy way but the true one, 

 namely, the avowal of a change of system. 



Further, we see a return to the allowance of infinitely small 

 quantities in 1713, in the second edition of the Prm«)j2fl. Before 

 I noticed the letter of May 1714', quoted in a preceding page, all 

 I could do was to feel thankful that the meaning of a moment in 

 this second edition was not to be settled by me. After the de- 

 claration of 1704, and the changes of language in the scholium, 

 I could but suppose that the principia nascentia of the second 

 edition were not those of the first : nevertheless, what they could 

 be except infinitely small, I had no power to imagine : I have 

 now made it clear that infinitely small quantities were still re- 

 tained. I may notice in passing, that there is something like 

 an impression among us that infinitesimals are repugnant to the 

 Enghsh taste and mode of thought, and that from the beginning 

 they were looked upon with dislike and suspicion. This it fully 

 appeal's was not the case : no mathematical novelty ever found a 

 readier acceptance among us. 



* Dishonesty must never be insinuated of Berkeley. But the Analyst 

 was intentionally a publieation involving the principle of Dr. Whateley's 

 argument against the existence of Buonaparte ; and Berkeley was strictly 

 to take what he found. The Analyst is a tract which could not have beeu 

 written except by a person who knew how to answer it. But it is singular 

 that Berkeley, though he makes his fictitious character nearly as clear as 

 aftenvards did Whatelcy, has generally 1)ecn treated as a real opponent of 

 fhixions. Let us hope that the arch Archbishop will fare better than the 

 arch Bishop. 



