2 50 L1MTTS AND FLUXIONS 



same objection that has been macie of ^the lemma 

 of Newton's Principia. In both instances, also, the 

 error is rather apparent than real. " The first theorem 

 in question states that the two intersecting perpendì- 

 culars to a curve drawn at the ends of *' an infìnitely 

 little portion of it of the first order," *'may be 

 assumed as equal to each other." We wonder what 

 Robins and Maclaurin would bave thought, had they 

 been alive in i8oi and 1805, and read these defini- 

 tions and comments ! What horrible visions would 

 these ghosts of departed quantities bave brought to 

 Bishop Berkeley, had he been alive ! But the nine- 

 teenth century was destined to bring back to British 

 soil stili greater accentuations of infinitesimals. 



T. Newton, 1805 



216. The Rev. T. Newton says in the preface of 

 bis lllustrations of Sir Isaac Newton's Method : ^ 



* ' Every Mathematician now considers the whole 

 doctrine of Prime and Ultimate Ratios in no other 

 light, than as a Doctrine of Limits. " Young 

 readers of Sir Isaac Newton's Principia encounter 

 difficulties because commentators bave made ''use 

 of the terms of Indivisibles, in their explana- 

 tions ; . . . Newton expressly says, that by the 

 ultimate ratios of quantities he means the ratios of 

 their limits. 2 And when he wants to infer the 



^ An Illitstration of Sir Isaac Newton^ s Method of Reasonitì}(. By 

 Prime and Ultimate Ratios. By the Rev. T. Newton, Kector of Tewin, 

 Herts ; late Fellow of Jesus College, Cambridge. Leeds, 1805. 



'^ Seeour§§ 12, 15. 



