8 DISSERTATION SECOND. [partii. 



known to him, and applied to investigation as early as 1665 

 or 1666. 1 Independently of that authority, we also know, 

 on the testimony of Barrow, that soon after the period just 

 mentioned, there was put into his hands by Newton a manu- 

 script treatise, 2 the same which was afterwards published 

 under the title of Analysis per JEquationes Numero Termino- 

 rum Lifinitas, in which, though the instrument; of investiga- 

 tion is nothing else than infinite series, the principle of flux- 

 ions, if not fully explained, is at least distinctly pointed out. 

 Barrow strongly exhorted his young friend to publish this 

 treasure to the world ; but the modesty of the author, of 

 which the excess, if not culpable, was certainly in the pre- 

 sent instance very unfortunate, prevented his compliance. 

 All this was previous to the year 1669; the treatise itself 

 was not published till 1711, more than forty years after it 

 was written. 



For a long time, therefore, the discoveries of Newton 

 were known only to his friends, and the first work in which 

 he communicated any thing to the world on the subject of 

 fluxions, was in the first edition of the Principia, in 1687, in the 

 second Lemma of the second book, to which, in the disputes 

 that have since arisen about the invention of the new analy- 

 sis, reference has been so often made. The principle of the 

 fluxionary calculus was there pointed out, but nothing ap- 

 peared that indicated the peculiar algorithm, or the new 

 notation, which is so essential to that calculus. About this 

 Newton had yet given no information ; and it was only from 

 the second volume of Wallis's Works, in 1693, that it be- 

 came known to the world. 3 It was no less than ten years 



1 Quadrature of Curves, Introduction. 



2 Com. Epist,. No. I. II. III. Lc. 



3 Wallis says, that he had inserted in the English edition of 

 his book, published in 1685, several extracts from Newton's 

 JMters, " O missis multis aliis inibi notatu dignis, co quod spe rave- 



