VOL. XXIX.] PHILOSOPHICAL TRANSACTIONS. 117 



method of doing that in all figures, which Lord Brounker and Mr. Mercator 

 did in the hyperbola alone. Mr, Mercator lived above 10 years longer, without 

 proceeding further than to the single quadrature of the hyperbola. The pro- 

 gress made by Mr. Newton, as to all curves in general, shows that he wanted 

 not Mr. Mercator's assistance. However, for avoiding disputes, he allows that 

 Lord Brounker invented, and Mr. Mercator demonstrated, the series for the 

 hyperbola some years before they published it, and consequently before he him- 

 self found out his general method. 



Mr. Newton, in his letter to Mr. Oldenburg, dated Oct. 24, 1676, mentions 

 the aforesaid treatise of Analysis, in the following manner: " At that very time 

 when Mercator's Logarithmotechnia was published, my friend Dr. Barrow, then 

 professor of mathematics at Cambridge, communicated to Mr. Collins a com- 

 pendium of these series, in which I signified, that the areas and lengths of all 

 sorts of curves, with the superficies and contents of solids, could be determined 

 by given right lines, and vice versa; and I illustrated the said method by divers 

 series." 



In the years 1669, 1670, ]671, and 1672, Mr. Collins gave notice of this 

 compendium to Mr. James Gregory in Scotland, to Mr. Bertet and Mr. Vernon, 

 then at Paris, to Mr. ^Iphonsus Borelli in Italy, and to Mr. Strode, Mr. 

 Townsend, Mr. Oldenburg, Mr. Dary, and others in England, as appears by 

 his letters. Also, Mr. Oldenburg, in a letter dated Sept. 14, 1669, and entered 

 in the letter-box of the Royal Society, gave notice of it to Mr. Francis Slusius 

 at Liege, and cited several passages out of it. And particularly Mr. Collins, in 

 a letter to Mr. James Gregory, dated Nov. 25, 1 669, spake thus of the method 

 contained in it: " Dr. Barrow has resigned his office of reading public lectures to 

 one Mr. Newton of Cambridge, whom he mentions in the preface to his Optical 

 Lectures, as a person of extraordinary genius; for that, before Mercator's 

 Logarithmotechnia was published, he had invented the same method, and 

 applied it to all curves in general, and to the circle in divers ways." And in a 

 letter to Mr. David Gregory, dated August 11, 1676, he mentions it in this 

 manner: " A few months after these books^ viz. Mercator's Logarithmotechnia 

 and Gregory's Exercitationes Geometricae, were published, they were sent to 

 Dr. Barrow at Cambridge ; and the Doctor returned answer, that this doctrine 

 of infinite series was invented by Mr. Newton two years before M. Mercator's 

 Logarithmotechnia was published, and that he had applied it to all curves in 

 general, and the Doctor at the same time sent Mr. Newton's MS. copy." The 

 last of the said two books came out towards the end of the year 1 608, and Dr. 

 Barrow sent the said compendium to Mr. Collins in July following, as appears 

 by three of Dr. Barrow's letters. And in a letter to Mr. Strode, dated July 26, 



