Note n — BOOK V.

Although the Quadrature of the Circle, hath in former Ages exercis’d some of the greatest mathematical Wits; yet nothing has been done in that Way so considerable, as in, and since the Middle of the last Century; when in the Year 1657, those very ingenious and great Men, Mr William Neile, and my Lord Brounker, and Sir Christopher Wren afterwards, in the same Year, geometrically demonstrated the Equality of some Curves to a strait Line. Soon after which, others at Home, and Abroad, did the like in other Curves. And not long afterwards, this was brought under an analytical Calculus: The first Specimen whereof, that was ever publish’d. Mr. Mercator gave in 1688, in a Demonstration of my Lord Brounker’s Quadrature of the Hyperbola, by Dr Wallis’s Reduction of a Fraction, into an infinite Series by Division. But the penetrating Genius of Sir Isaac Newton, had discover’d a Way of attaining the Quantity of all quadrible Curves analytically, by his Method of Fluxions, some Time before the Year 1668, as I find very probable from an historical Account, in a long Letter of Mr. Collins, written in his own Hand, and sent to Richard Townley, Esq; of Lancashire, whose Papers are in my Hands. In that Letter, Mr. Collins saith, That in September 1668, Mr. Mercator publish’d his Logarithmotechnia, one of which he soon sent to Dr. Barrow, who thereupon sent him up some Papers of Mr. Newton’s, [now Sir Isaac;] by which, and former Communications made thereof by the Author, to the Doctor; it appears that the said Method was invented some Years before, by the said Mr. Newton, and generally apply’d. And then he goes on to give some Account of the Method; what it performs in the Circle, &c. what Mr. Gregory had done in that kind, who intended to publish somewhat in Latin about it, but would not anticipate Mr. Newton, the first Inventor thereof; with much more of this Nature. The Design, I find, of that indefatigable Promoter of Mathematicks, Mr. Collins, was to acquaint Mr. Townley, in his Letter, with what had been done; and to get the Assistance of that ingenious Gentleman, towards the compleating a Body of Algebra.