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HISTORY OF ALGEBRA.

TRACT S3.

improved, and he meant to republish it, with the additionof his method of fluxions and infinite series ; but was pre-vented by the accidental burning of some of his papers.

In 1665 or 1666 Sir Isaac Newton made several of hisbrightest discoveries, though they were not published tillafterwards : such as the binomial theorem ; the method offluxions and infinite series ; the quadrature, rectification,&c of curves ; to find the roots of all sorts of equations, bothnumeral and literal,in infinite converging series; the rever-sion of series, &c. Of each of which a particular accountmay be seen in their proper articles.

In 1666 M. Frenicle gave several curious tacts concern-ing combinations, magic squares, triangular numbers, &c ;which were printed in the early volumes of the Memoirs ofthe Academy of Sciences.

In 1668 Thomas Brancker published a translation of Rho-nius’s Algebra, with many additions by Dr. John Pell, whoused a peculiar method of registering the steps in any alge-braical process, by means of marks and abbreviations in asmall column drawn down the margin, by which each line,or step, is clearly explained, as was before done by Harriotin words at length.

In 1668 Mercator published his Logarithmotechnia, ormethod of constructing logarithms ; in which he gives thequadrature of the hyperbola, by means of an infinite seriesof algebraical terms, found by dividing a simple algebraicquantity by a compound one, and for the first time that thisoperation was given to the public, though Newton had be-fore that expanded all sorts of compound algebraical quan-tities into infinite series.

In the same year was published James Gregory’s Exerci-tationes Geometrica, containing, among other things, ademonstration of Mercator’s quadrature of the hyperbola*by the same series.

And in the same year was published, in the PhilosophicalTransactions, Lord Brouncker’s quadrature of the hyper-bola, by another infinite series of simple rational terms,