TRACT 33.

HISTORY OF ALGEBRA.

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which he had been in possession of since the year 1657,when it was announced to the public by Dr. Wallis. LordBrouncker’s series for the quadrature of the circle, hadbeen published by Wallis in his Arithmetic of Infinites, asbeibre mentioned.

In 1669 Dr. Isaac Barrow published his Optical and Geo-metrical Lectures, abounding with profound researches onthe dimensions and properties of curve lines; but particu-larly to be noticed here for his method of tangents, by amode of calculation similar to that of Fluxions, or Incre-ments, from which these differ but little, except in the nota-tion. Of these lectures, the 13th merits the most specialnotice, being entirely employed on equations, and deliveredin a very curious way. He there treats of the nature andnumber of their roots, and the limits of their magnitudes,from the description of lines accommodated to each, viz,treating the subject as a branch of the doctrine of maximaand minima, which in the opinion of some persons, is theright way of considering them, and as far preferable to theso much boasted invention of the generation of equationsfrom each other, explained by Harriot and Descartes.

In 1673 was published, in 2 vols. folio, Elements of Alge-bra, by John Kersey ; a very ample and complete work, inwhich Diophantus’s problems are fully explained.

In £675 were published Nouvcaux Elemens des Mathe-matiques, par J. Prestet, pretre : a prolix and tedious work,which he presumptuously dedicated to God Almighty.

About 1677 Leibnitz discovered his Methoclus Differ-rentialis, or else made a variation in Newton’s Fluxions, oran extension of Barrow’s method, for it is not certain which.He gave the first instance of it in the Leipsic Acts for theyear 1684. He also improved infinite series, and gave asimple one for the quadrature of the circle, in the sameacts for 1682-.

In 1682 Ismael Bulliald published, in folio, his Opus No-vum ad Arithmeticam Infinitorum, being a large amplifica-tion of Wallis’s Arithmetic of Infinites.