300

HISTORY OP ALGEBRA.

TRACT 33.

In 1683 Tschirnausen gave a memoir, in the Leipsic Acts,concerning the extraction of the roots of all equations in agenera] way ; in which he promised too much, as the methoddid not succeed.

In 1684 came out, in English and Latin, 4to, ThomasBaker’s Geometrical Key, or Gate of Equations Unlock'd;being an improvement of Descartes’s construction of allequations under the 5th degree, by means of a circle andonly one and the same parabola for all equations, using anydiameter instead of the axis of the parabola.

In 1685 was published, in folio, Wallis’s Treatise of Alge-bra, both Historical and Practical, with the addition of seve-ral other pieces ; exhibiting the origin, progress, and ad-vancement of that science, from time to time. It cannot bedenied that, in this work, Wallis has shown too much par-tiality to the Algebra of Harriot. Yet, on the other hand,it is as true, that M. de Gua, in his account of it, in theMemoirs of the Academy of Sciences for 1741, has run atleast as far into the like extreme on the contrary side, withrespect to the discoveries of Vieta; and both these I believefrom the same cause, namely, the want of examining theworks of all former writers on Algebra, and specifyingtheir several discoveries; as has been done in the courseof this tract.

In 1687 Dr. Halley gave, in the Philos. Trans, the con-struction of cubic and biquadratic equations, by a parabolaand circle ; with improvements on what had been done byDescartes, Baker, 8cc. Also, in the same Transactions, amemoir on the number of the roots of equations, with theirlimits and signs.

In 1690 was published, in 4to, by M. Rolle, Traite d'Al-gebre ; in 1699 Une Methode pour la Resolution des Problemesindetermines ; and in 1704 Memoires sur Vinverse des tangents;and other pieces.

In 1690 Joseph Raphson published Analysis ACquationumUniversalis ; being a general method of approximating tothe roots of equations in numbers. And in 1715 he publishedthe History of Fluxions, both in English and Latin.