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HISTORY OF ALGEBRA.

TRACT 33.

circrimstantial way: and besides, these will be better ex-plained in a particular manner under the word or article toAvhich each of them severally belongs. It may thereforenow suffice, to enumerate, or announce only in a cursoryivay, the chief improvements and authors on algebra downto the present time.

After the publication of the Geometry of Descartes, agreat many other ingenious men followed the same course,applying themselves to algebra and the new geometry, tothe mutual improvement of them both ; which was donechiefly by reasoning on the nature and forms of equations,as generated and composed by Harriot. Before proceeding■upon these, however, it is but proper to take notice hereof Fermat, a learned and ingenious mathematician, whowas contemporary and a competitor of Descartes, for hisbrightest discoveries, which he was in possession of beforethe geometry of Descartes appeared. Namely, the appli-cation of algebra to curve lines, which he expressed by analgebraical equation, and by them constructed equationsof the 3d and 4th orders ; also a method of tangents, and amethod de maximis et minimis, which approach very nearto he method of Fluxion' or Increments, which they strik-ingly resemble, both in the manner of treating the problems,and in the algebraic notation and process. The particularsof which, see under the proper heads. Besides these, Fer-mat was deeply learned in the Diophantine problems, andthe best edition of Diophantus’s Arithmetic, is that whichcontains the notes of Fermat on that ingenious work.

But to return to the successors of Descartes. His geo-metry having been published in Holland, several learnedand ingenious mathematicians, of that country, presentlyapplied themselves to cultivate and improve it; as Schoo-ten, Hudde, Van-FIeuraet, De Witte, Slusius, Huygens,&c ; besides M. de Beaune, and perhaps some others inFrance.

Francis Schooten, professor of mathematics in the univer-sity of Leyden, was one of 'the first cultivators of the new