TRACT 33.

history of algebra.

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geometry. He translated Descartes’s Geometry out ofFrench into Latin, and published it in 1649, with his commen-tary on it, as also Brief Notes of M. de Beaune; both ofthem containing many ingenious and useful things. And in1659 he gave a new edition of the same, in two volumes,with the addition of several other ingenious pieces : as, twoposthumous tracts of de Beaune, the one on the nature andconstitution, the other on the limits of equations, showinghow to assign the limits between which are contained thegreatest and least roots of equations, extended and com-pleted by Erasmus Bartholine : two letters of M. Hudde onthe reduction of equations, and on the maxima and minima ofquantities, containing many ingenious rules; among whichare some concerning the drawing of tangents, and on theequal roots of equations, which he determines by multiply-ing the terms of the equation by the terms of any arithme-tical progression, 0 being one of the terms, the equation iscommonly depressed one degree lower ; also a tract of VanHeuraet on the rectification of curve lines; the elements ofcurves by De Witte ; Schooten’s principles of universal ma-thematics, or introduction to Descartes’s geometry, whichhad before been published by itself in 1651 ; and to the endof the work is added a posthumous piece of Schooten’s (forhe died while the 2d vol. was printing) intitled Tractatusde concinnandis demonstrationibus geometricis ex calculo alge-braico. Schooten also published, in 1657, ExercitationesMathematics, in which are contained many curious alge-braical and analytical pieces, among others of a geometricalnature.

An elaborate commentary on Descartes’s Geometry wasalso published by F. Rabuel, a Jesuit; and James Bernoulli,enriched with notes, an edition of the same, printed at Basilin 169—.

The celebrated Huygens also, among his great disco-veries, very much cultivated the algebraical analysis : andhe is often cited by Schooten, who relates divers inventions©f his, while he was his pupil.