. The cyclopaedia; or, Universal dictionary of arts, sciences, and literature. Encyclopedias and dictionaries. ALGEBRA. falfe ones as foccefTions of the fame (Igns ; which had before biquadratic equation. Des Cartes, after thcfe rcdiiAijiis, in been partly (hewn by Cardan and Viela from the rtlation of order to finipHfy and equations as much as pof. the CO efficients and their figns, and more fully by Harriot, fible, proceeds to give the conilruition of folid and other Hence Des Cartes was led to adopt Cardan's method of hlj;lier problems, or of cubic and higher equations by means
. The cyclopaedia; or, Universal dictionary of arts, sciences, and literature. Encyclopedias and dictionaries. ALGEBRA. falfe ones as foccefTions of the fame (Igns ; which had before biquadratic equation. Des Cartes, after thcfe rcdiiAijiis, in been partly (hewn by Cardan and Viela from the rtlation of order to finipHfy and equations as much as pof. the CO efficients and their figns, and more fully by Harriot, fible, proceeds to give the conilruition of folid and other Hence Des Cartes was led to adopt Cardan's method of hlj;lier problems, or of cubic and higher equations by means changing the true roots to falfe, and the falfe to tiiic, by of parabolas and circles ; obfeiving, that the fnlfe roots are merely changing the figns of the even ternii. He then di- denoted by the ordinatts to the parabola lying on the con- â¢rects his attention to other reductions or tranfmiitations trary fide of the axis to the true roots : and he clofcs the book taught by Cardan, ;ta, and Harriot ; futh as increafing with ilhiftrating thefe conllniftions by various problems Con- or diminiihing the roots by any quantity, taking away the fc- cernin-- the trifertiou of an angle, and the inveftigation of condterm, and altering the roots in any proportion, and thus two or *our mean proportionals. extricating the equation from fraiftions and radicals. Havirg Of the improvements contained in this work, it is ob. obferved (p. 76.) that the roots of equations, both true and fcrved by Dr. Huttun, that Des Cartes, with a view to the fahe, may be cither real or imaginary, which imaginaiy roots more eafy application of equations to the conftruaion of were firlt noticed by Albert Giiard, as in the equation problems, mentions many particulars concerning the nature .x' â + â10 >D o, that has only one real root, viz. and reduftion of equations, and ftates them in his own lan- 2 : he proceeds to the depreffion of a cubic equation to a gnage and manner, which is ufual
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