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HISTOIlICAr. VIEW OP THE

essential principles on which the analytical relations ofquantity are founded.

The first subject which arrests our attention on surveying the state of science in this period, is the theoryand solution of equations. Those of the first and seconddegree, or simple and quadratic equations, were ob-viously and completely capable of solution in all possiblecases. But it had long been felt that the moment anattempt was made to solve any of higher dimensions, as,for example, those of third degree, or cubic equations,(as by an adherence to the old geometrical analogy theyare still called) there, except in a few obvious cases, nosuch general principle had been assigned as could leadto a solution. To this subject the early algebraists di-rected their researches.

Among those who were earliest in the career of dis-covery, and whose fame will endure latest, we may rankCardan, who was born at Milan in 1501. His characterwas a strange compound of good and ill, of strength andweakness. With great abilities and industry, he wascapricious, false, and vainglorious. And such was hisinfatuation in astrology, that he starved himself to ac-complish the prediction of the day of his death.

Before his time very little advance had been made inattempts at the solution of any equations higher than thesecond degree: except that, about 1508, Scipio Ferreo,professor of mathematics at Bologna, had found out arule for resolving one of the cases of cubic equations ;which was made much more general by Tartalea ofBrescia: but he kept his method a profound secret.The curiosity of Cardan was stimulated; and, aftermany entreaties, and binding himself by oath not todivulge it, he succeeded in extorting from Tartalea hisrule, though without its demonstration. Cardan soonfound out the proof, and extended the rule to a large classof cubic equations. The greatest share of the merit wasthus his own ; but this will hardly excuse him in pro-ceeding to publish the whole (in 1545), utterly disre-garding his solemn compact with Tartalea.