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The Book of the Great Art was not published till six years after Cardan had become the sharer of Tartaglia's secret, which had thus had ample time to germinate and bear fruit in the fertile brain upon which it was cast. It is almost certain that the treatise as a whole leaving out of account the special question of the solution of cubic equations must have gained enormously in completeness and lucidity from the fresh knowledge revealed to the writer thereof by Tartaglia's reluctant disclosure, and, over and beyond this, it must be borne in mind that Cardan had been working for several years at Giovanni Colla's questions in conjunction with Ferrari, an algebraist as famous as Tartaglia or himself. The opening chapters of the book show that Cardan was well acquainted with the chief properties of the roots of equations of all sorts. He lays it down that all square numbers have two different kinds of root, one positive and one negative, vera and ficta: thus the root of 9 is either 3. or
His most judicious remarks differ from the remarks of a really philosophical historian, as a sum correctly cast up by a bookkeeper from a general expression discovered by an algebraist. The former is useful only in a single transaction; the latter may be applied to an infinite number of cases. This opinion will, we fear, be considered as heterodox.
A man who understands the four fundamental rules of arithmetic, aided by a little good sense, shall amass prodigious wealth in trade, shall become a Sir Peter Delme, a Sir Richard Hopkins, a Sir Gilbert Heathcote, whilst a poor algebraist spends his whole life in searching for astonishing properties and relations in numbers, which at the same time are of no manner of use, and will not acquaint him with the nature of exchanges.
He took fire with unexampled rapidity; he seemed unable to tear himself away from the symbolic art; an hour's lesson occupied the whole evening; and the original two was soon increased to four, and then to five. I bade him beware of female blandishments. "The first thing you know, you'll be falling in love with the algebraist," said I. "Don't say it, even in jest," he cried.
If, then, before the art of multiplying the productions of the human mind existed, the doctrines of a philosopher in manuscript or by lecture could diffuse themselves throughout a literary nation, it will baffle the algebraist of metaphysics to calculate the unknown quantities of the propagation of human thought.
It is true that a is commonly supposed to equal 10, but there are exceptions, and these may reduce it to 8, or 3, or 0; b also popularly means 10, but being chiefly used by the algebraist as a "moral" value, you cannot do much with it in the addition or subtraction of mathematical values; c also is quite "summary," and if you go into the details of which it is made up, many of them may be wrong, and their sum total equal to 0, or even to a minus quantity.
There is no Algebraist nor Mathematician so expert in his science, as to place entire confidence in any truth immediately upon his discovery of it, or regard it as any thing, but a were probability.
He took fire with unexampled rapidity; he seemed unable to tear himself away from the symbolic art; an hour's lesson occupied the whole evening; and the original two was soon increased to four, and then to five. I bade him beware of female blandishments. "The first thing you know, you'll be falling in love with the algebraist," said I. "Don't say it even in jest," he cried. "She's a lady I revere.
He will simply allude, in conclusion, to the performances of the Mysterious Foundling, as exhibiting perfection hitherto unparalleled in the Art of Legerdemain, with wonders of untraceable intricacy on the cards, originally the result of abstruse calculations made by that renowned Algebraist, Mohammed Engedi, extending over a period of ten years, dating from the year 1215 of the Arab Chronology.
Busy calculation and restless labor appear at first to be the grand elements of American life; mirth is apparently excluded, as the superfluous members of his equations are eliminated by the algebraist.
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