448 



CARDAN. 



Cardan, the deceit. Cardan, indeed, seems to have been the 

 ~y- ' most determined impostor of his times. He ascribed 

 the extravagance of his opinions, and the eccentri- 

 cities of his conduct, to the influence of the celestial 

 bodies. He had the audacity to calculate the nati- 

 vity of our Saviour; and having foretold the time of 

 his own decease, he is said to have starved himself to 

 death, in order to verify the prediction. 



The irregularities of conduct into which Cardan 

 was continually hurried, by the violence and caprice 

 of his temper, became the source of great misery and 

 distress ; and the vices and misfortunes of his chil- 

 dren, fil'led up the measure of his suffering. His 

 eldest son married a woman who possessed neither 

 character nor fortune ; and having killed her by poison, 

 he was condemned to death, and executed in the pri- 

 son at midnight. This distressing event produced a 

 deep impression upon the mind of Cardan, who en- 

 deavoured to justify the murder on the ground of 

 the wife's infidelity, and who maintained that the ven- 

 geance of heaven had followed the judges who pro- 

 nounced sentence upon his son. His other son was 

 also an abandoned character, and his father was un- 

 der the necessity of throwing him into prison, and 

 of cutting off one of his ears, and disinheriting him. 

 The payment of his daughter's dowry, and the cir- 

 cumstance of her having no children, were the only 

 distresses which she occasioned. 



From such a degrading picture, it is pleasing to 

 turn to those marks of genius and talents by which 

 Cardan has perpetuated his name. As a philosopher, 

 he is entitled to no praise, and as a medical writer he 

 is chiefly famed for his industry and fidelity in the 

 collection of facts. The philosophical speculations 

 which he has published in his works De siiblilitali 

 and De Varietate reritm, are the mere ravings of an 

 unfettered imagination ; and if arguments were want- 

 ing to prove that Cardan laboured under a partial in- 

 sanity, we should appeal to these works, as weH as 

 to the whole of his conduct. 



As a mathematician, however, the merits of Car- 

 dan are beyond all praise. In the year 1539, he 

 had completed nine books on arithmetic, algebra, 

 and geometry, under the title of Liber Arlis magnoB ; 

 and when it was nearly printed, having heard ac- 

 cidentally of Tartalea's discoveries in cubic equa- 

 tions, he was extremely anxious to obtain these dis- 

 coveries for insertion in his work. Cardan first ap- 

 plied to Tartalea through the medium of a book- 

 seller, and, along with the most flattering compli- 

 ments, he sent him a number of questions to resolve. 

 Tartalea, however, refused to disclose his rules, 

 which Cardan again attempted to obtain from him 

 by personal correspondence. Finding every effort 

 unsuccessful, Cardan at last endeavoured to gain by 

 cunning what he co"uld not acquire by the most 

 urgent supplication. He wrote to Tartalea, that 

 he had recommended him to his particular friend 

 and patron the Marquis dal Vasto, who was very 

 anxious to see him ; and he invited him to spend a 

 a few days with him at Milan, accompanying the in- 

 vitation, however, with a distinct notification, that 

 such a visit might be useful to Tartalea, and that it 

 would be dangerous to offend the Marquis by a re- 

 fusal. More intimidated by the threat than allured 



by the invitation, Tartalea set out for Milan ; but as Cardan. 

 the Marquis had gone to Vigeveno before his arrival, ^"""V^" 

 he was induced to spend three days with Cardan till 

 the Marquis should return. Cardan employed every 

 artifice to obtain from his guest the secret for which 

 he so ardently longed. " I shall swear to you," says 

 he, " on the holy evangelists, and by the honour of 

 a gentleman, not only never to publish your inven- 

 tions, if you reveal them to me ; but I also promise 

 to you, and pledge my faith as a true Christian, to 

 note them down in cyphers, so that after my death 

 no other person may be able to understand them." 

 To these protestations Tartalea replied, t( If I re- 

 fuse to give credit to these assurances, I should de- 

 servedly be accounted utterly void of belief; but as 

 I intend to ride to Vigeveno to see his excellency 

 the Marquis, as I have been here now these three 

 days, and am weary of waiting so long ; whenever I 

 return, therefore, I promise to shew you the whole." 

 Cardan, however, having renewed his entreaties to 

 obtain the rule before the departure of his friend, 

 Tartalea replied, " I am content ; but you must 

 know, that to be able on all occasions to remember 

 such operations, I have brought the rule into rhyme ; 

 for if I bad not used that precaution, I should often 

 have forgot it ; and though my rhymes are not very 

 good, I do not value that, as it is sufficient that they 

 serve to bring the rule to mind as often as I repeat 

 them. I shall here write the rule with my own hand, 

 that you may be sure I give you the discovery 

 exactly." These verses contained the rule for the 

 three cases 



Tartalea reminded Cardan, at parting, of his obliga- 

 tion to secrecy ; and during a subsequent correspon- 

 dence, in which the latter proposes some difficulties 

 in the solution of cubic equations, Tartalea displays 

 the greatest suspicion that Cardan would betray the 

 secret, and never fails to remind him of the vow 

 which he had made. 



Notwithstanding all these promises so solemnly 

 made, and so frequently repeated, Cardan published in 

 the year 154-5, his tenth book, which contained the 

 whole doctrine of cubic equations, and of course the 

 substance of the rules which he had received from 

 Tartalea. He acknowledges that Tartalea gave him 

 the rule, but without the demonstration, and he as- 

 serts, (see cap. xi.), that by the help of the rule alone 

 he discovered the geometrical investigation. Tartalea 

 complained bitterly of this violation of his promise ; 

 and Cardan defended himself on the ground, that he 

 greatly extended the method of Tartalea, and was 

 therefore entitled to publish his own improvements. 

 A controversial correspondence was carried on be- 

 tween the two mathematicians with the greatest acri- 

 mony, till it was terminated by the death of Tar- 

 talea in 1557. 



Though Tartalea is certainly entitled to the high 

 honour of originality, yet Cardan has the merit of 

 having prosecuted the subject of cubic equations 

 with singular assiduity and success. His tenth book 

 contains rules for all the forms and varieties of cubic 

 equations, with their geometrical demonstrations,; 



