Notwithstanding all these promises so solemnly made, and so frequently repeated, Cardan published in the year 1545, 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 ac knowledges that Tartalea gave him the rule, but with out the demonstration, and he asserts, (sec cap. xi.) that by the help of the rule alone he discovered the geo metrical investigation. Tartalea complained bitterly of this violation of his promise ; and Cardan defended him self 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 between the two mathematicians with the greatest acrimony, till it was terminated by the death of Tartalea in 1557.
Though Tartalea is certainly entitled to the high ho nour of originality, yet Catalan has the merit of having prosecuted the subject of cubic equations with singular assiduity and success. Ilis tenth book contains rules for all the forms and varieties of cubic equations, with their geometrical demonstrations ; and in every part of it he slims himself eminently skilled in the various branches of algebra. Dr Hutton" has given a very full and interesting analysis of Cardan's work, and a list of his analytical improvements, to which we must refer our readers for farther information on this subject.
The writings of Cardan, which are extremely numer ous, were collected into ten volumes folio, and published at Lyons in 1663. Many of them arc hasty productions, which were printed only to relieve his pecuniary wants.
The following is a complete list of the different works of our author.
Libor de vita propria. _Ephemeris de libris propriis. Dc Soc•atis studio. Oratio ad Cardinalem Alciatum. In Thessalunz Medicum Actio sccunda. Encomium Xeronis. Encomium Podagrx,et /llncmosynon. Dc Orthographia. De Ludo alece. Pialectica. Contradictioncs Logicce de Hyperchon. ..V07'171a vitce consarrinatc, Sacra vo Cain. Proxeneta, scu do Prudentia civili. Dc Preccep as ad Ethos. De optimo vita genere. De Sapicntia. De sumino bono. Dc Consolatione. Dialogus Hieronymi Cardani rt Facii Cardani patris. Dialogus Antigorgias, sett de recta vivendi rations. Dialogus Team, sett de humunis Dialogus do Morte, sett Guglie/mus. IJc Minimis et propinquis. Hymns ad Dcum. De uti brute ex udversis cupienda. De .Aratura. Theognosten lihri V. De Immortalitatr unimarum. Dc Dr Gtmmis et Coloribus. De Aqua. Dc Vitali Aqua, sru Ariz( re. De .1e( tz .Airtura. Problenzatum Sectioncs N'11. Discorso del Vacuo. Sr la qualita Jiuo trupassarr di sub jetto in suljetto. De Fulgure. De Subtilitatt'•. Actio prima in calunzniatorum librorum de Subtilitate. De
Rerun: Varietate. Dc Xunterorum Proprietatibus. Prac tica Arithmetice. Computus minor. Dc R(gulis Alge braFcis. Liber liras magnce. De Aliza Regula. Scrmo de plus rt minus. Esc reton Mathematico•urn Encomi um Geometric. Operatione della Linea. De Propor tionibus numerorum,motztunz, ponderum, sonorum. Della Xatura do e Regole Musicali. De Restitutione temportinz et motztunt celestizi»z. Dc Providentia rx anni constitutions. ?phorismorunz Astronomicorum Segmata VII. Conznzentarii in Ptolonlcum, de astrorum Jur/tells. De septenz erraticarum stellarum Viribus. Dc Inlerroga tionibus Libellus. De Jocliciis geniturarum. De Exem li/is centum geniturarum. Liber duodecim geniturarum. De Revolutionibus. De Supplenzento Ainzanuch. Som niorum Synesiorum Libri. Encomium 111edicince. De Sanitate tuenda. Contradicentiurn Medicorum libri X. De usu ciborum. De Calais, Signis, ac Locismorborum. De Urinis. Ars curandi parva. De Method° tnedendi. De Radice China. De decoctis magnis. De Sarsaparilla. De Oxymelitie usu in pleuritide. De ;Townie. Com znentarii in lil,ruttz Hippocratis, de Aliment°. Comnzenta rii in librum Hipporratis de .4ere, Aquis, et Locis. Com mentarii in Aphorismos Hippocratis. Conclusiones Lapi dibus Galeni, in explicatione Aphorismorum. Apologia ad _dntirrum Canzutiunz. Commcntarii in librum Prognosti comity: Hippocratis. Comment. in librzinz Hippocralts, de Septimestri Partu. Examen XXII. cegrorum Hippocra tes in Epidenz. Consilia varia. Ojzuscula Medica Senilia, sive de Dtntibus liber V. sett de Illorbis articularibus. Floridorum Libri, sive Comment. in Princilienz Hazen. Vita Ludovici Fc•rarii et Alciati. De Arcanis aternitatis. Politica., sett Moralium, liber I. Elemetzta Linguce Grcecce. De Inventione. De Xaturalibus Viribus. De Musica. De hztrgris, Tractatus Arithmeticus. Exposi tio Anatomic Mundini. Commentarii in libros Hippocra tis de Victu in acutis, et in libros II. priores lipident. ejusdent. De Epilepsia. De Apoplexia. De hurnanis civilibus Successionibus. De hunzana Perfectione. De Admi•andis. De Dubiis naturalibus. De Rebus, Factis t rails, et Artificiis. De /zumana Compositione naturalium. De Mirabilibus nzorbis et SynOtonzatibus. De astrc.rum ct temporum Ratione et Divisionibus. De Mathematicis qucesitis. Historic lapidum metallicorunz, et metallorum. Ilistorice animalium. Historic planta•um. De Anima. Dr Dubiis ex Historia. De cluro•um viro•um Vita et Libris. De hominum antiquorunz illustrium Judicio. De usu hominutn, et dignotione roman, tum czt•a, et errore.
See Nandeus Judicium de Cardano ; 11.111cr's Med. Practic. &c.; Eloy's Diet. Historiqzte ; Tessier Eloges des Hammes Savans,p. 97 ; Ilayle's Dict. tticla's Hist. Muthenzat. vol. i. p. 591 ; Hutton Mathenzat.
Diet. ALGEBRA, p. 68. (o)