CARDAN, JEROME. 



CARDAN, JEROME. 



78 



1544, 'De Judiciis Geniturarum exemplis illustratum,' Nuremburg. 

 1545, 'Ars Magna,' &c., Nuremburg. 1545, 'De Malo recent. 

 Medic, medendi usu,' Venice. 1545, 'De Animi Immortalitate,' 

 Venice. 1547, 'De Supplemento Almanacb,' Nuremburg. 1547, 'De 

 Genituris, Revolutionibus,' Ac., Nuremburg. 1550, 'De Rerum Sub- 

 tilitate,' Nuremburg (again in 1557). 1553, 'An Bain. Articulari 

 Morbo Competat,' Venice. 1554, 'In quadripart. Cl. Ptolemaei. Ejus- 

 dum Geniturarum xii.,' Basel. 1557, 'De Rerum Varietate," lib. xviL, 

 folio, Basel. 1559, ' In Hippocratem de Aere,' &c. Oratio de Medic. 

 Inscitia,' Basel. 1559, 'Opuac. Artem Med. exerceut. utiliasima,' 

 Basel. 1561, ' De Utilitate ex Rebus Adveraia capienda,' Basel. 1562, 

 ' H. Card. Somniorum Synesiorum,' libri iv., Basel. 1563, ' De Pro- 

 videntia ex Anni Constitutione,' Bologna. 1564, 'Comrn. in vii 

 Particulas Aphorism. Hippocratis,' Basel. 1564, 'Ars Curandi parva,' 

 Basel. 1565, 'De Simpl. Medicament. Noxa,' Paris. 1565, 'Da 

 Methodo Medendi,' Paris. 1566, ' Anti-Gorgias, Basel. 1570, 'H. 

 Card. &c. de Proportionibug Numerorum Motuum, 4c. . . . Preterea 

 Artis Magnic siva de Regulis Algebra, liber unus, &c. . . . Item de 

 Aliza Regula liber," Basel. 1573, 'Examea 22 Aegrotorum Hippocratis,' 

 Rome. 



Vi'e have chosen this list as containing all we can certainly ascertain 

 to have been published during his lifetime. We have found the 

 dates mostly in old catalogues, and it is very possible that several may 

 be reprints. The list of his works is of considerable length; but 

 many were not published until after his death ; and some not till the 

 collection in ten volumes, already mentioned, was made. Ue states 

 of himself that he had printed 12S books, had written 40 more, and 

 that 60 authors had cited him. 



Jerome Cardan was bom at Pavia in the autumn of 1501 ; his father 

 was a physician and lawyer at Milan. From two circumstances men- 

 tioned by himself, namely, that his mother and father did not live 

 together, and also that the former endeavoured to procure a mis- 

 carriage, it is presumed that he was illegitimate. At twenty years of 

 age he studied in the university of Pavia ; at twenty-two he taught 

 Euclid in the same place. He went to Padua in 1524, and was there 

 received doctor in medicine in 1525. He was successively professor 

 of mathematics or of medicine at Milan, Pavia, or Bologna, aud waa 

 imprisoned in the latter place (but for what offence is not stated) in 



1570. Having obtained his liberty, he left Bologna in September 



1571, and went to Rome, where he was admitted into the college of 

 physicians, and received a pension from pope Pius V. He died after 

 Oct. 1, 1576, and probably not long after, but when is not well known. 

 He was unfortunate in his family, which consisted of two sons and a 

 daughter. The elder poisoned his wife, and died by the hands of the 

 law ; Cardan protested against the sentence, and rested his son's 

 justification upon the conduct of the wife, who, he affirms, had made 

 his son believe that she was a woman of good fame and fortune, being 

 neither. It is an evidence of the extreme vanity of his character, that 

 not denying the fact for which his son suffered, he left on record his 

 belief that the judges, in passing the sentence, had no other object 

 than to deprive him of life or reason. The younger son turned out 

 badly, and was disinherited by bin father. His daughter, according to 

 his own account, never caused him any other vexation than the pay- 

 ment of her marriage portion. The treatise 'De Utilitate,' &c. was 

 written on the death of his eldest son. 



If Cardan had left nothing but writings on astrology, mathematics, 

 medicine, or morals, he would have passed among the rest as an 

 eccentric genius, with a full share of all the folly and mysticism which 

 pervaded the philosophy of his day. It is to his own account of him- 

 self that we are indebted for the quantity of description and speculation 

 relative to his personal character which is found in all biographies. 

 There may be in this production a touch of the insanity which delights 

 in accusing itself of crimes, or in exaggerating its foibles : as it is, and 

 taking the character of Cardan as he has given it himself, we see a man 

 of unequalled self-conceit, as when he says liu book of logic (written 

 in seven days, but hardly to be understood by any one else in a year) 

 has not a letter either of omission or superfluity ; aud that he is born 

 to deliver the world from a multitude of errors : of little benevolence, 

 as when he avows that his greatest delight in conversation is to say 

 things which he knows will be disagreeable to bis bearers : of no 

 veracity, as witness his assertion that he acquired a perfect knowledge 

 of Greek, Latin, French, and Spanish in twenty-four hours from 

 an edition of Apuleius : of violent temper, instanced by his striking 

 one in the face with a dagger whom he discovered to be cheating him 

 at play : and of little honesty, as evidenced by his justification of his 

 refusal to return a pledge, namely, that it was deposited in presence 

 of no witness. He was also a superstitious free-thinker; attached to 

 his religion, but disposed to treat it in his own way, to an extent 

 which made s worthy divine who claimed, we suppose, to be the 

 adjutant-general of heretics, call him tho " chief of the hidden Atheists 

 of th second class." His refusal to accept an advantageous settlement 

 in Denmark, on condition of apostatising, ought to establixh his right 

 to some principle. His four gifts 1. the power of throwing his 

 oul out of his body (for his words can mean nothing less) 2. his 

 faculty of seeing whatever he pleased with kit eyei, 'oculis, non 

 vi mentis ' 3. his dreams, which uniformly and owevery occasion 

 foretold what was to happen to him ; and 4. his finger nails, which 

 did the lame thing ; to sy nothing of his astrology, hia good demon, 



&c., &c. establish his claim to be tho chief of the visionaries " of the 

 first class." Bayle has drawn the distinction between him and other 

 men of equal talent with some point : he says that "nullum magnum 

 ingenium sine mixtura dementise " is not a maxim which includes 

 Cardan ; for that with him the folly is improved by talent, not the 

 talent adulterated by folly. 



It would hardly have been worth while to have entered into the 

 preceding detail, if Cardan had been a common man. As a physician, 

 his reputation extended through Europe, both as a practitioner and a 

 writer. In 1552 he went to Scotland to the assistance of Hamilton, 

 archbishop of St. Andrews, whom he cured : in the memoirs of Melvill 

 the fact is stated, and Cardan is mentioned by name, with the addition 

 that he was an Italian magician. His medical writings have procured 

 him no lasting reputation : those who follow such pursuits seem to 

 have tacitly consented that Cardan shall be left to the mathematicians ; 

 and it is to his discoveries in algebra that he must be considered as 

 entitled to a prominent place in biography. Before proceeding to 

 consider him in this character, we shall only state that De Thou, who 

 knew him personally, and records that he always dressed in a different 

 manner from the rest of the world, says that it was commonly believed 

 his end arose from starvation, voluntarily undergone, that he might 

 not outlive the time which ho had predicted for his own death. This 

 story has been frequently copied, as if the fact had been positively 

 asserted by the historian, whereas he only speaks of a rumour. 



The 'Ars Magna,' published in 1545, contains the extensions which 

 Cardan made in the solution of equations. Algebra was then an art 

 contained not in formula; but in rules, and extended no further than 

 the methods of solving numerical equations of the second degree. 

 \Ve shall not here enter into the celebrated dispute between Cardan 

 and Tartaglia, further than to specify the part taken by the former. 

 When he was informed of the solution of cubic equations which 

 Tartaglia had discovered, he applied to the latter, March 25, 1539, aud 

 requested he would communicate his method, which Tartaglia declined, 

 intending to reserve the same for the work which he published after- 

 wards in 1554. Cardan then swore "upon the Holy Gospels, and the 

 faith of a gentleman," that he would not only not divulge the secret, 

 but would engage to write it in such a cipher as no one should be abb 

 to read in ease of his death. Tartaglia, upon this assurance, commu- 

 nicated his method. This detail rests upon the authority of Tartaglia 

 himself (' Quesiti et Invention!,' folio, 120), but is amply confirmed by 

 Cardan's subsequent letters, and was never denied by him. Notwith- 

 standing his word thus pledged Cardan published these methods in 

 his ' Ars Magna' (1545), giving the credit of them indeed to Tartaglia, 

 but concealing the promise he had made. 



The communication made to Cardan amounted to the solution, 

 without demonstration, of x* + ax + 6 = 0, in the cases where a and 6 

 are, one or both, negative. Cardan himself supplied the demonstrations, 

 showed how to reduce all equations of the third degree to the preceding 

 form, and how to extract the cube root of the binomial surd quantities 

 which the well-known solution involves. He may be said to have 

 arrived, in detached and isolated theorems, at as much, relative to 

 equations of the third degree, as could afterwards be established, in 

 the time of Des Cartes, for equations of all degrees. He was the first 

 who considered negative roots, and comprehended the nature of the 

 connection between them and the positive roota of other equations ; 

 and he even gave the first idea of a method of approximation. 



The algebra of Cardan, owing to the want of general symbols, is 

 difficult to read ; and Montucla, biassed perhaps in favour of his 

 countryman Vieta, has somewhat underrated his merits. On the other 

 hand we have Cossali ('Origine, &c., dell' Algebra,' Parma, 17U7), 

 whoss object it seems to be to discover something like modern and 

 symbolic analysis in the obscure and verbal rules of the Italians of the 

 16th century. If this learned and estimable writer be considered as 

 holding a brief for Tartaglia, Cardan, and Bombelli, his work may be 

 highly useful For instance, when he shows, by collecting the various 

 cases propounded by Cardan, that the latter had all the element) 

 which if put together would have been the celebrated rule of signs of 

 Descartes, and thence affirms that Cardan was in possession of that 

 rule so far as equations of the third degree were concerned, he forgets 

 that Cardan neither did nor could put those elements together. And 

 when he attributes a symbolic (or, as it was technically called, a 

 specious) notation to Cardan, because the latter sometimes uses a 

 letter to stand for a number in his general enunciations, he does not 

 remember that Euclid has a prior claim, if in that circumstance merely 

 consists the leading feature of the method of Viets. 



There is in the algebra of Cardan considerable power of developing 

 the details of his subject, and of explaining the modifications presented 

 by solutions, but not much inventive sagacity. He states himself that 

 he was originally prevented from attempting the solution of cubic 

 equations by the simple assertion of Lucas di Borgo, in his work on 

 algebra, that the solution was impossible ; thovigh Cossali has shown 

 that, had he even read that author with attention, he would have seen 

 that the assertion was not meant to apply to more than algebra as it 

 then existed. In the case of biquadratic equations he attempted 

 nothing himself, but requested his pupil, Ludovico Ferrari, to under- 

 take the investigation, who accordingly produced tho reduction now 

 know by his name, aud which was published by Cardan. But if wu 

 take the whole extent of the ' Ars Magna,' it is sufficiently obvious that 



