CAR'DAN, JEROME, often referred to as HIERONYMUS CARDANUS or GIROLAMO CARDANO (1501-76). An Italian mathematician. born at Pavia, the illegitimate son of Facia Cardan, a jurist. He was at once an astrologer and a genu ine philosopher; a gambler and charlatan, and a true devotee of science. As early as 152:3 Car dun taught mathematics at Pavia. In 1526 he took the degree of doctor of medicine at J'adna, and spent the following seven years practicing medicine at Sacco. Here Cardan met his wife, and is said to have squandered her fortune in gambling. In 1534 he was appointed to the chair of mathematics at Milan. and while holding this post, and at the same time practicing and teach ing medicine, he produced his principal works, 'which are noticed below.
In 1552 he started on an extensive journey through central and northern Europe, and in 1559 obtained the chair of medicine at Pavia, and later at Bologna, remaining there from 1562 until 1570. \Mire living in Bologna he was im prisoned for debt, or on the charge of heresy for having published the horoscope of Christ, and on his release resigned his professorship at the uni versity. He then went to Rome, and was admit ted by Pope Gregory XIII. to the College of Phy sicians. and allowed a pension. He died in Rome in 1576.
The rs Magna (1545), by far the greatest work of Cardan, contains the celebrated solu tion of the cubic equation. The solution had been discovered in 1541 by Tartaglia, who com municated it to Cardan under the most solemn vows of secrecy. Cardan, nevertheless, published the solution under his own name, and hence arose a dispute over the authorship of the discovery. After ten years of controversy, challenge and counter-ehallenge, Tartaglia began publishing his own work (1556), but died before reaching the chapter on the cubic equation. Thus the great est mathematical discovery of the Sixteenth Cen tury came to be known as Cardan's method. The solution, as given by Cardan in geometrical terms, is, briefly. as follows: To solve the equa
tion fix = 20, take two cubes such that the rectangle of their respective edges is 2 and the difference of their volumes is 20: then r is equal to the difference between the edges of the cubes.
In the general equation .r'-i- = q, the rect angle of the edges is a third of and the dif ference of the volumes of the cubes is q. The publication of the Ars Magna stimulated mathe matical research, and hastened the general solu tion of biquadratie equations, of which Cardan himself had solved special cases, as = ,r' 2r' 2x although the credit of producing the first general solution belongs to his pupil Ferrari. Cardan recognized negative roots, which he designated as fictitious; he also ob served that imaginary roots occur in pairs, but discarded them as impossible, and failed to un derstand the irreducible case of the cubic. Ile found the relation of the roots to the coefficients of an equation, recognized that the change of sign of a function implies a solution. and gave a method of approximating the roots of nu merical equations. His discussions of quadratic equations are hardly superior to those of Mo hammed ben Musa.
Besides the A rs Magna, his most important works include: Praetiea Arithmetie• Unirersalis (1539) ; • Dc Subtilitate Berm (1551), and its sequel. Dr Varietal(' Rerun), Artis Magna. sire de Regulis .Ilgebraieis lib. unus (1545); De Fitu Propria and Dc Libris Propriis (1571-75); En comium Geometria' (1535); De Regula Erwreton Mathematicorum. yermo de plus et minus (1540-50). The standard collection of Cardan's works is that of Sponius (Lyons, 1663 ) . Consult : :Morley, Jerome Cardan (Lon don, 1854), and Rixner and Siber. Lebcn end Lehrmeinungen, beriihmter Physiker am Ernie des Si'!. and am infange des XVIL Jahrhun derts (Sulzba•h, 1820).