CARDAN, or CARDANO, Girolamo, Italian philosopher, physician and mathemati cian: b. Pavia, 24 Sept. 1501; d. Rome, 21 Sept. 1576. He was educated from his fourth year in the house of his father. At 20 he went to Pavia to complete his studies, and after two years began to explain Euclid. In 1524 he took the degree of doctor of medicine at Padua and spent the following seven years practising medicine at Sacco. He was sub sequently professor of mathematics and medi cine in Milan (1534). In 1552 he journeyed through Europe. He became professor of medicine at Pavia and at Bologna, where he remained eight years. He was forced to re sign from the university after his imprison ment on the charge of teaching heretical doc trines. Pope Gregory admitted him to the College of Physicians at Rome, where he con tinued until his death. His biographers differ with regard to his religious opinions, but he was lost in cabalistic dreams and paradoxes, and pretended to have a familiar demon from whom he received warnings, etc. All this ex cited the theologians against him, who even accused him of atheism, though the charge Was without foundation. He believed so implicitly in astrology that he drew his own horoscope several times, and ascribed the falsehood of his predictions, not to the uncertainty of the art, but to his own ignorance. His two works, 'De Subtilitate Rerum> (1551) and 'De Varie tate Rerum' (1545) contain the whole of his natural philosophy and metaphysics. Cardan
wrote also on medicine, and his fame as a physician was very great. His highest claims to the gratitude of the learned rest on his mathematical discoveries. Cardan, it is said, was told that Tartaglia had discovered the solution of cubic equations, and obtained the secret from him by stratagem and under prom ise of silence, but published the method in 1545, in his 'Ars Magna.' The honor of giving his name to the invention has remained to him who first made it known, and it is still called the formula of Cardan. It is universally be lieved that Cardan discovered some new cases, which were not comprehended in the rule of Tartaglia; that .he discovered the multiplicity of the roots of the higher equations, and finally the existence of negative roots, the use of which he did not, however, understand.
Besides the works already mentioned there remain also 'Practica Arithmetica Uni versalis> (1539); (De Vita Propria' and 'De Libris Propriis' (1571-75); Geo metria' (1535); We Regula Aliza, Excereton Mathematicorum, Sermo de Plus et Minus) (1540-50). The standard collection of Car dan's works is that of Sponius (Lyons 1663). Consult Morley, 'Jerome Cardan (London 1854); Rixner and Siber, 'Leben und Lehr meinungen beriihmter Physiker am Ende des XVI und am Anfange des XVII Jahrhun derts' (Sulbach 1820); Firmiani, 'Girolamo Cardano, la vita e l'opere' (Naples 1904).