CARDAN (or, in the Italian form of the name, CAEDANO), GIROLAMO (1501-1576), famous as a mathematician, a physician, and an astrologer, born at Pavia, September 24, 1501, was the illegitimate son of Fazio Cardano, a learned jurist of Milan, himself distinguished by a taste for mathe-matics. After a sickly childhood and a stormy boyhood, during which he received a very irregular education, he was sent to the university of Pavia, and subsequently to that of Padua, where he graduated in medicine. He was, however, excluded from the College of Physicians at Milan on account of his illegitimate birth, and his first endeavours to establish himself in practice had so little success that he and his young wife were at one time compelled to take refuge in the workhouse. It is not surprising that his first book should have been an exposure of the fallacies of the faculty. A fortunate cure of the child of the Milanese senator Sfon-drato now brought him into notice, and the interest of his patron procured him admission into the medical body. About this time (1539) he obtained additional celebrity by the publication of his Practice of Arithmetic, a work of great merit for the time, which indirectly led to his renown as a mathematician by engaging him in a correspondence with Nicolo Tartaglia, an ingenious calculator who had discovered an important improvement in the method of cubic equations. This discovery Tartaglia had kept to himself, but he was ultimately induced to communicate it to Cardan under a solemn promise that it should never be divulged. Cardan observed this promise in publishing his arithmetic, but when, several years afterwards, the isolated rule of Tartaglia had developed itself in his mind into a principle capable of transforming algebraical science, he thought himself justified in disclosing it as the ground-work of his own comprehensive treatise on algebra, which appeared at Nuremberg in 1545. This memorable volume marks an era in the history of mathematics, being the first in which the principle of cubic equations was fully ex-plained, and the first example of the application of alge-braical reasoning to geometrical problems. Its publication naturally involved Cardan in a violent controversy with Tartaglia, and it must be admitted that his conduct cannot be strictly justified, notwithstanding his ample acknow-ledgment of his obligations to his original instructor. Two years previously he had published a work even more highly regarded by his contemporaries, his celebrated treatise on astrology. This will hardly be enumerated in our day among his titles to fame, but it would be exceedingly unjust to regard it as a proof of superstition or weakness of mind. As a believer in astrology Cardan was on a level with the best minds of his age; the distinc-tion consisted in the comparatively cautious spirit of his inquiries and his disposition to confirm his assertions by an appeal to facts, or what he believed to be such. A very considerable part of his treatise is based upon observations carefully collected by himself, and, it must in candour be owned, seemingly well calculated to support his theory so far as they extend. If the testimony is nevertheless quite inadequate to its purpose, it must in fairness be considered that the proposition of the influence of the heavenly bodies on human affairs appeared to Cardan's contemporaries almost a truism. From this point of view it may be understood that the book should have been intended by the author as a contribution to natural science, and should be almost entirely free from the superstitious whims and hallucinations which, while leaving his faculties as a thinker and a natural philosopher almost unaffected, fre-quently misled him in the affairs of practical life. Nume-rous instances of his belief in dreams and omens may be collected from his writings, and he especially valued him-self on being one of the five or six celebrated men to whom, as to Socrates, had been vouchsafed the assistance of a guardian daemon.
Cardan's authorship may have interferedwith his medical practice, and he himself ingenuously confesses that he and his family were mainly supported during a considerable part of this period by the complaisance of a Milanese patrician, who allowed him to win of him at play. The sudden loss of this resource reduced him for a time to penury, from which he was extricated by receiving the appointment of professor of medicine at Pavia. The publication of his works on algebra and astrology at this juncture gave him a European renown, and procured him flattering offers from Pope Paul III and the king of Denmark, both of which he declined. In 1551 his reputa-tion was crowned by the publication of his great work Be Subtilitate Rerum, which, crude and fanciful as it may now appear, in his own age embodied the soundest physical learning of the time and simultaneously represented its most advanced spirit of speculation. It was followed some years later by a similar treatise De Varielate Rerum, the two making in effect but one book. A great portion of this is occupied by endeavours, commonly futile, to explain ordinary natural phenomena, but its chief interest for us consists in the hints and glimpses it affords of principles beyond the full comprehension of the writer himself, and which the world was then by no means ready to entertain. The inorganic realm of Nature he asserts to be animated no less than the organic; all creation is progressive development; all animals were origin-ally worms; the inferior metals must be regarded as conatus naturae towards the production of gold. The indefinite variability of species is implied in the remark that Nature is seldom content with a single variation from a customary type. The oviparous habits of birds are explained by their tendency to favour the perpetuation of the species, precisely in the manner of modern naturalists. Animals were not created for the use of man, but exist for their own sakes. The origin of life depends upon cosmic laws, which Cardan naturally connects with his favourite study of astrology. The physical divergencies of mankind arise from the effects of climate, and the variety of human circum-stances in general. Cardan's views on the dissimilarity of languages are much more philosophical than usual at his time ; and his treatise altogether, though weak in particular details, is strong in its pervading sense of the unity and omnipotence of natural law, which renders it in some degree an adumbration of the course of science since the author's day. It was attacked by J. C. Scaliger, whom Cardan refuted without difficulty.
The celebrity which Cardan had acquired led in the same year (1551) to one of the most interesting episodes of his life, his journey to Scotland as the medical adviser of Archbishop Hamilton of St Andrews. The archbishop was /supposed to be suffering from consumption, a complaint which Cardan, under a false impression, as he frankly admits, had represented himself as competent to cure. Failing to meet his patient at Lyons as had been arranged, he was induced to continue his journey to Scotland. He was of great service to the archbishop, whose complaint proved to be asthmatical; but the principal interest attaching to his expedition is derived from his account of the disputes of the medical faculty at Paris, and of the court of Edward VI. of England, particulars which he had an opportunity of observing in going and returning. The Parisian doctors-were disturbed by the heresies of Vesalius, who was beginning to introduce anatomical study from the human subject. Cardan's liberality of temper led him to sympathize with the innovator. His account of Edward. VI.'s disposition and understanding is extremely favourable, and is entitled to credit as that of a competent observer without bias towards either side of the religious question. He cast the king's nativity, and indulged in a number of predictions which were effectually confuted by the royal youth's death in the following year. His impressions of England seem to have been very pleasant.
Cardan had now attained the summit of his prosperity, and the rest of his life was little but a series of disasters. His principal misfortunes arose from the crimes and calamities of his sons, one of whom was an utter reprobate, while the tragic fate of the other overwhelmed the father with anguish. This son, Giovanni Battista, also a physi-cian, had contracted an imprudent marriage with a girl of indifferent character, Brandonia Seroni, who subsequently proved unfaithful to him. The injured husband revenged himself in the Italian fashion with poison ; the deed was detected, and the exceptional severity of the punishment seems to justify Cardan in attributing it to the rancour of his medical rivals, with whom he had never at any time been on good terms. He exerted himself greatly as his son's advocate, but to no purpose. The blow all but crushed him; his reputation and his practice waned ; he addicted himself to gaming, a vice to which he had always been prone ; his mind became unhinged, and filled with distempered imaginations. He was ultimately banished from Milan on some accusation not specified, and although the decree was ultimately rescinded, he found it advisable to accept a professorship at Bologna (1563). While resid-ing there in moderate comfort, and mainly occupied with the composition of supplements to his former works, he was suddenly arrested on a charge not stated, but in all pro-bability heresy. Though he had always been careful to keep on terms with the ;Chnrch, the bent of his mind had been palpably towards free thought, and the circumstance had probably attracted the attention of Pius V., who then ruled the Church in the spirit, as he had formerly exercised the functions, of an inquisitor. Through the intercession, as would appear, of some influential cardinals, Cardan was released, but was deprived of his professorship, prohibited from teaching and publishing any further, and removed to Rome, where he spent his remaining years in receipt of a pension from the Pope. It seems to have been urged in his favour that his intellect had been disturbed by grief for the loss of his son,an assertion to which his frequent hallucinations lent some countenance, though the existence of any serious derangement is disproved by the lucidity and coherence of his last writings. He occupied his time at Rome in the composition of his commentaries De Vita Propria, which, along with a companion treatise Be Libris Propriis, is our principal authority for his biography. Though he had burned much, he left behind him more than a hundred MSS., not twenty of which have been printed. He died on September 20, 1576.
Alike intellectually and morally, Cardan is one of the most interesting personages connected with the revival of science in Europe. He had no especial bent towards any scientific pursuit, but appears as the man of versatile ability, delighting in research for its own sake, and capable of prosecuting it to great lengths by dint of perseverance and sagacity. He possessed the true scientific spirit in perfection; nothing, he tells us, among the king of France's treasures appeared to him so worthy of admira-tion as a certain natural curiosity which he took for the horn of a unicorn. It has been injurious to his fame to have been compelled to labour, partly in fields of research where no important discovery was then attainable, partly in those where his discoveries could only serve as the step-ping-stones to others, by which they were inevitably eclipsed. His medical career serves as an illustration of the former case, and his mathematical of the latter. His medical knowledge was wholly empirical ; restrained by the authority of Galen, and debarred from the practice of anatomy, nothing more could be expected than that he should stumble on some fortunate nostrums. As a mathe-matician, on the other hand, he effected most important advances in science, but such as merely paved the way for discoveries which have obscured his own. From his astro-logy no results could be expected; but even here the scien-tific character of his mind is displayed in his common sense treatment of what usually passed for a mystical and occult study. His prognostications are as strictly empirical as his prescriptions, and rest quite as much upon the observa-tions which he supposed himself to have made in his practice. As frequently is the case with men incapable of rightly ordering their own lives, he is full of wisdom and sound advice for others; his ethical precepts and practical rules are frequently excellent. To complete the catalogue of his accomplishments, he is no contemptible poet.
The work of Cardan's, however, which retains most interest for this generation is his autobiography, De Vita Propria. In its clearness and frankness of self revelation this book stands almost alone among records of its class. It may be compared with the autobiography of another celebrated Italian of the age, Benvenuto Cellini, but is much more free from vanity and self-consciousness, unless the extreme candour with which Cardan reveals his own errors is to be regarded as vanity in a more subtle form. The general impression is highly favourable to the writer, whose impetuosity and fits of reckless dissipation appear as mere exaggerations of the warmth of heart which imparted such strength to his domestic affections, and in the region of science imparted that passionate devotion to research which could alone have enabled him to persevere so reso-lutely, and effect such marked advances in such multi-farious fields of inquiry.
Cardan's autobiography has been most ably condensed, and at the same time supplemented by information from the general body of his writings and other sources, by Professor Henry Morley (Jerome Cardan, 1854, 2 vols.). His capital treatises De Subtilitate and De Varielate Berum are combined and fully analyzed in vol. ii. of Rixner and Siher's Leben und Lehrmeinungen berühmter Physiker am Ende des xvi. und am Anfange des xvii. Jahrhunderts (Sulzbach, 1820). Cardan's works were edited in ten volumes by Sponius (Lyons, 1663). A biography was prefixed by Gabriel Naude,whose unreasonable depreciation has unduly lowered Cardan's character with posterity. (R. G.)