race at this period, very peculiar, and well worthy of attentive study. The most remarkable example of this kind of hybrid between a philosopher and a quack, is Cardan, who was at once one of the most renowned of the mathematicians and of the astrological practitioners of medicine of his age. He was born, according to his own autobiography,' in Pavia, A.D. 1501. His father was a Milanese, of good family, who, according to his son's description, was distinguished by peculiarities which may, in some degree, account for the extravagances of his offspring. He could see as well in the dark as in the light, and had a familiar spirit whose society seems to have superseded that of his wife, the mother of little Jerome. At least, his two parents lived apart, and, by his own account, he was subjected to very rough usage at the hands of his father. However, veracity was by no means Jerome Cardan's forte, and all he says must be taken cum grano salis. His boyhood was afflicted with various forms of disease, and till his nineteenth year he attended his father in what is denominated. the capacity of a servant; but, possibly, he merely served as a page, which was common enough then, and far from dishonourable. When nineteen, he went to the gymnasium, and devoted himself to Latin, dialectics, and mathematics. His father was carried off by the plague, and the youth was left to struggle on through poverty in his strange career. At twenty-one he gave public lectures on Euclid, and was chosen Rector of the University of Padua―an honour his penury forced him to resign. He took his degree in his twenty-fourth year, and applied himself to the practice of medicine with such success that soon he acquired an immense reputation. In the year 1550, he made a journey all the way to St. Andrew's, in Scotland, at the request of Archbishop Hamilton, whom he calls Amulthon. He is said to have cured him of some affection of the chest, for which

1 De Vità Propriâ.

he received a fee like a royal ransom. He was afterwards invited to Pavia, Milan, and Bologna; yet he never seems to have been what we should call comfortably off, for we hear of his lying in prison for a year for his debts. He died in the year 1576, for the sake, as it was said, of fulfilling his own astrological prediction.

Such is an outline of his career. When we examine it more closely, we find it made up of two aspects so entirely dissimilar, as to be generally considered mutually exclusive. He was, undoubtedly, a great mathematician. On this head, we shall quote the words of Professor Playfair' :"The name of Cardan is famous in the history of Algebra . . . Before this time, very little advance had been made in the solution of any equations higher than the second degree; except that, as we are told, about the year 1508, Scipio Ferrei, Professor of Mathematics at Bologna, had found out a rule for resolving one of the cases of cubic equations— which, however, he concealed, or communicated only to a few of his scholars. One of these, Florido, on the strength of the secret he possessed, agreeable to a practice then common among mathematicians, challenged Tartalea of Brescia, to contend with him in the solution of Algebraic problems. Florido had, at first, the advantage, but Tartalea, being a man of ingenuity, discovered his rule, and also another much more general, in consequence of which he came off at last much more victorious. By the report of this victory, the curiosity of Cardan was strongly excited; for, although he was himself much versed in the mathematics, he had not been able to discover a method of resolving equations higher than the second degree. By the most earnest and importunate solicitations, he wrung from Tartalea the secrets of his rules, but not till he had bound himself by promises and oaths never to divulge Tartalea did not communicate the demonstrations,

them.

1 Preliminary Dissertation to the Encyclopædia Britannica, p. 441.

which, however, Cardan soon found out, and extended in a very ingenious and systematic manner to all cubic equations whatsoever. Thus possessed of an important discovery, which was at least in a great part his own, he soon forgot his promises to Tartalea, and published the whole in 1545, not concealing, however, what he owed to the latter.

Thus was first published the rule which still bears the name of Cardan, and which at this day marks a point in the progress of Algebraic investigation which all the efforts of succeeding analysts have hardly been able to go beyond."

Thus high stands Cardan in the history of science: let us now consider the other aspect of his character. He was an out-and-out astrologer; his faith in astral influences was founded on a theory of oriental origin, still holding its ground in the east-that there was one pervading vitality diffused through the whole universe, entwining all the parts in the bonds of sympathy; that the various organs of the human body were related by more near or more distant affinity with the different planets; and hence, that the positions of these stars at the hour of birth influenced the organism of the new-born member of this great circle, and absolutely fixed his inevitable character. Cardan himself, unfortunately, was born when Venus, Mercury, and Jupiter were in a particular conjunction; and hence he was foredoomed to be an unsteady, envious, calumnious man, unable to keep any secret, to forget any injury, or to reverence religion. No prediction is more likely to be the means of its own fulfilment than such an one as this. For any man to believe himself doomed to be bad, will make him bad; and we are only surprised that, notwithstanding such a sentence of death hung round his neck while in the cradle, Cardan contrived to make so much of his life.

He had, besides, an absolute faith in dreams and visions, and had interviews with a demon who foretold coming

events. He said he had four special gifts, for which he was thankful:

I. He could at pleasure throw himself into an ecstasy or

trance.

II. He could see with his eyes, not his fancy, any vision he pleased.

III. All future events were revealed to him in dreams. IV. It was also given to him to know the future by certain appearances in his nails.

The "gifts" clearly indicate a condition of the nervous system allied to somnambulism; and, doubtless, when he thought his nails told him anything, he had produced a state of hypnotism in himself, by steadily gazing at his fingertips. In short, he was all his life half mad. Properly speaking, he was not an impostor; he believed in himself, and addressed not the ignorant, but the learned. Still he had a certain unmistakable dash of quackery in him, and employed very questionable methods of getting into practice. His first book was entitled, "De Malo Medendi Usu," the fallacies of the faculty, as we now say. The book was clever, gave the profession great offence, was much talked of, and brought the writer into notice and extensive practice. One of his first great patients was the son of a senator, named Spondrato; the child had suffered from convulsions, and was under the care of a well-known physician, Lucca della Croce. When Cardan saw the boy, he pronounced the complaint to be Opisthotonos, a word unknown to the other attendants; and on being asked how he would cure it, he replied by a string of quotations from Hippocrates and Galen. The long and short of it was, that he ousted his colleagues, and cured the disease. His fame soon spread, and he became one of the most renowned men of his age. It was not, however, as a physician he was celebrated, but as a magician. Melville, in his memoirs, says that the Archbishop Hamilton fell dangerously ill, with loss of

speech, and was believed to be in a hopeless state, but was rescued by the aid of an Italian magician called Cardan. When he passed through London, he was consulted about the health of Edward VI., not as to his treatment, but that he might cast his horoscope and foretell his fate. Cardan gave him a longish life, and the king died in a few months. Cardan excused his failure by saying that he had not given sufficient attention to the case-hardly likely, when we consider the magnitude of the venture.

His journey to Scotland was the acme of his renown; and, perhaps, with the view of keeping its memory fresh, he procured, when there, a suit of clothes made according to the fashion of that country, which he continued to wear after his return to Rome, where he was seen by the famous De Thou, "dressed as no other mortal." To "the garb of old Gaul," let us add his own account of his gait :— "For a few steps he walked with a slow, measured tread, as if at a funeral; then broke into a run, as if flying from the police." If a gaunt figure in kilts were to conduct himself in such a fashion in the streets of London at the present day, he would undoubtedly attract a mob; and we cannot but think Cardan rather liked a little mobbing, for he was the vainest of men, and preferred any kind of notice to none at all. He boasted himself as the seventh physician from the time of Adam, only one worthy of the name being born in a thousand years.'

Such was Cardan, of whom Bayle observes that there is a saying about no genius being without a dash of folly ; but that here we have an example of folly with a dash of genius-the quantity of the folly so greatly preponderating. Characters like Cardan exist at the present

1 For Cardan's life, see his own Autobiography, Vita Propria; Bayle's Dictionary; and Morley's Life of Cardan. Some of his works are translated

into English, some into French: they occupy ten folio volumes. Their title is "Hieronymi Cardani Opera Omnia." Lyons, 1663.