Jerome Cardan by William George Waters (important books to read .txt) π
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matter briefly: "Ex hoc ad artem magnam, quam collegi, dum Jo. Colla certaret nobiscum, et Tartalea, a quo primum acceperam capitulum, qui maluit aemulum habere, et superiorem, quam amicum et beneficio devinctum, cum alterius fuisset inventum."--ch. xlv. p. 175.
[106] Prefixed to the _De Vita Propria_.
[107] In a question of broken faith, Cardan laid himself open especially to attack by reason of his constant self-glorification in the matter of veracity.
[108] Leonardo knew that quadratic equations might have two positive roots, and Cardan pursued this farther by the discovery that they might also have negative roots.
[109] "Caput xxviii. De capitulo generali cubi et rerum aequalium numero, Magistri Nicolai Tartagliae, Brixiensis--Hoc capitulum habui a prefato viro ante considerationem demonstrationum secundi libri super Euclidem, et aequatio haec cadit in [Symbol: Rx]. cu v binomii ex genere binomii secundi et qunti [m~]. [Symbol: Rx]. cuba universali recisi ejusdem binomii."--_Opera_, tom. iv. p. 341.
[110] Montucla, who as a historian of Mathematics has a strong bias against Cardan, gives him credit for the discovery of the _fictae radices_, but on the other hand he attributes to Vieta Cardan's discovery of the method of changing a complete cubic equation into one wanting the second term.--Ed. 1729, p. 595.
[111] _Opera_, tom. i. p. 66.
CHAPTER VI
IT has been noted that Cardan quitted Pavia at the end of 1544 on account of the bankruptcy of the University, and that in 1546 a generous offer was made to him on condition of his entering the service of Pope Paul III.; an offer which after some hesitation he determined to refuse. In the autumn of this same year he resumed his teaching at Pavia, a fact which sanctions the assumption that this luckless seat of learning must have been once more in funds. In the year following, in 1547, there came to him another offer of employment accompanied by terms still more munificent than the Pope's, conveyed through Vesalius[112] and the ambassador of the King of Denmark. "The emolument was to be a salary of three hundred gold crowns per annum of the Hungarian currency, and in addition to these six hundred more to be paid out of the tax on skins of price. This last-named money differed in value by about an eighth from the royal coinage, and would be somewhat slower in coming in. Also the security for its payment was not so solid, and would in a measure be subject to risk. To this was farther added maintenance for myself and five servants and three horses. This offer I did not accept because the country was very cold and damp, and the people well-nigh barbarians; moreover the rites and doctrines of religion were quite foreign to those of the Roman Church."[113]
Cardan was now forty-six years of age, a mathematician of European fame, and the holder of an honourable post at an ancient university, which he might have exchanged for other employment quite as dignified and far more lucrative. In dealing with a character as bizarre as his, it would be as a rule unprofitable to search deeply for motives of action, but in this instance it is no difficult matter to detect upon the surface several causes which may have swayed him in this decision to remain at Pavia. However firmly he may have set himself to win fame as a physician, he was in no way disposed to put aside those mathematical studies in which he had already made so distinguished a name, nor to abandon his astrology and chiromancy and discursive reading of all kinds. At Pavia he would find leisure for all these, and would in addition be able to make good any arrears of medical and magical knowledge into which he might have fallen during the years so largely devoted to the production of the _Book of the Great Art_. Moreover, the time in question was one of the prime epochs in the history of the healing art. A new light had just arisen in Vesalius, who had recently published his book, _Corporis Humani Fabrica_, and was lecturing in divers universities on the new method of Anatomy, the actual dissection of the human body. He went to Pavia in the course of his travels and left traces of his visit in the form of a revived and re-organized school of Anatomy. This fact alone would have been a powerful attraction to Cardan, ever greedy as he was of new knowledge, but there was another reason which probably swayed him more strongly still, to wit, the care of his eldest son's education and training. Gian Battista Cardano was now in his fourteenth year, and, according to the usages of the time, old enough to make a beginning of his training in Medicine, the profession he was destined to follow. It is not recorded whether or not he chose this calling for himself; but, taking into account the deep and tender affection Jerome always manifested towards his eldest son, it is not likely that undue compulsion was used in the matter. The youth, according to his father's description, strongly favoured in person his grandfather Fazio.[114] He had come into the world at a time when his parents' fortunes were at their lowest ebb, during those terrible months spent at Gallarate,[115] and in his adolescence he bore divers physical evidences of the ill nurture--it would be unjust to call it neglect--which he had received. At one time he was indeed put in charge of a good nurse, but he had to be withdrawn from her care almost immediately through her husband's jealousy, and he was next sent to a slattern, who fed him with old milk, and not enough of that; or more often with chewed bread. His body was swollen and unhealthy, he suffered greatly from an attack of fever, which ultimately left him deaf in one ear. He gave early evidence of a fine taste in music, an inheritance from his father, and was, according to Cardan's showing, upright and honest in his carriage, gifted with talents which must, under happier circumstances, have placed him in the first rank of men of learning, and in every respect a youth of the fairest promise. The father records that he himself, though well furnished by experience in the art of medicine, was now and again worsted by his son in disputation, and alludes in words of pathetic regret to divers problems, too deep for his own powers of solution, which Gian Battista would assuredly have mastered in the course of time. He does not forget to notice certain of the young man's failings; for he remarks that he was temperate of speech, except when he was angered, and then he would pour forth such a torrent of words that he scarce seemed in his right mind. Cardan professes to have discerned a cause for these failings, and the calamities flowing therefrom, in the fact that Gian Battista had the third and fourth toes of his right foot united by a membrane; he declares that, if he had known of this in time, he would have counteracted the evil by dividing the toes.[116] Gian Battista eventually gained the _baccalaureat_ in his twenty-second year, and two years after became a member of the College.
The life which Cardan planned to lead at Pavia was unquestionably a full one. He had several young men under his care as pupils besides his son, amongst them being a kinsman of his, Gasparo Cardano, a youth of sterling virtue and a useful coadjutor in times to come. He was at this time engaged on his most important works in Medicine and Physical Science. He worked hard at his profession, practising occasionally and reading voraciously all books bearing on his studies. He wrote and published several small works during the four years--from 1547 to 1551--of his Professorship at Pavia; the most noteworthy of which were the Book of Precepts for the guidance of his children, and some Treatises on the Preservation of Health. He also wrote a book on Physiognomy, or as he called it Metoposcopy, an abstract of which appears as a chapter in _De Utilitate_ (lib. iii. c. 10), but the major part of his time must have been consumed in collecting and reducing to form the huge mass of facts out of which his two great works, _De Subtilitate_ and _De Varietate Rerum_, were built up.
A mere abstract of the contents of these wonderful books would fill many pages, and prove as uninteresting and unsuggestive as abstracts must always be; and a commentary upon the same, honestly executed, would make a heavy draft on the working life-time of an industrious student. In reference to each book the author has left a statement of the reasons which impelled him to undertake his task, the most cogent of which were certain dreams.[117] Soon after he had begun to write the _De Astrorum Judiciis_ he dreamt one night that his soul, freed from his body, was ranging the vault of heaven near to the moon, and the soul of his father was there likewise. But he could not see this spirit, which spake to him saying, "Behold, I am given to you as a comrade." The spirit of the father then went on to tell the son how, after various stages of probation, he would attain the highest heaven, and in the terms of this discourse Cardan professed to discern the scheme of his more important works.
The _De Subtilitate_ represents Cardan's original conception of a treatise dealing with the Cosmos, but during the course of its preparation a vast mass of subsidiary and contingent knowledge accumulated in his note-books, and rendered necessary the publication of a supplementary work, the _De Varietate_,[118] which, by the time it was finished, had grown to a bulk exceeding that of the original treatise. The seminal ideas which germinated and produced such a vast harvest of printed words, were substantially the same which had possessed the brains of Paracelsus and Agrippa. Cardan postulates in the beginning a certain sympathy between the celestial bodies and our own, not merely general, but distributive, the sun being in harmony with the heart, and the moon with the animal humours. He considers that all organized bodies are animated, so that what we call the Spirit of Nature is present everywhere. Beyond this everything is ruled by the properties of numbers.[119] Heat and moisture are the only real qualities in Nature, the first being the formal, and the second the material, cause of all things; these conceptions he gleaned probably from some criticisms of Aristotle on the archaic doctrines of Heraclitus and Thales as to the origin of the universe.
It is no marvel that a writer, gifted with so bizarre and imaginative a temper, so restless and greedy of knowledge, sitting down to work with such a projection before him, should have produced the richest, and at the same time the most chaotic, collection of the facts of Natural Philosophy that had yet issued from the press. The erudition and the industry displayed in the gathering together of these vast masses of information, and in their verification by experiment, are indeed amazing; and, in turning over his pages, it is impossible to stifle regret that Cardan's confused method and incoherent system should have rendered his work comparatively useless for the spread of true knowledge, and qualified it only for a place among the _labores ineptiarum_.
Cardan begins with a definition of Subtilty. "By subtilty I mean a certain faculty of the mind by which certain phenomena, discernible by the senses and comprehensible by the intellect, may be understood, albeit with difficulty." Subtilty, as he understood it, possesses a threefold character: substance, accident, and manifestation. With regard to the senses he admits but four to the first rank: touch, sight, smell, and hearing; the claims of taste, he
[106] Prefixed to the _De Vita Propria_.
[107] In a question of broken faith, Cardan laid himself open especially to attack by reason of his constant self-glorification in the matter of veracity.
[108] Leonardo knew that quadratic equations might have two positive roots, and Cardan pursued this farther by the discovery that they might also have negative roots.
[109] "Caput xxviii. De capitulo generali cubi et rerum aequalium numero, Magistri Nicolai Tartagliae, Brixiensis--Hoc capitulum habui a prefato viro ante considerationem demonstrationum secundi libri super Euclidem, et aequatio haec cadit in [Symbol: Rx]. cu v binomii ex genere binomii secundi et qunti [m~]. [Symbol: Rx]. cuba universali recisi ejusdem binomii."--_Opera_, tom. iv. p. 341.
[110] Montucla, who as a historian of Mathematics has a strong bias against Cardan, gives him credit for the discovery of the _fictae radices_, but on the other hand he attributes to Vieta Cardan's discovery of the method of changing a complete cubic equation into one wanting the second term.--Ed. 1729, p. 595.
[111] _Opera_, tom. i. p. 66.
CHAPTER VI
IT has been noted that Cardan quitted Pavia at the end of 1544 on account of the bankruptcy of the University, and that in 1546 a generous offer was made to him on condition of his entering the service of Pope Paul III.; an offer which after some hesitation he determined to refuse. In the autumn of this same year he resumed his teaching at Pavia, a fact which sanctions the assumption that this luckless seat of learning must have been once more in funds. In the year following, in 1547, there came to him another offer of employment accompanied by terms still more munificent than the Pope's, conveyed through Vesalius[112] and the ambassador of the King of Denmark. "The emolument was to be a salary of three hundred gold crowns per annum of the Hungarian currency, and in addition to these six hundred more to be paid out of the tax on skins of price. This last-named money differed in value by about an eighth from the royal coinage, and would be somewhat slower in coming in. Also the security for its payment was not so solid, and would in a measure be subject to risk. To this was farther added maintenance for myself and five servants and three horses. This offer I did not accept because the country was very cold and damp, and the people well-nigh barbarians; moreover the rites and doctrines of religion were quite foreign to those of the Roman Church."[113]
Cardan was now forty-six years of age, a mathematician of European fame, and the holder of an honourable post at an ancient university, which he might have exchanged for other employment quite as dignified and far more lucrative. In dealing with a character as bizarre as his, it would be as a rule unprofitable to search deeply for motives of action, but in this instance it is no difficult matter to detect upon the surface several causes which may have swayed him in this decision to remain at Pavia. However firmly he may have set himself to win fame as a physician, he was in no way disposed to put aside those mathematical studies in which he had already made so distinguished a name, nor to abandon his astrology and chiromancy and discursive reading of all kinds. At Pavia he would find leisure for all these, and would in addition be able to make good any arrears of medical and magical knowledge into which he might have fallen during the years so largely devoted to the production of the _Book of the Great Art_. Moreover, the time in question was one of the prime epochs in the history of the healing art. A new light had just arisen in Vesalius, who had recently published his book, _Corporis Humani Fabrica_, and was lecturing in divers universities on the new method of Anatomy, the actual dissection of the human body. He went to Pavia in the course of his travels and left traces of his visit in the form of a revived and re-organized school of Anatomy. This fact alone would have been a powerful attraction to Cardan, ever greedy as he was of new knowledge, but there was another reason which probably swayed him more strongly still, to wit, the care of his eldest son's education and training. Gian Battista Cardano was now in his fourteenth year, and, according to the usages of the time, old enough to make a beginning of his training in Medicine, the profession he was destined to follow. It is not recorded whether or not he chose this calling for himself; but, taking into account the deep and tender affection Jerome always manifested towards his eldest son, it is not likely that undue compulsion was used in the matter. The youth, according to his father's description, strongly favoured in person his grandfather Fazio.[114] He had come into the world at a time when his parents' fortunes were at their lowest ebb, during those terrible months spent at Gallarate,[115] and in his adolescence he bore divers physical evidences of the ill nurture--it would be unjust to call it neglect--which he had received. At one time he was indeed put in charge of a good nurse, but he had to be withdrawn from her care almost immediately through her husband's jealousy, and he was next sent to a slattern, who fed him with old milk, and not enough of that; or more often with chewed bread. His body was swollen and unhealthy, he suffered greatly from an attack of fever, which ultimately left him deaf in one ear. He gave early evidence of a fine taste in music, an inheritance from his father, and was, according to Cardan's showing, upright and honest in his carriage, gifted with talents which must, under happier circumstances, have placed him in the first rank of men of learning, and in every respect a youth of the fairest promise. The father records that he himself, though well furnished by experience in the art of medicine, was now and again worsted by his son in disputation, and alludes in words of pathetic regret to divers problems, too deep for his own powers of solution, which Gian Battista would assuredly have mastered in the course of time. He does not forget to notice certain of the young man's failings; for he remarks that he was temperate of speech, except when he was angered, and then he would pour forth such a torrent of words that he scarce seemed in his right mind. Cardan professes to have discerned a cause for these failings, and the calamities flowing therefrom, in the fact that Gian Battista had the third and fourth toes of his right foot united by a membrane; he declares that, if he had known of this in time, he would have counteracted the evil by dividing the toes.[116] Gian Battista eventually gained the _baccalaureat_ in his twenty-second year, and two years after became a member of the College.
The life which Cardan planned to lead at Pavia was unquestionably a full one. He had several young men under his care as pupils besides his son, amongst them being a kinsman of his, Gasparo Cardano, a youth of sterling virtue and a useful coadjutor in times to come. He was at this time engaged on his most important works in Medicine and Physical Science. He worked hard at his profession, practising occasionally and reading voraciously all books bearing on his studies. He wrote and published several small works during the four years--from 1547 to 1551--of his Professorship at Pavia; the most noteworthy of which were the Book of Precepts for the guidance of his children, and some Treatises on the Preservation of Health. He also wrote a book on Physiognomy, or as he called it Metoposcopy, an abstract of which appears as a chapter in _De Utilitate_ (lib. iii. c. 10), but the major part of his time must have been consumed in collecting and reducing to form the huge mass of facts out of which his two great works, _De Subtilitate_ and _De Varietate Rerum_, were built up.
A mere abstract of the contents of these wonderful books would fill many pages, and prove as uninteresting and unsuggestive as abstracts must always be; and a commentary upon the same, honestly executed, would make a heavy draft on the working life-time of an industrious student. In reference to each book the author has left a statement of the reasons which impelled him to undertake his task, the most cogent of which were certain dreams.[117] Soon after he had begun to write the _De Astrorum Judiciis_ he dreamt one night that his soul, freed from his body, was ranging the vault of heaven near to the moon, and the soul of his father was there likewise. But he could not see this spirit, which spake to him saying, "Behold, I am given to you as a comrade." The spirit of the father then went on to tell the son how, after various stages of probation, he would attain the highest heaven, and in the terms of this discourse Cardan professed to discern the scheme of his more important works.
The _De Subtilitate_ represents Cardan's original conception of a treatise dealing with the Cosmos, but during the course of its preparation a vast mass of subsidiary and contingent knowledge accumulated in his note-books, and rendered necessary the publication of a supplementary work, the _De Varietate_,[118] which, by the time it was finished, had grown to a bulk exceeding that of the original treatise. The seminal ideas which germinated and produced such a vast harvest of printed words, were substantially the same which had possessed the brains of Paracelsus and Agrippa. Cardan postulates in the beginning a certain sympathy between the celestial bodies and our own, not merely general, but distributive, the sun being in harmony with the heart, and the moon with the animal humours. He considers that all organized bodies are animated, so that what we call the Spirit of Nature is present everywhere. Beyond this everything is ruled by the properties of numbers.[119] Heat and moisture are the only real qualities in Nature, the first being the formal, and the second the material, cause of all things; these conceptions he gleaned probably from some criticisms of Aristotle on the archaic doctrines of Heraclitus and Thales as to the origin of the universe.
It is no marvel that a writer, gifted with so bizarre and imaginative a temper, so restless and greedy of knowledge, sitting down to work with such a projection before him, should have produced the richest, and at the same time the most chaotic, collection of the facts of Natural Philosophy that had yet issued from the press. The erudition and the industry displayed in the gathering together of these vast masses of information, and in their verification by experiment, are indeed amazing; and, in turning over his pages, it is impossible to stifle regret that Cardan's confused method and incoherent system should have rendered his work comparatively useless for the spread of true knowledge, and qualified it only for a place among the _labores ineptiarum_.
Cardan begins with a definition of Subtilty. "By subtilty I mean a certain faculty of the mind by which certain phenomena, discernible by the senses and comprehensible by the intellect, may be understood, albeit with difficulty." Subtilty, as he understood it, possesses a threefold character: substance, accident, and manifestation. With regard to the senses he admits but four to the first rank: touch, sight, smell, and hearing; the claims of taste, he
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