Jerome Cardan, William George Waters [reading list TXT] 📗

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[75] There is a full account of this episode in _De Libris Propriis_, p. 128, and in _De Vita Propria_, ch. xl. p. 133.

[76] Exotericarum exercitationum, p. 987.

[77] _Cardanus Comforte, translated into Englishe_, 1573. It was the work of Thomas Bedingfield, a gentleman pensioner of Queen Elizabeth.

[78] _De Vita Propria_, ch. xxxvii. p. 116.

[79] "Delectant me gladii parvi, seu styli scriptorii, in quos plus viginti coronatis aureis impendi: multas etiam pecunias in varia pennarum genera, audeo dicere apparatum ad scribendum ducentis coronatis non potuisse emi."--_De Vita Propria_, ch. xviii. p. 57.

[80] _De Vita Propria_, ch. iv. p. 15.

[81] "At ego qui, ut dixi, Harpocraticus sum dicebam:--Summus Pont: decrepitus est: murus ruinosus, certa pro incertis derelinquam?"--_De Vita Propria_, ch. iv. p. 15. It is quite possible that Paul III. may have desired to have Cardan about him on account of his reputation as an astrologer, the Pope being a firm believer in the influence of the stars.--_Vide_ Ranke, _History of the Popes_ i. 166.

[82] "Neque ego tum Moroni probitatem, nec Pharnesiorum splendorem intelligebam."--_De Vita Propria_, ch. iv. p. 15.

[83] In writing of his own horoscope (_Geniturarum Exempla_, p. 461) he records that she miscarried thrice, brought forth three living children, and lived with him fifteen years. He dismisses his marriage as follows: "Duxi uxorem inexpectato, a quo tempore multa adversa concomitata sunt."--_De Vita Propria_, ch. xli. p. 149. But in _De Rerum Subtilitate_, p. 375, he records his grief at her death:--"Itaque cum a luctu dolor et vigilia invadere soleant, ut mihi anno vertente in morte uxoris Luciae Bandarenae quanquam institutis philosophiae munitus essem, repugnante tamen natura, memorque vinculi c[o=]jugalis, suspiriis ac lachrymis et inedia quinque dierum, a periculo me vindicavi."


CHAPTER V

AT this point it may not be inopportune to make a break in the record of Cardan's life and work, and to treat in retrospect of that portion of his time which he spent in the composition of his treatises on Arithmetic and Algebra. Ever since 1535 he had been working intermittently at one or other of these, but it would have been impossible to deal coherently and effectively with the growth and completion of these two books--really the most important of all he left behind him--while chronicling the goings and comings of a life so adventurous as that of the author.

The prime object of Cardan's ambition was eminence as a physician. But, during the long years of waiting, while the action of the Milanese doctors kept him outside the bounds of their College, and even after this had been opened to him without inducing ailing mortals to call for his services, he would now and again fall into a transport of rage against his persecutors, and of contempt for the public which refused to recognize him as a master of his art, and cast aside his medical books for months at a time, devoting himself diligently to Mathematics, the field of learning which, next to Medicine, attracted him most powerfully. His father Fazio was a geometrician of repute and a student of applied mathematics, and, though his first desire was to make his son a jurisconsult, he gave Jerome in early youth a fairly good grounding in arithmetic and geometry, deeming probably that such training would not prove a bad discipline for an intellect destined to attack those formidable tomes within which lurked the mysteries of the Canon and Civil Law. Mathematical learning has given to Cardan his surest title to immortality, and at the outset of his career he found in mathematics rather than in medicine the first support in the arduous battle he had to wage with fortune. His appointment to the Plat lectureship at Milan has already been noted. In the discharge of his new duties he was bound, according to the terms of the endowment of the Plat lecturer, to teach the sciences of geometry, arithmetic, and astronomy, and he began his course upon the lines laid down by the founder. Few listeners came, however, and at this juncture Cardan took a step which serves to show how real was his devotion to the cause of true learning, and how lightly he thought of an additional burden upon his own back, if this cause could be helped forward thereby. Keenly as he enjoyed his mathematical work, he laid a part of it aside when he perceived that the benches before him were empty, and, by way of making his lectures more attractive, he occasionally substituted geography for geometry, and architecture for arithmetic. The necessary research and the preparation of these lectures led naturally to the accumulation of a large mass of notes, and as these increased under his hand Jerome began to consider whether it might not be worth his while to use them in the composition of one or more volumes. In 1535 he delivered as Plat lecturer his address, the _Encomium Geometriae_, which he followed up shortly after by the publication of a work, _Quindecim Libri Novae Geometriae_. But the most profitable labour of these years was that which produced his first important book, _The Practice of Arithmetic and Simple Mensuration_, which was published in 1539, a venture which brought to the author a reward of ten crowns.[84] It was a well-planned and well-arranged manual, giving proof of the wide erudition and sense of proportion possessed by the author. Besides dealing with Arithmetic as understood by the modern school-boy, it discusses certain astronomical operations, multiplication by memory, the mysteries of the Roman and Ecclesiastical Calendars, and gives rules for the solution of any problem arising from the terms of the same. It treats of partnership in agriculture, the Mezzadria system still prevalent in Tuscany and in other parts of Italy, of the value of money, of the strange properties of certain numbers, and gives the first simple rules of Algebra to serve as stepping-stones to the higher mathematics. It ends with information as to house-rent, letters of credit and exchange, tables of interest, games of chance, mensuration, and weights and measures. In an appendix Cardan examines critically the work of Fra Luca Pacioli da Borgo, an earlier writer on the subject, and points out numerous errors in the same. The book from beginning to end shows signs of careful study and compilation, and the fame which it brought to its author was well deserved.

Cardan appended to the Arithmetic a printed notice which may be regarded as an early essay in advertising. He was fully convinced that his works were valuable and quite worth the sums of money he asked for them; the world was blind, perhaps wilfully, to their merits, therefore he now determined that it should no longer be able to quote ignorance of the author as an excuse for not buying the book. This appendix was a notification to the learned men of Europe that the writer of the _Practice of Arithmetic_ had in his press at home thirty-four other works in MS. which they might read with profit, and that of these only two had been printed, to wit the _De Malo Medendi Usu_ and a tract on _Simples_. This advertisement had something of the character of a legal document, for it invoked the authority of the Emperor to protect the copyright of Cardan's books within the Duchy of Milan for ten years, and to prevent the introduction of them from abroad.

The Arithmetic proved far superior to any other treatise extant, and everywhere won the approval of the learned. It was from Nuremberg that its appearance brought the most valuable fruits. Andreas Osiander,[85] a learned humanist and a convert to Lutheranism, and Johannes Petreius, an eminent printer, were evidently impressed by the terms of Cardan's advertisement, for they wrote to him and offered in combination to edit and print any of the books awaiting publication in his study at Milan. The result of this offer was the reprinting of _De Malo Medendi_, and subsequently of the tract on Judicial Astrology, and of the treatise _De Consolatione_; the _Book of the Great Art_, the treatises _De Sapientia_ and _De Immortalitate Animorum_ were published in the first instance by these same patrons from the Nuremberg press.

But Cardan, while he was hard at work on his Arithmetic, had not forgotten a certain report which had caused no slight stir in the world of Mathematics some three years before the issue of his book on Arithmetic, an episode which may be most fittingly told in his own words. "At this time[86] it happened that there came to Milan a certain Brescian named Giovanni Colla, a man of tall stature, and very thin, pale, swarthy, and hollow-eyed. He was of gentle manners, slow in gait, sparing of his words, full of talent, and skilled in mathematics. His business was to bring word to me that there had been recently discovered two new rules in Algebra for the solution of problems dealing with cubes and numbers. I asked him who had found them out, whereupon he told me the name of the discoverer was Scipio Ferreo of Bologna. 'And who else knows these rules?' I said. He answered, 'Niccolo Tartaglia and Antonio Maria Fiore.' And indeed some time later Tartaglia, when he came to Milan, explained them to me, though unwillingly; and afterwards I myself, when working with Ludovico Ferrari,[87] made a thorough study of the rules aforesaid. We devised certain others, heretofore unnoticed, after we had made trial of these new rules, and out of this material I put together my _Book of the Great Art_."[88]

Before dealing with the events which led to the composition of the famous work above-named, it may be permitted to take a rapid survey of the condition of Algebra at the time when Cardan sat down to write. Up to the beginning of the sixteenth century the knowledge of Algebra in Italy, originally derived from Greek and Arabic sources, had made very little progress, and the science had been developed no farther than to provide for the solution of equations of the first or second degree.[89] In the preface to the _Liber Artis Magnae_ Cardan writes:--"This art takes its origin from a certain Mahomet, the son of Moses, an Arabian, a fact to which Leonard the Pisan bears ample testimony. He left behind him four rules, with his demonstrations of the same, which I duly ascribe to him in their proper place. After a long interval of time, some student, whose identity is uncertain, deduced from the original four rules three others, which Luca Paciolus put with the original ones into his book. Then three more were discovered from the original rules, also by some one unknown, but these attracted very little notice though they were far more useful than the others, seeing that they taught how to arrive at the value of the _cubus_ and the _numerus_ and of the _cubus quadratus_.[90] But in recent times Scipio Ferreo of Bologna discovered the rule of the _cubus_ and the _res_ equal to the _numerus_ (_x^3 + px=q_), truly a beautiful and admirable discovery. For this Algebraic art outdoes all other subtlety of man, and outshines the clearest exposition mortal wit can achieve: a heavenly gift indeed, and a test of the powers of a man's mind. So excellent is it in itself that whosoever shall get possession thereof, will be assured that no problem exists too difficult for him to disentangle. As a rival of Ferreo, Niccolo Tartaglia of Brescia, my friend, at that time when he engaged in a contest with Antonio Maria Fiore, the pupil of Ferreo, made out this same rule to help secure the victory, and this rule he imparted to me after I had diligently besought him thereanent. I, indeed, had been deceived by the words of Luca Paciolus, who denied that there could be any general rule besides these which