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It may be conceded at once that the impression received from a perusal of this criticism is in the main an unfavourable one of Cardan as a man, although Naudé shows himself no niggard of praise when he deals with Cardan's achievements in Medicine and Mathematics.
Veracity was not a common virtue in those days, but Cardan laid claim to it with a display of insistence which was not, perhaps, in the best taste. Over and over again he writes that he never told a lie; a contention which seems to have roused especially the bile of Naudé, and to have spurred him on to make his somewhat clumsy assault on Cardan's veracity.
The receipt of this letter seems to have disquieted Tartaglia somewhat; for he has added a note to it, in which he says that Cardan has placed him in a position of embarrassment. He had evidently wished for an introduction to D'Avalos, but now it was offered to him it seemed a burden rather than a benefit. He disliked the notion of going to Milan; yet, if he did not go, the Marchese d'Avalos might take offence. But in the end he decided to undertake the journey; and, as D'Avalos happened then to be absent from Milan on a visit to his country villa at Vigevano, he stayed for three days in Cardan's house. As a recorder of conversations Tartaglia seems to have had something of Boswell's gift. He gives an abstract of an eventful dialogue with his host on March 25, 1539, which Cardan begins by a gentle reproach anent his guest's reticence in the matter of the rule of the cosa and the cubus equal to the numerus. Tartaglia's reply to this complaint seems reasonable enough (it must be borne in mind that he is his own reporter), and certainly helps to absolve him from the charge sometimes made against him that he was nothing more than a selfish curmudgeon who had resolved to let his knowledge die with him, rather than share it with other mathematicians of whom he was jealous. He told Cardan plainly that he kept his rules a secret because, for the present, it suited his purpose to do so. At this time he had not the leisure to elaborate farther the several rules in question, being engaged over a translation of Euclid into Italian; but, when this work should be completed, he proposed to publish a treatise on Algebra in which he would disclose to the world all the rules he already knew, as well as many others which he hoped to discover in the course of his present work. He concludes: "This is the cause of my seeming discourtesy towards your excellency. I have been all the ruder, perhaps, because you write to me that you are preparing a book similar to mine, and that you propose to publish my inventions, and to give me credit for the same. This I confess is not to my taste, forasmuch as I wish to set forth my discoveries in my own works, and not in those of others." In his reply to this, Cardan points out that he had promised, if Tartaglia so desired, that he would not publish the rules at all; but here Messer Niccolo's patience and good manners gave way, and he told Messer Hieronimo bluntly that he did not believe him. Then said Cardan: "I swear to you by the Sacred Evangel, and by myself as a gentleman, that I will not only abstain from publishing your discoveries if you will make them known to me but that I will promise and pledge my faith of a true Christian to set them down for my own use in cypher, so that after my death no one may be able to understand them. If you will believe this promise, believe it; if you will not, let us have done with the matter." "If I were not disposed to believe such oaths as these you now swear," said Tartaglia, "I might as well be set down as a man without any faith at all. I have determined to go forthwith to Vigevano to visit the Signor Marchese, as I have now been here for three days and am weary of the delay, but I promise when I return that I will show you all the rules." Cardan replied: "As you are bent on going to Vigevano, I will give you a letter of introduction to the Marchese, so that he may know who you are; but I would that, before you start, you show me the rule as you have promised." "I am willing to do this," said Tartaglia, "but I must tell you that, in order to be able to recall at any time my system of working, I have expressed it in rhyme; because, without this precaution, I must often have forgotten it. I care naught that my rhymes are clumsy, it has been enough for me that they have served to remind me of my rules. These I will write down with my own hand, so that you may be assured that my discovery is given to you correctly." Then follow Tartaglia's verses: "Quando chel cubo con le cose apresso Se agualia
For this reason I lament deeply my share in this affair, I who had most obvious reasons for engaging in this conflict, and the clearest ones for inventing a story as to the victory I hoped to gain; reasons which a man of sober temper could never anticipate, which a brave man would never desire. "Cardan's fame has its surest foundation in the praise of his adversaries.
In a nature so complex and many-sided as Cardan's, strange resemblances may be sought for and discovered, and it certainly is an unexpected revelation to find a mental attitude common to Cardan, a man tied and bound by authority and the traditions of antiquity, and such a daring assailant of the schools and of Aristotle as Doctor Joseph Glanvil.
The vastness and catholicity of Galen's scheme of Medicine must have been peculiarly attractive to a man of Cardan's temper; and that Galen attempted to reconcile the incongruous in the teleological system which he devised, would not have been rated as a fault by his Milanese disciple.
Tartaglia has given a version of this part of the transaction; and, according to what is there set down, Cardan's request, even when recorded in Tartaglia's own words, does not appear an unreasonable one, for up to this time Tartaglia had never announced that he had any intention of publishing his discoveries as part of a separate work on Mathematics.
He desired that his works should be corrected and printed, and that, if heirs failed entirely, his house at Bologna should pass to the University, and be styled, after his family, Collegium Cardanorum. There is no authentic record of the exact date of Cardan's death.
WHEN dealing with Cardan's sudden incarceration in 1570, in the chronicle of his life, it was assumed that his offence must have been some spoken or written words upon which a charge of impiety might have been fastened. Leaving out of consideration the fiery zeal of the reigning Pope Pius V., it is hard to determine what plea could have been found for a serious charge of this nature.
Moreover, Hamilton writes somewhat querulously about Cassanate's absence abroad on a visit to his family, a fact which would make him all the more eager to secure Cardan's services.
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