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

again for Tartaglia's answers. The end of the matter was that Tartaglia handed over to the messenger the questions which Fiore had propounded in the Venetian contest, and authorized Juan Antonio to get a copy of his own from the notary who had drawn up the terms of the disputation with Fiore. The date of this communication is January 2, 1539, and on February 12 Cardan writes a long letter to Tartaglia, complaining in somewhat testy spirit of the reception given to his request. He is aggrieved that Tartaglia should have sent him nothing but the questions put to him by Fiore, thirty in number indeed, but only one in substance, and that he should have dared to hint that those which he (Cardan) had sent for solution were not his own, but the property of Giovanni Colla. Cardan had found Colla to be a conceited fool, and had dragged the conceit out of him--a process which he was now about to repeat for the benefit of Messer Niccolo Tartaglia. The letter goes on to contradict all Tartaglia's assertions by arguments which do not seem entirely convincing, and the case is not made better by the abusive passages interpolated here and there, and by the demonstration of certain errors in Tartaglia's book on Artillery. In short a more injudicious letter could not have been written by any man hoping to get a favour done to him by the person addressed.

In the special matter of the problems which he sent to Tartaglia by the bookseller Juan Antonio, Cardan made a beginning of that tricky and crooked course which he followed too persistently all through this particular business. In his letter he maintains with a show of indignation that he had long known these questions, had known them in fact before Colla knew how to count ten, implying by these words that he knew how to solve them, while in reality all he knew about them was the fact that they existed. Tartaglia in his answer is not to be moved from his belief, and tells Cardan flatly that he is still convinced Giovanni Colla took the questions to Milan, where he found no one able to solve them, not even Messer Hieronimo Cardano, and that the mathematician last-named sent them on by the bookseller for solution, as has been already related.

This letter of Tartaglia's bears the date of February 13, 1539, and after reading it and digesting its contents, Cardan seems to have come to the conclusion that he was not working in the right way to get possession of this secret which he felt he must needs master, if he wanted his forthcoming book to mark a new epoch in this History of Mathematics, and that a change of tactics was necessary. Alfonso d'Avalos, Cardan's friend and patron, was at this time the Governor of Milan. D'Avalos was a man of science, as well as a soldier, and Cardan had already sent to him a copy of Tartaglia's treatise on Artillery, deeming that a work of this kind would not fail to interest him. In his first letter to Tartaglia he mentions this fact, while picking holes in the writer's theories concerning transmitted force and views on gravitation. This mention of the name of D'Avalos, the master of many legions and of many cannons as well, to a man who had written a Treatise on the management of Artillery, and devised certain engines and instruments for the management of the same, was indeed a clever cast, and the fly was tempting enough to attract even so shy a fish as Niccolo Tartaglia. In his reply to Jerome's scolding letter of February 12, 1539, Tartaglia concludes with a description of the instruments which he was perfecting: a square to regulate the discharge of cannon, and to level and determine every elevation; and another instrument for the investigation of distances upon a plane surface. He ends with a request that Cardan will accept four copies of the engines aforesaid, two for himself and two for the Marchese d'Avalos.

The tone of this letter shows that Cardan had at least begun to tame the bear, who now seemed disposed to dance _ad libitum_ to the pleasant music of words suggesting introductions to the governor, and possible patronage of these engines for the working of artillery. Cardan's reply of March 19, 1539, is friendly--too friendly indeed--and the wonder is that Tartaglia's suspicions were not aroused by its almost sugary politeness. It begins with an attempt to soften down the asperities of their former correspondence, some abuse of Giovanni Colla, and an apology for the rough words of his last epistle. Cardan then shows how their misunderstanding arose chiefly from a blunder made by Juan Antonio in delivering the message, and invites Tartaglia to come and visit him in his own house in Milan, so that they might deliberate together on mathematical questions; but the true significance of the letter appears in the closing lines. "I told the Marchese of the instruments which you had sent him, and he showed himself greatly pleased with all you had done. And he commanded me to write to you forthwith in pressing terms, and to tell you that, on the receipt of my letter, you should come to Milan without fail, for he desires to speak with you. And I, too, exhort you to come at once without further deliberation, seeing that this said Marchese is wonted to reward all men of worth in such noble and magnanimous and liberal fashion that none of them ever goes away dissatisfied."

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 a qualche numero discreto
Trouan dui altri differenti in esso
Dapoi terrai questo per consueto
Ch'el lor' produtto sempre sia eguale
Al terzo cubo delle cose neto
El residuo poi suo generale
Delli lor lati cubi ben sottratti
Varra la tua cosa principale.
In el secondo de cotesti atti
Quando chel cubo restasse lui solo
Tu osseruarai quest' altri contratti
Del numer farai due tal part 'a uolo
Che luna in l'altra si produca schietto
El terzo cubo delle cose in stolo
Delle qual poi, per commun precetto
Torrai li lati cubi insieme gionti
Et cotal summa sara il tuo concetto
Et terzo poi de questi nostri conti
Se solve col recordo se ben guardi
Che per natura son quasi congiunti
Questi trouai, et non con passi tardi
Nel mille cinquecent' e quatro e trenta
Con fondamenti ben sald' e gagliardi
Nella citta del mar' intorno centa."

Having handed over to his host these rhymes, with the precious rules enshrined therein, Tartaglia told him that, with so clear an exposition, he could not fail to understand