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Updated: June 2, 2025
The fact that Algebra as a science had made such scant progress for so many years, gave to this new process, about which Giovanni Colla was talking, an extraordinary interest in the sight of all mathematical students; wherefore when Cardan heard the report that Antonio Maria Fiore, Ferreo's pupil, had been entrusted by his master with the secret of this new process, and was about to hold a public disputation at Venice with Niccolo Tartaglia, a mathematician of considerable repute, he fancied that possibly there would be game about well worth the hunting.
He goes on to acknowledge other obligations to Tartaglia: how the Brescian had first taught him that algebraical discovery could be most effectively advanced by geometrical demonstration, and how he himself had followed this counsel, and had been careful to give the demonstration aforesaid for every rule he laid down.
Opera, tom. iv. p. 222. In the conclusion of the Treatise on Arithmetic, Cardan points out certain errors in the work of Fra Luca. Fra Luca was a pupil of Piero della Francesca, who was highly skilled in Geometry, and who, according to Vasari, first applied perspective to the drawing of the human form. Tartaglia, i.e. the stutterer. Papadopoli, Hist. Gymn. Pata.
This book was published at Nuremberg in 1545, and in its preface and dedication Cardan fully acknowledges his obligations to Tartaglia and Ferrari, with respect to the rules lately discussed, and gives a catalogue of the former students of the Art, and attributes to each his particular contribution to the mass of knowledge which he here presents to the world.
However, the time was not yet come for Jerome to begin to quibble with his conscience. On May 12, 1539, he wrote another letter to Tartaglia, also in a very friendly tone, reproaching him gently for his suspicions, and sending a copy of the Practice of Arithmetic to show him that they were groundless.
Tartaglia searched, and though he could not put his finger on any spot which showed that Messer Hieronimo had broken his oath, he found what must have been to him as a precious jewel, to wit a mistake in reckoning, which he reported to Cardan in these words: "In this process your excellency has made such a gross mistake that I am amazed thereat, forasmuch as any man with half an eye must have seen it indeed, if you had not gone on to repeat it in divers examples, I should have set it down to a mistake of the printer."
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.
My dancing and posturing at Florence had given me something of a name among the dilettanti, and I was at once engaged by the manager, who took me to Venice, where I subsequently joined the company of the excellent Tartaglia with whom I am now acting.
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 them, ending with a warning hint to Cardan that, if he should publish the rules, either in the work he had in hand, or in any future one, either under the name of Tartaglia or of Cardan, he, the author, would put into print certain things which Messer Hieronimo would not find very pleasant reading.
The play-bill, with a wealth of theatrical rhetoric, invited Odo to attend the Performance to be given that evening at the Philodramatic Academy by the celebrated Capo Comico Tartaglia of Rimini and his world-renowned company of Comedians, who, in the presence of the aristocracy of Vercelli, were to present a new comedy entitled "Le Gelosie di Milord Zambo," with an Intermezzo of singing and dancing by the best Performers of their kind.
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