Abstract
In 1546, one of the great geometers of the 16th century, Nicolo Tartaglia or Tartalea of Brescia, published the most important of his works under the title of Quesiti et Inventioni diverse.1 This curious work consists of nine books and is written in the form of a dialogue in which Tartaglia converses with different personalities of his time. We can read learned dissertations delivered by Tartaglia to such renowned noblemen as François Marie, the Duke of Urbino, Richard Ventuorth, subject of his Majesty the King of England, Gabriel Tadino di Martinengo, Knight of Rhodes and Prior of Barletta, and Don Diego Hurtado di Mendozza, Ambassador of the Empire to the Republic of Venice. We see Tartaglia conversing with persons of all conditions, such as Brother Beretino, Master Zuanne di Tonini da Coi, who has a school at Brescia, the excellent physician and philosopher, Marc Antonio Morosini, and mathematicians such as Antonio Maria Fior or his Excellency, Hieronimo Cardano. Sometimes, Tartaglia’s interlocutors are persons of lesser social stature whose names have not come down to us, such as an artilleryman, a mortar man or a fusilier.
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References
Quesiti et Inventioni diverse di Nicolo Tartaglia, Venetia, Vent. Ruffinelli, 1546 — Various editions of this work follow rapidly. One can cite the following: Quesiti et Inventioni diverse. La nova Scientia, Venetia, Nie. de Bascarini, 1550; — Quesiti et Inventioni diverse, Ragionamenti sopra la travagliata Inventione,con supplemento, Venetia, Nie. de Bascarini, 1551; — Quesiti et Inventioni diverse, Regola generale de solevare con ragione e misura non solamente ogni affondata nave, ma una torre solida di metallo, Venetia, Nie. de Bascarini, 1551; — Quesiti et Inventioni diverse, con una giunta al sesto libro, nella quale si mostra duoi modi di redur una città inespugnabile, Venetia, Nie. de Bascarini, 1554. — Furthermore, one can mention; Opere del famosissimo Nicolo Tartaglia, cioè Quesiti, Nova Scientia, Travagliata Inventione, Ragionamenti sopra Archimede, etc., Venetia, 1606. (T. N.: The Italian reads respectively, Diverse Questions and Inventions of Nicolo Tartaglia; Diverse Questions and Inventions. The New Science; Diverse Questions and Inventions, Reflections on burdensome inventions, with supplements; Diverse Questions and Inventions, General Rules to raise with logic and control not only any sunken ship but a solid metal tower; Diverse Questions and Inventions with an addition to the sixth book, in which is demonstrated two methods for breaching an impregnable city; Works of the famous Nicolo Tartaglia, that is, Questions, New Science, burdensome Inventions, Reflections on Archimedes, etc.
Les Manuscrits de Léonard de Vinci, published by Ch. Ravaisson-Mollien, Ms. G de la Bibliothèque de l’Institut, folio 77, recto.
Tartaglia, Quesiti et Inventioni diverse, edition of 1544, p. 8, verso.
Quesiti et Inventioni diverse, Libro ottavo, Quesiti XXVII, Petitione VI.
Quesiti et Inventione diverse, Libro ottavo, Quesiti XLI, XLII; Propositioni XIV, XV.
T. N.: The Italian reads, “I am his protegé.”
I sei cartelli di matematica disfida primamenti intorno alla generale risoluzione delle equazioni cubiche di Ludovico Ferrari, Coi sei contro-cartelli in riposta di Nicolo Tartaglia comprendenti le soluzioni de’ quesiti dall’ una et dall’ altra parte propositi. Raccolti, autografati e publicati da Enrico Giordani, Bolognese. Premesse notizie bibliografiche ed illustrazioni sui Cartelli medesimi, estratte da documenti già a stampa ed altri manoscritti favoriti dal Comm. Prof. Silvestro Gherardi. Milano, 1876. (T. N.: The Italian reads, The six letters of the mathematical challenge primarily concerned with the general solution to cubic equations by Ludovico Ferrari, with six letters of reply by Nicolo Tartaglia concerning the solution of problems posed by both parties. Collected, printed and published by Enrico Giorodani of Bologna. Prefaced by a bibliographic reference and illustrations of the same letters, taken from documents previously published and other manuscripts given by Commendatore Professor Silvestro Gherardi. Milano, 1876.) These six challenges by Ferrari and Tartagliai six ripostes remained unknown to mathematicians until Silvestro Gherardi had the good fortune to reassemble the entire collection. The six challenges by Ferrari which he found all bore in the author’s handwriting the address: Al Signor Nicolo Simo: Nicolo Simo was actually one of the geometers to whom the two adversaries sent their works. This collection is quite unique. Only the second of Ferrari’s challenges is in the St. Mark Library in Venice. Gherardi published the twelve texts in Bologna in 1846 appended to his own book entitled: Di alcuni materiali per la storia della facoltà matematica in Bologna. (T. N.: The Italian reads, Some Reference Material on the History of the Mathematical School in Bologna)He later lent them to Libri. They were sold in London in 1861 together with the library of Libri. In 1876 this collection was reproduced in facsimile by Enrico Giordani and was dedicated to Prince Baldassare Boncompagni. (Cf. Catalogue of mathematical, historical, bibliographical, and miscellaneous portion of the celebrated library of Guglielmo Libri: Part I: A-L, London 1861, no. 178, pp. 19 and 20: On page 1 there is a facsimile of the signature of Ferrari. — J. Ch. Bruner, Manuel du Librarie et de l’amateur de livres, Vol. V, 1864, column 661 — and the announcement preceding the reprinting of 1876.)
Ferrari, Primo cartello, p. 2.
Ferrari, Secondo cartello, p. 6.
Seconda riposta data da Nicolo Tartalea Brisciano, pp. 7 and 8.
Jordani Opusculum de ponderositate, Nicolai Tartaleale studio correctum, novisque figuris auctum. Cum privilegio. Venetiis, apud Curtium Trojanum, MDLXV. (T. N.: The Latin title reads, A Treatise on Weights by Jordanus, corrected and enlarged with new figures by Nicolo Tartaglia. With Imperial Privilege. Venice, Curtius Trojanus, 1565.)
Hieronymi Cardani De numerorum proprietatibus liber unicus; Caput LXVI, de Ponderibus. (T. N.: The Latin title reads, A Single Book on the Properties of Numbers, by Jerome Cardan, Chapter 66, “On Weights.”) According to Niceron (a) this work was printed for the first time after the death of its author in: Hieronymi Cardani Opera omnia, tomus IV. (T. N.: The Latin title reads, The Complete Works of Jerome Cardan, Vol. IV.)
(a) Niceron, Mémoires pour servir à l’histoire des hommes illustres, Vol. XIV, p. 271; Paris, 1731.
Les Livres de Hierome Cardanus, médecin milannois, intitulés de la Subtilité et subtiles Inventions, ensemble les causes occultes et raisons d’icelles, traduis de Latin en François par Richard Le Blanc, Paris, Charles l’Angelier, 1556. (T. N.: The French title reads, The Book on Subtlety and Subtle Inventions, Together with the Occult Causes and their Reasons, by Jerome Cardan, Milanese physician, translated from Latin into French by Richard Le Blanc, Paris, Charles l’Angelier, 1556.)
Alexandri Piccolominei in mechanicas quaestiones Aristotelis paraphrase paulo quidem plenior, ad Nicolaum Ardinghellum Cardinalem amplissimum. (On the last page: Excussum Romae apud Antonium Bladum Asulanum, Tertio Non. Januarii MDXLVII). — The same work was re-edited: Venetiis, apud Curtium Trojanum, MDLXV. — It was also translated into Italian under the title: A. Piccolomini, Sopra le mecaniche dAristotile, translated by O. V. Biringucci. Roma, Zanetti, 1582. (T. N.: The Latin reads, A Somewhat Fuller Paraphrase of the Mechanical Problems of Aristotle by Alexander Piccolomini, dedicated to the illustrious Cardinal Nicolas Ardinghello, published at Rome by Antonius Baldus Asulanus, the third of January 1547.)
Edition of 1547, p. 22, verso.
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Duhem, P. (1991). The School of Jordanus in the 16th Century Nicolo Tartaglia. In: The Origins of Statics. Boston Studies in the Philosophy of Science, vol 123. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3730-0_9
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