TARTAGLIA, Niccolò.

Quesiti, et inventioni diverse. [Colophon:] Venice: Venturino Ruffinelli, 1546. [Bound with:] Ibid., La nova scientia … con una gionta al terzo libro. Venice: Niccolò Bascarini for the author, 1550. [And with:] BIRINGUCCIO, Vannoccio. Pirotechnia: li diece libri della pirotechnia, nelliquali si tratta non solo la diuersita delle minere, ma ancho quanto si ricer ca alla prattica di esse e di quanto s’appartiene all’ arte della fusione ouer getto de me talli, e d’ogni altra cofa a questa fomigliante.

Venice: Giovanni Padovano for Curzio Troiano Navò, 1550.

First edition of Tartaglia’s Quesiti, second edition of the other two works. The Quesiti continues the discussion of ballistics in Tartaglia’s Nova scientia (first published in 1537), pointing out for the first time that the trajectory of a projectile is curved throughout (in the Nova Scientia he argued that the path of a projectile consisted of rectilinear parts at the beginning and end of the trajectory, with a curved part between). The Quesiti is also famous for containing Tartaglia’s solution of cubic equations, which until a few years earlier had been considered impossible; he had kept it secret since discovering it in 1535 (Cardano had published Tartaglia’s solution in his Artis magnae (1545), without his permission.) Tartaglia (1499-1557) “reshaped the character of military discourse by identifying a ‘new science’ of artillery and casting it as a mathematical discipline. As a mathematician he was first directed to military questions in 1531 or 1532 in Verona when he was consulted on the maximum range of cannon … Few European mathematicians of the 16th century had been as directly affected by war as Niccolò Tartaglia. In 1512, when still a boy, he received a facial wound during the sack of Brescia by the French. Left with a speech defect he adopted the nickname of Tartaglia (‘stammerer’) to replace his original surname Fontana. If Tartaglia’s very identity was marked by war, he in turn reshaped the character of military discourse by identifying a ‘new science’ of artillery and casting it as a mathematical discipline … A measure of Tartaglia’s importance for the study of artillery is that [his] account was still being paraphrased and parroted into the later 17th century” (Bennett & Johnston). “Tartaglia proved both mathematically and experimentally that the trajectory of a missile fired from a cannon was a curved line throughout, thus contradicting the ‘impetus’ theory derived from Aristotle's Physics, which stated that a projectile’s trajectory was described by two straight lines united by a curved line (Tartaglia was the first Renaissance scientist to point out serious flaws in the Physics). Tartaglia demonstrated that from the beginning of its flight, a projectile was affected by gravity, which, along with wind resistance, caused its forward velocity to lessen while increasing the speed of its fall. Tartaglia also observed a relationship between the speed of projection and the speed of fall: the greater the initial speed, the less the gravitational influence. Through experimentation, he determined that the maximum cannon range, at any given initial speed, was obtained with a firing elevation of forty-five degrees” (Norman 2053). The work by Biringuccio (1480-1539) is the second edition of the first book entirely dedicated to metallurgy. It “was written for the practicing metallurgist, foundryman, dyer, type-founder, glass-maker, and maker of gunpowder, fireworks and chemicals used in warfare” (Dibner, on the first edition, 1540).

Provenance: Benedetto Sertori, doctor; Giovanni Battista da Filicaia, a citizen of Florence, early inscriptions on title-page; Thomas Francis Fremantle, armorial bookplate.

Second edition of Tartaglia’s first work, Nova scientia, the foundation of the new sciences and a major catalyst for the researches of Galileo. “The New Sciences stands at the threshold of a new age in the history of mechanics” (Printing and the Mind of Man). Tartaglia investigated problems of ballistics, fortification, surveying and engineering and sought to apply mathematical analysis to physical problems, free from the conceptual constraints of Aristotelianism and Scholasticism. “Tartaglia proved both mathematically and experimentally that the trajectory of a missile fired from a cannon was a curved line throughout, thus contradicting the ‘impetus’ theory derived from Aristotle’s Physics, which stated that a projectile’s trajectory was described by two straight lines united by a curved line (Tartaglia was the first Renaissance scientist to point out serious flaws in the Physics). Tartaglia demonstrated that from the beginning of its flight, a projectile was affected by gravity, which, along with wind resistance, caused its forward velocity to lessen while increasing the speed of its fall. Tartaglia also observed a relationship between the speed of projection and the speed of fall: the greater the initial speed, the less the gravitational influence. Through experimentation, he determined that the maximum cannon range, at any given initial speed, was obtained with a firing elevation of forty-five degrees” (Norman Catalogue 2053). “The latter result was obtained through an erroneous argument, but the proposition is correct (in a vacuum) and might well be called ‘Tartaglia’s theorem’” (DSB).

Dibner describes the allegory of the frontispiece as follows: “Euclid greets the students at the outer gate of the circle in which Tartaglia is surrounded by Arithmetic, Geometry, Music, Astronomy, Astrology, etc. — the mathematical disciplines. A fired cannon and a mortar show the trajectories defined by Tartaglia. In the farther circle sits Philosophy. Beneath the scroll in Plato's hand, reading ‘None not expert in Geometry may enter here’, Aristotle moves forward to welcome the students.”

II. First edition of the Quesiti, in which Tartaglia continued his discussion of ballistics begun in Nova scientia. “Dedicated to Henry VIII, this work contains nine books of questions posed to Tartaglia by various people, and demonstrates his skill in non-mathematical areas: solving problems in the firing of artillery; topographical surveying; equilibrium in balances and statics; a new method for raising sunken ships; etc. In the course of the discussions, some fundamental issues in the theory of motion and of statics are raised, which are elaborated upon in the eighth book … Among its other important points are the anticipation of the principle of inertia in book three, the observations on the use of compasses in book five, and the solution of cubic equations in book nine” (Roberts and Trent, p. 313).

“From the sixteenth to the end of the eighteenth century numerous works were produced which deal with gun-founding, the composition of gunpowder, and in the later years the absorbing question of range-finding, elevation and cognate matters of interest to the gunner in those days. In most cases these works are illustrated, but, by collation of the several editions, it will be found that each author reproduces much of the information given in works of earlier date and that the fons et origo of them all is Tartaglia’s Colloquies [the English translation of the Quesiti]” (Ffoulkes, The Gun-founders of England, p. 7).

The Quesiti also included what, without exaggeration, can be called the first real advance in algebra since antiquity. “Tartaglia’s Quesiti contains his most important mathematical accomplishment: the independent discovery of the rule for solving third-degree (cubic) equations, a rule first formulated but left unpublished by Scipione del Ferro in the first or second decade of the sixteenth century. Tartaglia re-solved the problem in 1535 but kept the details a secret for many years, using his knowledge to gain advantage in the frequent public disputations held between scholars in his era. He finally revealed the rule to Girolamo Cardano in 1539 after Cardano swore to keep it secret, but six years later Cardano broke his promise by publishing the rule in his Ars magna ... Tartaglia was incensed at Cardano’s breach of promise and abused him roundly in Book IX of the Quesiti, in which he also published his own version of his researches into third-degree equations” (Norman).

“With the publication of the Quesiti began a protracted battle between Tartaglia and Ferrari, Cardano’s faithful student who fought on his teacher’s behalf. Ferrari challenged Tartaglia to a public debate – or, rather, a showdown. During the full year leading up to their public contest, the two exchanged a series of public letters (six each) now known as the Cartelli di sfida. The letters of this remarkably vicious but fascinating correspondence were printed by both Tartaglia and Ferrari and sent to hundreds of mathematicians and scholars. At the height of the controversy, Tartaglia was invited to apply for a position as lecturer of mathematics at the University in Brescia – but the job offer was conditional on his triumphing publicly over Ferrari. Instead, when Tartaglia and Ferrari finally presented their work at the church of Santa Maria del Giardino in Milan, before a large audience of mathematicians and lay people, Ferrari won. Tartaglia himself (and some historians since) have insisted that Tartaglia was actually the victor, but a surviving hand-written sonnet tucked into a collection of the Tartaglia-Ferrari cartelli suggests that Tartaglia failed to win over public opinion. The sonnet, composed by a Milanese priest at the time of the contest, condemns Tartaglia as ‘pazzo a tuffi’ (totally mad) in his attacks on Cardano, and sings the praises of Ferrari for valiantly and justly defending Cardano’s name. Tartaglia also failed to win the job at Brescia.

“After the contest, Tartaglia returned to Venice. In the final decade of his life he was poor, scorned, and bitter, but busy writing his General trattato. Death, unfortunately, came before he finished the last few books of this massive tome – the books that would have included his treatise on cubic equations” (Saiber, pp. 116-117).

III. Second edition of Biringuccio’s Pirotechnia. “Biringuccio’s reputation derives from a single work, his Pirotechnia, published posthumously in 1540. The work is divided into ten books, which deal with (1) metallic ores; (2) the ‘semiminerals’ (including mercury, sulfur, alum, arsenic, vitriol, several pigments, gems, and glass); (3) assaying and preparing ores for smelting; (4) the parting of gold and silver, both with nitric acid and with antimony sulfide or sulfur; (5) alloys of gold, silver, copper, lead, and tin; (6) the art of casting large statues and guns; (7) furnaces and methods of melting metals; (8) the making of small castings; (9) miscellaneous pyrotechnical operations (including alchemy; the distillation of acids, alcohol, and other substances; the working of a mint ‘both honestly and with profit’ the goldsmith, silversmith, and ironsmith; the pewterer; wire-drawing; mirror-making; pottery; and bricks); and (10) the making of saltpeter, gunpowder, and fireworks for warfare and celebration. Virtually all of Biringuccio’s descriptions are original. He is important in art history for his description of the peculiarly Renaissance arts of casting medallions, statues, statuettes, and bells. His account of typecasting, given in considerable detail, is the earliest known. The Pirotechnia contains eighty-three woodcuts, the most useful being those depicting furnaces for distillation, bellows mechanisms, and devices for boring cannon and drawing wire.

“As the first comprehensive account of the fire-using arts to be printed, the Pirotechnia is a prime source on many practical aspects of inorganic chemistry. Biringuccio emphasizes the adaptation of minerals and metals to use – their alloying, working, and especially the art of casting, of which he writes in great detail. In this area he is far better than the two other sixteenth-century authors with whom he is inevitably compared, Georgius Agricola and Lazarus Ercker. Although Agricola excels on mining and smelting, his famed sections on glass, steel, and the purification of salts by crystallization are in fact taken nearly verbatim from the Pirotechnia.

“Biringuccio’s approach is in strong conflict with that of the alchemists, whose work he evaluates in eleven pages of almost modern criticism, distinguishing their practical achievements from their theoretical motivations. His interest in theoretical questions is limited to the repetition of an essentially Aristotelian view of the origins of metallic ores and the nature of metals, with a rather forced extension to account for the observed increase in weight of lead when it is turned to litharge [lead monoxide].

“Biringuccio has been called one of the principal exponents of the experimental method, for he states that ‘It is necessary to find the true method by doing it again and again, continually varying the procedure and then stopping at the best’ and ‘I have no knowledge other than what I have seen with my own eyes.’ He gives quantitative information wherever appropriate. He was certain that the failure of an operation was due to ignorance or carelessness, not to either ill luck or occult influences: Fortune could be made to favor the foundryman by paying careful attention to details. Biringuccio’s method, however, is not that of the scientist, for none of his operations is planned to test theory or even reflects the conscious application of it. He represents the strain of practical chemistry that had to develop and to be merged with philosophy before it could become science. Yet the enjoyment of the diverse properties of matter and the careful recording of a large number of substances and types of reactions that had been established by various craftsmen were just as necessary as the works of the philosophers, and in some sense were nearer the truth” (DSB).

Adams T-183; Cockle 660; Edit16 29899; Roberts and Trent, Bibliotheca Mechanica, p. 313; Norman 2055; Parkinson, Breakthroughs p. 41. II. Adams T-189; Cockle 658; Edit16 31855; Dibner 102; Printing and the Mind of Man 66; Norman 2053; Parkinson, Breakthroughs p. 35 (the last four for the first edition). III. Adams B-2081; Cockle 931; Duveen 79; Edit16 6157. Bennett & Johnston, The Geometry of War 1500-1750, 2012. Drake (tr. & ed.), Galileo Galilei, Operations of the Geometric and Military Compass 1606, 1979; Saiber, Measured Words: Computation and Writing in Renaissance Italy, 2017.

Three works in one volume, 4to (212 x 155mm). I. ff. [6], 5-132, with woodcut portrait of Tartaglia on title, numerous woodcut illustrations and diagrams in text, manuscript note by Filicaia on EE2v. II. ff. [4], 32, with allegorical woodcut title and numerous woodcut diagrams in text. III. ff. [8], 167, [1], title within woodcut border incorporating pyrotechnic instruments, woodcut initials and illustrations, woodcut printer’s device on final leaf. Contemporary limp vellum (worn at edges with minor loss).

Item #4938

Price: $17,500.00