Niccolò Tartaglia

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Niccolò Tartaglia

Niccolò Tartaglia [ nik: o'lɔ tar'ta: ʎ: a ] (* 1499 or 1500 in Brescia , Italy ; † December 13, 1557 in Venice ) was a Venetian mathematician of the Renaissance who was known for his contributions to solving the cubic equation is known.

Life

In his book Quesiti et Inventioni Diverse (Various tasks and inventions), published in 1546, Tartaglia answered questions about his origins and his childhood in a dialogue: His father was a mailman on horseback and was called Michele. He doesn't know a family name. When asked why he called himself Tartaglia, he said that in February 1512, when the French sacked his native Brescia and wreaked a terrible massacre , a soldier with sword cuts inflicted three wounds on the head and two in the face, making him like look like a monster if the beard didn't hide it. Among the injuries was one across his mouth and teeth that made him unable to speak properly for a while, only stuttering. Therefore the children gave him the nickname Tartaglia (stutterer), which he kept as a memento of his misfortune. At that time he was about 12 years old. That is, he was born around 1500. In a document from 1529 a Nicolo from Brescia, master of arithmetic, certainly Tartaglia, is mentioned at the age of 30. This results in 1499 as the year of birth.

In the second edition of Quesiti from 1554, the dialogue was printed unchanged. That means, even three years before his death, Tartaglia still did not know whether his father had a family name and if so, which one.

At the age of 14, as he reported, Niccolò learned the ABC to K for two weeks in a writing school. Then he ran out of money and stole a finished alphabet with which he taught himself the remaining letters. ... and so, from that day on, I was never again with any teacher, but only in the company of a daughter of poverty called Diligence. In other words, he acquired all of his knowledge of mathematics and military studies as a self-taught self.

Tartaglia left Brescia around 1516, went via Crema , Bergamo and Milan to Verona , where he lived from around 1521 to 1534, and then moved to Venice, where he lived with the exception of a year and a half in Brescia from 1548/49 until his death in 1557.

Tartaglia earned his living mostly as a commercial calculator and private teacher. Occasionally he gave lectures and, during the 18 months in Brescia, lectures on Euclid's Elements , for which he received only a fraction of the fixed fee. (The lectures and lectures prove that Tartaglia no longer stuttered later.) A list of his poor legacy that still exists shows the poverty in which one of the great mathematicians of the Italian Renaissance lived.

About the name Tartaglias

In all of his works and surviving documents, Tartaglia writes his first name Nicolo with a c and without the accent on the second o. The claim that his real name was not Tartaglia but Fontana is also incorrect. In his will, which is kept in the State Archives in Venice , his biological brother Zuampiero Fontana is listed as a universal heir, but that does not necessarily mean, as some mathematicians have suggested, that Niccolò also had this family name. His older brother, like himself, had taken on a name. We don't know why Fontana in particular. In earlier centuries there were many people who only had a first name. Think of Leonardo da Vinci - Leonardo from Vinci , a small town near Florence. The public notary Rocco de Benedetti, who drew up the will and certified it with two witnesses, wrote the name of the father Michiel da Bressa (from Brescia, in dialect) without any family name and that of the testator Nicolo Tartaia. As an official he would have been obliged to write Nicolo Fontana if the testator had been called that way. But he obviously didn’t find it because the brothers had two different family names. Also on the outside of the nude is Nicolaus Tartalea, son of Michael from Brixia (Brescia in Latin). (Incidentally, Niccolò himself wrote his name Tartalea until about 1550 and only after that Tartaglia.) The name Fontana is not found in a single book of Tartaglia or a document about him. All of his works bear the name Tartaglia, of which he was obviously proud.

Fonts

General trattato de 'numeri et misure , 1556

From his first book La Nova Scientia on ballistics , printed in 1537 , it emerges that Tartaglia was the first to discover that a projectile has its greatest range when it is fired at an angle of 45 degrees above the horizon.

In February 1543, Tartaglia published the first translation of the elements of Euclid into Italian under the title Euclide Megarense Philosopho: Sole Introductory Guide to the Mathematical Sciences ... after the two translations . The title is wrong because Euclid of Megara was a philosopher who lived a century before the actually intended mathematician Euclid of Alexandria. The two translations used by Tartaglia for this, both in Latin, came from Giovanni Campano, Latinized by Johannes Campanus (1220–1296), printed in 1482, and by Bartolomeo Zamberti or Zamberto (1473-after 1543), printed in 1505. As a connoisseur of Euclid, Tartaglia was an expert the basics of geometry.

The formula for solving cubic equations

Tartaglia became known less for his books than because he was embroiled in a heated argument over the solution of the cubic equations. Today we speak of a single cubic equation x³ + ax² + bx + c = 0, where a, b and c can also be negative or 0, but at that time negative numbers were rejected. Therefore, a distinction was made between 13 different cubic equations: seven complete equations in which all powers are represented, three without a linear term and three without a square term, namely in modern notation x³ + px = q, x³ = px + q and x³ + q = px. The third of these equations has a negative main solution and has therefore mostly not been discussed.

A solution to the cubic equations had been sought for a long time. Finally, the lecturer at the University of Bologna Scipione dal Ferro (1465–1526) had found the solution to the first two equations without a quadratic term around 1505 or 1515, but did not publish them. Such knowledge was extremely valuable as a weapon of attack or defense at a time when the reappointment of a university professor and the level of his salary depended on how he performed in the frequent public scholarly competitions in which the two opponents posed tasks and problems for each other.

Arithmetic masters also fought such mathematical battles, and so at the beginning of January 1535 Tartaglia and his Venetian competitor Antonio Maria Fior faced each other 30 tasks that were to be solved within 40 or 50 days. Fior, as a student of dal Ferros, boasted of having the solution to the cubic equation (modern) x³ + px = q. All 30 tasks in Fior were of this form. Thereupon Tartaglia made an effort and found the solution rule on February 12, 1535 and one day later also the one for the equation (modern) x³ = px + q. According to him, he solved all of Fior's tasks within two hours, while Fior could not solve a single one.

In the Quesiti , Tartaglia reports that on January 2, 1539, a bookseller from Milan came to see him. He had been sent by the doctor Hieronimo Cardano (1501–1576), who was considered a very great mathematician, read Euclid publicly in Milan and was now having a work on the practice of arithmetic and geometry and on algebra printed. And because he had heard that Tartaglia in a competition with Master Fior had solved all 30 problems using the equation Cosa and Cubo (the unknown and the cube) equal to one number within two hours, “he asks that you give him these from yourselves discovered rule and if you please, he will publish it in his present work under your name and if it is not right for you that he should publish it, he will keep it secret. "Tartaglia's answer:" Tell his Excellency, for forgiving me, but if I want to publish this invention of mine, it will be in my own works and not in those of others. "

But Cardano did not give up. He pressed Tartaglia by letter and invited him to Milan on the pretext that the Spanish governor of Milan wanted to see him, and in Cardano's house, according to Tartaglia, on March 25, 1539: “I swear to you by the holy Gospels and as a real nobleman never to publish these discoveries of yours if you teach them to me. ”Then Tartaglia told him the solution for all three cubic equations in the form of a poem. And Tartaglia warned Cardano: "If you do not keep my word of honor, I promise you to print a book immediately afterwards, which you will not be very comfortable with."

Tartaglia could now have published his discovery. But he did not do it because he had no way of solving the other ten cubic equations with a quadratic term and also did not know what to do in the case of the (later so-called) casus irreducibilis , namely the case that in the solution formula Square roots of negative numbers occur.

In 1539 and 1545 a book by Cardano appeared under the title Artis magnae sive de Regulis algebraicis Liber unus , in which he published the solutions of cubic equations without a quadratic term as the discovery of Scipione dal Ferros, but in two places also indicated Nicolaus Tartalea as the second discoverer. In this algebra book Cardano showed how cubic equations with a quadratic term can be transformed into equations with a linear term and thereby lead to a solution, which Tartaglia never succeeded in doing. This means that in this work you will find the instructions for solving all 13 cubic equations and also the fourth-degree equations, which Cardano's student Lodovico Ferrari (1522–1565) discovered.

Tartaglia was furious at Cardano's betrayal . And he wrote the Quesiti in 1546 in order to revile Cardano in Task LX as being stupid, endowed with little intelligence and reason, trembling out of fear of a second-rate mathematician, as a poor man and incapable of solving easy tasks. Lodovico Ferrari then stepped on the scene to defend his former teacher. On February 10, 1547, he addressed the first pamphlet (Italian: cartello) as a challenge to Tartaglia and sent it to numerous prominent Italian personalities, whom he listed at the end of the twelve-page pamphlet. The then 25-year-old Ferrari challenged Tartaglia to a competition on geometry, arithmetic and all the disciplines that depend on them.

The two opponents exchanged six Cartelli and six Risposte (answers). The last one is dated July 24, 1548 by Tartaglia, who was then already in Brescia. In the second answer Tartaglia gives 31 tasks, in the third Cartello Ferrari just as many. Both later stated that the opponent had not solved them or not solved them correctly.

In the second Cartello, the only one in Latin, Ferrari reports that he accompanied Cardano to Bologna in 1542 and that they visited Annibale della Nave there, who had given them a little book written some time ago by the hand of his father-in-law Scipione dal Ferro, who died 16 years ago showed in which that invention, explained elegantly and expertly, was communicated. Cardano therefore no longer felt bound by his oath. Ferrari: “If you don't admit Cardanus that he is yours, will you at least allow him to teach us the invention of others?” Many mathematicians who did not know this detail condemned Cardano for breaking his word.

Tartaglia taught Euclid in Brescia from March to the end of July 1548. When the listeners drove to the country for the harvest, he decided to end the exchange of pamphlets with Ferrari and to go to Milan for a public debate with Cardano and Ferrari. But Cardano, who had previously stayed out of the discussion, left Milan and so only Tartaglia and the ingenious math lecturer Ferrari faced each other on August 10, 1548 in the church of Santa Maria del Giardino, which was later to become the Teatro alla Scala . The majority of the audience was on Ferrari's side, but that wasn't the only reason Tartaglia fell short.

In May 1551, Tartaglia published a book of only 38 pages, the general rule for lifting not only every sunken ship but also a solid metal tower with reason and measure, called the Travagliata Inventione (agonizing, arduous invention). At the same time, Nicolo Tartaglia discussed his Travagliata Inventione , a book of 48 pages. In the Third Discussion , the reason given for calling his invention agonizing invention is given. “I chose the title because I was among the greatest sufferings and torments of my life when I found the main subject of this invention” and then Tartaglia describes on 13 pages how he agreed on his at his Euclidean lectures in Brescia in 1548/49 Payment was cheated.

In the last years of his life in Venice, Tartaglia wrote a large work on arithmetic, geometry and algebra, but only up to quadratic equations and without a word about cubic ones , the General trattato di numeri et misure (General Discussion of Numbers and Measures) in six parts, with many remarkable details - the best mathematics encyclopedia of its time. The beginning appeared in 1556 while Tartaglia was still alive. The last parts came out posthumously in 1560.

Fonts

  • Noua scientia inuenta da Nicolo Tartalea brisciano ... , Venice 1537, doi : 10.3931 / e-rara-10432
  • Quesiti et inventioni diverse , Venice 1546, 1554; Edition of 1554: doi : 10.3931 / e-rara-9183
    Here the solution of the three cubic equations without a quadratic term is described.
  • General trattato di numeri e misure di Nicolo Tartaglia, nella quale in diecisette libri si dichiara tutti gli atti operatiui, pratiche, et regole necessarie non solamente in tutta l'arte negotiaria, & mercantile, ma anchor in ogni altra arte, scientia, ouer disciplina , doue interuenghi il calculo , Venice 1556–60, 6 parts in 3 volumes
  • Opere del famosissimo Nicolo Tartaglia cioe Quesiti, Trauagliata inuentione, Noua scientia, Ragionamenti sopra Archimede ... , Venice 1606

literature

  • Renato Acampora: The “Cartelli di matematica disfida”: the dispute between Nicolò Tartaglia and Ludovico Ferrari . Institute for History d. Naturwiss., Munich 2000.
  • Friedrich Katscher: The cubic equations in Nicolo Tartaglia: the relevant passages from his "Quesiti et inventioni diverse" translated into German and commented on . Vienna 2001.
  • Marcus du Sautoy The moonlight seekers. Mathematicians unlock the secret of symmetry . CH Beck 2008. ISBN 978-3406576706 .
  • Stillman Drake , Israel Edward Drabkin Mechanics in 16th century italy , University of Wisconsin Press 1969 (English translation of excerpts from Tartaglia's writings on mechanics).
  • Arnaldo Masotti: Tratagila, Niccolò . In: Charles Coulston Gillispie (Ed.): Dictionary of Scientific Biography . tape 13 : Hermann Staudinger - Giuseppe Veronese . Charles Scribner's Sons, New York 1976, p. 258-262 .
  • GB Gabrieli Nicolo Tartaglia: invenzioni, disfide e sfortune , Siena 1986.
  • Gerhard Arend: The mechanics of Niccolò Tartaglia in the context of contemporary epistemology and science . Munich 1998. ISBN 3-89241-025-9 .

Fiction

  • Dieter Jörgensen: The arithmetic master . Rütten & Loening 1999. A novel based on the life of Tartaglia.

Web links

Individual evidence

  1. ↑ after Friedrich Katscher
personal data
SURNAME Tartaglia, Niccolò
ALTERNATIVE NAMES Tartaglia, Nicolo
BRIEF DESCRIPTION Italian mathematician
DATE OF BIRTH 1499
PLACE OF BIRTH Brescia
DATE OF DEATH December 13, 1557
Place of death Venice