Niccolò Fontana Tartaglia.
Niccolò Fontana Tartaglia (Italian pronunciation: ; 1499/1500, Brescia – 13 December 1557, Venice) was an Italian mathematician, engineer (designing fortifications), a surveyor (of topography, seeking the best means of defense or offense) and a bookkeeper from the thenRepublic of Venice (now part of Italy). He published many books, including the first Italian translations of Archimedes and Euclid, and an acclaimed compilation of mathematics. Tartaglia was the first to apply mathematics to the investigation of the paths of cannonballs, known as ballistics, in his Nova Scientia, “A New Science;” his work was later partially validated and partially superseded by Galileo's studies on falling bodies. He also published a treatise on retrieving sunken ships.
Personal life
Niccolò Fontana was the son of Michele Fontana, a dispatch rider who travelled to neighboring towns to deliver mail. But in 1506, Michele was murdered by robbers, and Niccolo, his two siblings, and his mother were left impoverished. Niccolò experienced further tragedy in 1512 when the King Louis XII's troops invaded Brescia during the War of the League of Cambrai against Venice. The militia of Brescia defended their city for seven days. When the French finally broke through, they took their revenge by massacring the inhabitants of Brescia. By the end of battle, over 45,000 residents were killed. During the massacre, Niccolò and his family sought sanctuary in the local cathedral. But the French entered and a soldier sliced Niccolò's jaw and palate with a saber and left him for dead. His mother nursed him back to health but the young boy would never recover the power of speech, prompting the nickname "Tartaglia" ("stammerer"). After this he would never shave, and grew a beard to camouflage his scars.^{[1]}
There is a story that Tartaglia learned only half the alphabet from a private tutor before funds ran out, and he had to learn the rest by himself. Be that as it may, he was essentially selftaught. He and his contemporaries, working outside the academies, were responsible for the spread of classical works in modern languages among the educated middle class.
Major works
His edition of Euclid in 1543, the first translation of the Elements into any modern European language, was especially significant. For two centuries Euclid had been taught from two Latin translations taken from an Arabic source; these contained errors in Book V, the Eudoxian theory of proportion, which rendered it unusable. Tartaglia's edition was based on Zamberti's Latin translation of an uncorrupted Greek text, and rendered Book V correctly. He also wrote the first modern and useful commentary on the theory. Later, the theory was an essential tool for Galileo, just as it had been for Archimedes.
However, his best known work is his treatise General Trattato di numeri, et misure published in Venice 1556–1560. This has been called the best treatise on arithmetic that appeared in the sixteenth century.^{[2]} Not only does Tartaglia have complete discussions of numerical operations and the commercial rules used by Italian arithmeticians in this work, but he also discusses the life of the people, the customs of merchants and the efforts made to improve arithmetic in the 16th century.
Solution to cubic equations
Tartaglia is perhaps best known today for his conflicts with Gerolamo Cardano. Cardano cajoled Tartaglia into revealing his solution to the cubic equations, by promising not to publish them. Tartaglia divulged the secrets of the solutions of three different forms of the cubic equation in verse.^{[3]} Several years later, Cardano happened to see unpublished work by Scipione del Ferro who independently came up with the same solution as Tartaglia. As the unpublished work was dated before Tartaglia's, Cardano decided his promise could be broken and included Tartaglia's solution in his next publication. Even though Cardano credited his discovery, Tartaglia was extremely upset. He responded by publicly insulting Cardano. Mathematical historians now credit both with the paternity of the formula to solve cubic equations, referring to it as the "CardanoTartaglia Formula".
Volume of a tetrahedron
Tartaglia is also known for having given an expression (Tartaglia's formula) for the volume of a tetrahedron (including any irregular tetrahedra) as the Cayley–Menger determinant of the distance values measured pairwise between its four corners:

V^2 = \frac{1}{288} \det \begin{bmatrix} 0 & d_{12}^2 & d_{13}^2 & d_{14}^2 & 1 \\ d_{21}^2 & 0 & d_{23}^2 & d_{24}^2 & 1 \\ d_{31}^2 & d_{32}^2 & 0 & d_{34}^2 & 1 \\ d_{41}^2 & d_{42}^2 & d_{43}^2 & 0 & 1 \\ 1 & 1 & 1 & 1 & 0 \end{bmatrix}
where d_{ ij} is the distance between vertices i and j. This is a generalization of Heron's formula for the area of a triangle.
Notes
References

Katz, Victor J. (1998), A History of Mathematics: An Introduction (2nd ed.), Reading: Addison Wesley Longman,

Strathern, Paul (2013), Venetians, New York, NY: Pegas Books
External links

"Tartaglia or Tartaglia (Nicholas)" in A Philosophical and Mathematical Dictionary by Charles Hutton (1815) p.482; @GoogleBooks

Tartaglia's work (and poetry) on the solution of the Cubic Equation at Convergence

The Cubic Tutorials by John H. Mathews
This article was sourced from Creative Commons AttributionShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, EGovernment Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a nonprofit organization.