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**Niccolò Fontana Tartaglia** (Italian: [nikkoˈlɔ ffonˈtaːna tarˈtaʎʎa] ; 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 then-Republic 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known as ballistics, in his * Nova Scientia * (*A New Science*); his work was later partially validated and partially superseded by Galileo's studies on falling bodies.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.

**Brescia** is a city and *comune* in the region of Lombardy in northern Italy. It is situated at the foot of the Alps, a few kilometres from the lakes Garda and Iseo. With a population of more than 200,000, it is the second largest city in the region and the fourth of northwest Italy. The urban area of Brescia extends beyond the administrative city limits and has a population of 672,822, while over 1.5 million people live in its metropolitan area. The city is the administrative capital of the Province of Brescia, one of the largest in Italy, with over 1,200,000 inhabitants.

**Venice** is a city in northeastern Italy and the capital of the Veneto region. It is situated on a group of 118 small islands that are separated by canals and linked by over 400 bridges. The islands are located in the shallow Venetian Lagoon, an enclosed bay that lies between the mouths of the Po and the Piave rivers. In 2018, 260,897 people resided in the *Comune di Venezia*, of whom around 55,000 live in the historical city of Venice. Together with Padua and Treviso, the city is included in the Padua-Treviso-Venice Metropolitan Area (PATREVE), which is considered a statistical metropolitan area, with a total population of 2.6 million.

A **mathematician** is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

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 Niccolò, 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 was left with a speech impediment, prompting the nickname "Tartaglia" ("stammerer"). After this he would never shave, and grew a beard to camouflage his scars.^{ [1] }

The **War of the League of Cambrai**, sometimes known as the **War of the Holy League** and by several other names, was a major conflict in the Italian Wars. The main participants of the war, fought from 1508 to 1516, were France, the Papal States and the Republic of Venice; they were joined, at various times, by nearly every significant power in Western Europe, including Spain, the Holy Roman Empire, England, the Duchy of Milan, Florence, the Duchy of Ferrara and Swiss mercenaries.

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 self-taught. He and his contemporaries, working outside the academies, were responsible for the spread of classical works in modern languages among the educated middle class.

An **alphabet** is a standard set of letters that represent the phonemes of any spoken language it is used to write. This is in contrast to other types of writing systems, such as syllabaries and logographic systems.

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.

**Euclid**, sometimes called **Euclid of Alexandria** to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry". He was active in Alexandria during the reign of Ptolemy I. His *Elements* is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics from the time of its publication until the late 19th or early 20th century. In the *Elements*, Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigour.

The * Elements* is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates, propositions, and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines.

**Latin** is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from the Etruscan and Greek alphabets and ultimately from the Phoenician alphabet.

However, his best known work is his treatise * General Trattato di Numeri et Misure* published in Venice 1556–1560.^{ [2] } This has been called the *best* treatise on arithmetic that appeared in the sixteenth century.^{ [3] } 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.

**Arithmetic** is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division. Arithmetic is an elementary part of number theory, and number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra, geometry, and analysis. The terms *arithmetic* and *higher arithmetic* were used until the beginning of the 20th century as synonyms for *number theory* and are sometimes still used to refer to a wider part of number theory.

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.^{ [4] } 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 and a famous public challenge match resulted between himself and Cardano's student, Ludovico Ferrari. Widespread stories that Tartaglia devoted the rest of his life to ruining Cardano, however, appear to be completely fabricated.^{ [5] } Mathematical historians now credit both Cardano and Tartaglia with the formula to solve cubic equations, referring to it as the "Cardano–Tartaglia formula".

**Gerolamo****Cardano** was an Italian polymath, whose interests and proficiencies ranged from being a mathematician, physician, biologist, physicist, chemist, astrologer, astronomer, philosopher, writer, and gambler. He was one of the most influential mathematicians of the Renaissance, and was one of the key figures in the foundation of probability and the earliest introducer of the binomial coefficients and the binomial theorem in the western world. He wrote more than 200 works on science.

**Scipione del Ferro** was an Italian mathematician who first discovered a method to solve the depressed cubic equation.

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:

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.

- ↑ Strathern 2013 , p. 189
- ↑ Chisholm 1911.
- ↑ Smith 1985 , p. 298
- ↑ Katz 1998 , p. 359
- ↑ Tony Rothman, Cardano v Tartaglia: The Great Feud Goes Supernatural.

The area of study known as the **history of mathematics** is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, together with Ancient Egypt and Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the field of astronomy and to formulate calendars and record time.

**Lodovico de Ferrari** was an Italian mathematician.

In mathematics, **Galois theory** provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is in some sense simpler and better understood.

**Omar Khayyam** was a Persian mathematician, astronomer, and poet. He was born in Nishapur, in northeastern Iran, and spent most of his life near the court of the Karakhanid and Seljuq rulers in the period which witnessed the First Crusade.

In algebra, a **cubic function** is a function of the form

In mathematics, an **algebraic equation** or **polynomial equation** is an equation of the form

In algebra, the **theory of equations** is the study of algebraic equations, which are equations defined by a polynomial. The main problem of the theory of equations was to know when an algebraic equation has an algebraic solution. This problem was completely solved in 1830 by Évariste Galois, by introducing what is now called Galois theory.

In Euclidean geometry, the **Poncelet–Steiner theorem** is one of several results concerning compass and straightedge constructions with additional restrictions. This result states that whatever can be constructed by straightedge and compass together can be constructed by straightedge alone, provided that a single circle and its centre are given.

**Diocles** was a Greek mathematician and geometer.

**Rafael Bombelli** was an Italian mathematician. Born in Bologna, he is the author of a treatise on algebra and is a central figure in the understanding of imaginary numbers.

**Abu-Abdullah Muhammad ibn Īsa Māhānī** was a Persian Muslim mathematician and astronomer born in Mahan, and active in Baghdad, Abbasid Caliphate. His known mathematical works included his commentaries on Euclid's *Elements*, Archimedes' *On the Sphere and Cylinder* and Menelaus' *Sphaerica*, as well as two independent treatises. He unsuccessfully tried to solve a problem posed by Archimedes of cutting a sphere into two volumes of a given ratio, which was later solved by 10th century mathematician Abū Ja'far al-Khāzin. His only known surviving work on astronomy was on the calculation of azimuths. He was also known to make astronomical observations, and claimed his estimates of the start times of three consecutive lunar eclipses were accurate to within half an hour.

Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics and Indian mathematics. Important progress was made, such as the full development of the decimal place-value system to include decimal fractions, the first systematised study of algebra, and advances in geometry and trigonometry.

The * Ars Magna* is an important Latin-language book on algebra written by Gerolamo Cardano. It was first published in 1545 under the title

A timeline of key algebraic developments are as follows:

A timeline of **algebra** and **geometry**

* Why Beauty Is Truth: A History of Symmetry* is a 2007 book by Ian Stewart.

**Ostilio Ricci** (1540–1603) was an Italian mathematician.

The year **1537 in science** and technology included many events, some of which are listed here.

The year **1545 in science** and technology involved some significant events.

Chisholm, Hugh, ed. (1911). . *Encyclopædia Britannica*.**26**(11th ed.). Cambridge University Press.- Katz, Victor J. (1998),
*A History of Mathematics: An Introduction*(2nd ed.), Reading: Addison Wesley Longman, ISBN 0-321-01618-1 - Smith, D.E. (1958),
*History of Mathematics*,**I**, New York: Dover Publications, ISBN 0-486-20429-4 - Strathern, Paul (2013),
*Venetians*, New York, NY: Pegasus Books Herbermann, Charles, ed. (1913). . *Catholic Encyclopedia*. New York: Robert Appleton Company.- Charles Hutton (1815). "Tartaglia or Tartaglia (Nicholas)".
*A philosophical and mathematical dictionary*. Printed for the author. p. 482.

- History Today
- The Galileo Project
- O'Connor, John J.; Robertson, Edmund F., "Niccolò Fontana Tartaglia",
*MacTutor History of Mathematics archive*, University of St Andrews . - Tartaglia's work (and poetry) on the solution of the Cubic Equation at Convergence
- La Nova Scientia (Venice, 1550)

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