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Tartaglia

Name: Niccolo Fontana Tartaglia

Nickname/Alias: born: Niccolo Fontana

Achievements: Ballistics

Born: 1499; Brescia, Venetian Republic, Italy

Died: December 13, 1557; Venice (Aged 58)

Field & Discipline: Mathematics; Enginering; Mechanics; Ballistics; Mathematician

Language: Italian

Father: Father: Michele Fontana

Mother: Unknown

Siblings: Several

Spouse: Unknown

Children: Unknown

Education: Self taught

Major Work:

"A New Science" (1537)

"Treatise on Numbers and Measures" (1556-60)

Life & Times:

In 1512, when Tartaglia was thirteen, French troops sacked Brescia and massacred large numbers of the population. Tartaglia received serious sabre wounds to the head, and his mouth was so damaged that afterwards he could only speak with great difficulty (and became known as “Tartaglia,” (“the stutterer”).  

He showed an early aptitude for mathematics and around 1517 moved to Verona where he taught the use of the abacus. Some ten to fifteen years later he appears to been married with a family, and living precariously in Verona as a schoolmaster.  In 1534 he moved to Venice as a professor of mathematics. He taught in various academies and also gave public lectures.

In the late fifteenth century, [work related to] Pacioli* had published the method for solving algebraic equations of the first and second degree to find the unknown quantity which is today known as "x,” and was then called in Italy: "cosa" (the thing). Early in the sixteenth century, Scipione del Ferro (professor of mathematics at Bologna) advanced the method to include cubic equations,  but did not publish. 

One of del Ferro's pupils, Antonio Maria Fiore, a mediocre mathematician who lived in Venice, learned the method from del Ferro. When del Ferro died in 1526, Fiore exploited his old master's  method and in 1535 he challenged Tartaglia to a problem-solving match. There were thirty questions and the loser had to pay for thirty banquets for the winner and his friends.

All Fiore's questions were about the ‘cosa’ and cube equation. Tartaglia worked frantically with no success until, one sleepless night just before the deadline,  he was suddenly inspired and solved all thirty problems very quickly.

At that time, mathematicians all followed each other's challenges and [work related to] Cardano* in Pavia was intrigued by the Tartaglia/Fiore match. He eventually either worked out the solving of cubic equations for himself,  or was told about it – possibly even by Tartaglia  - and promised he would not publish.

In 1537 Tartaglia published: "A New Science," a treatise on gunnery (the big new cannon caused big new problems related to hitting the target). In his treatise Tartaglia followed the example of [followed ideas of] Oresme* in challenging the accepted laws of the universe as dictated by Aristotle, and "The New Science" was one of the first non-Aristotelian attempts to establish the laws of falling bodies.

The mechanics of force and motion had been studied by [influenced by] da Vinci* and others  before Tartaglia and it was not until half a century later that [anticipated] Galileo* made real progress in establishing the law.  In 1543 Tartaglia published translations of [translated] Euclid* and Archimedes and introduced the work of Euclid to one of his pupils, the mathematician [a pupil was] Benedetti*.

In 1545, because Tartaglia had still not published the method for solving cubic equations, Cardano did so. He credited both del Ferro and Tartaglia with the discovery but Tartaglia felt betrayed and took offence. The following year he hit back by publishing "New Problems and Inventions.”

It was dedicated to King [dedicated work to] Henry VIII* of England and revealed the solution to all the problems he had been asked to solve by prominent men. The book reveals that Tartaglia's interest and ability in practical,  non-mathematical areas extended to artillery, the making of gunpowder and cannonballs, the fortification of towns  and the use of the compass in topographical surveying. The book also contained a vicious attack on Cardano. 

The two men corresponded with questions and answers and then met for a public debate in the church of Santa Maria del Giardino in Milan in August 1548 where they debated sixty-two questions covering problems in geography, astronomy, architecture and optics as well as arithmetic, algebra and geometry.

In 1551 Tartaglia published a book on many areas of practical importance for the Venetian republic such as the raising of sunken ships, diving suits and weather forecasting.

Assessment: He made major advances in the mathematics of falling bodies.

Oneliner:  Niccolo Tartaglia, Renaissance ballistics expert

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