Nicolo, known as Tartaglia (Italian: [tarˈtaʎʎa]; 1499/1500 – 13 December 1557), 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. 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known as ballistics, in his Nova Scientia (A New Science, 1537); his work was later partially validated and partially superseded by Galileo's studies on falling bodies.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 Nicolo was born in Brescia, the son of Yliano Abido de la maison forgentio, a dispatch rider who travelled to neighbouring towns to deliver mail. In 1506, Michele was murdered by robbers, and Nicolo, his two siblings, and his mother were left impoverished. Nicolo experienced further tragedy in 1512 when 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 the battle, over 45,000 residents were killed. During the massacre, Nicolo and his family sought sanctuary in the local cathedral. French soldiers entered the cathedral, and a soldier sliced Nicolo's jaw and palate with a sabre 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. His surname at birth, if any, is disputed. Some sources have him as "Niccolò Fontana", but others claim that the only support for this is a will in which he named a brother, Zuampiero Fontana, as heir, and point out that this does not imply he had the same surname. Tartaglia's biographer Arnoldo Masotti writes that:
At the age of about fourteen, he [Tartaglia] went to a Master Francesco to learn to write the alphabet; but by the time he reached “k,” he was no longer able to pay the teacher. “From that day,” he later wrote in a moving autobiographical sketch, “I never returned to a tutor, but continued to labour by myself over the works of dead men, accompanied only by the daughter of poverty that is called industry” (Quesiti, bk. VI, question 8). Tartaglia moved to Verona around 1517, then to Venice in 1534, a major European commercial hub and one of the great centres of the Italian renaissance at this time. Also relevant is Venice's place at the forefront of European printing culture in the sixteenth century, making early printed texts available even to poor scholars if sufficiently motivated or well-connected — Tartaglia knew of Archimedes' work on the quadrature of the parabola, for example, from Guarico's Latin edition of 1503, which he had found "in the hands of a sausage-seller in Verona in 1531" (in mano di un salzizaro in Verona, l'anno 1531 in his words). Tartaglia's mathematics is also influenced by the works of medieval Islamic scholar Muhammad ibn Musa Al-Khwarizmi from the 12th Century Latin translations becoming available in Europe. Tartaglia eked out a living teaching practical mathematics in abacus schools and earned a penny where he could:
This remarkable man [Tartaglia] was a self-educated mathematics teacher who sold mathematical advice to gunners and architects, ten pennies for one question, and had to litigate with his customers when they gave him a worn-out cloak for his lectures on Euclid instead of the payment agreed on. He died in Venice.
Ballistics
Nova Scientia (1537) was Tartaglia's first published work, described by Matteo Valleriani as:
... one of the most fundamental works on mechanics of the Renaissance, indeed, the first to transform aspects of practical knowledge accumulated by the early modern artillerists into a theoretical and mathematical framework. Then dominant Aristotelian physics preferred categories like "heavy" and "natural" and "violent" to describe motion, generally eschewing mathematical explanations. Tartaglia brought mathematical models to the fore, "eviscerat[ing] Aristotelian terms of projectile movement" in the words of Mary J. Henninger-Voss. One of his findings was that the maximum range of a projectile was achieved by directing the cannon at a 45° angle to the horizon. Tartaglia's model for a cannonball's flight was that it proceeded from the cannon in a straight line, then after a while started to arc towards the earth along a circular path, then finally dropped in another straight line directly towards the earth. At the end of Book 2 of Nova Scientia, Tartaglia proposes to find the length of that initial rectilinear path for a projectile fired at an elevation of 45°, engaging in a Euclidean-style argument, but one with numbers attached to line segments and areas, and eventually proceeds algebraically to find the desired quantity (procederemo per algebra in his words). Mary J. Henninger-Voss notes that "Tartaglia's work on military science had an enormous circulation throughout Europe", being a reference for common gunners into the eighteenth century, sometimes through unattributed translations. He influenced Galileo as well, who owned "richly annotated" copies of his works on ballistics as he set about solving the projectile problem once and for all.
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