Nicolo was born in Brescia, the son of Michele, a dispatch rider who travelled to neighbouring towns to deliver mail.

Nicolo experienced further tragedy in 1512 when King Louis XII's troops invaded Brescia during the War of the League of Cambrai against Venice.

His mother nursed him back to health but the young boy was left with a speech impediment, prompting the nickname "Tartaglia" ("stammerer").

“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.

[3]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).

[4] Tartaglia's mathematics is also influenced by the works of medieval Islamic scholar Muhammad ibn Musa Al-Khwarizmi from 12th Century Latin translations becoming available in Europe.

[7]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.

[9] 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).

[10] 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.

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.

[14] This work went through many editions in the sixteenth century and helped diffuse knowledge of mathematics to a non-academic but increasingly well-informed literate and numerate public in Italy.

Maestros d'abaco like Tartaglia taught not with the abacus but with paper-and-pen, inculcating algorithms of the type found in grade schools today.

David Eugene Smith wrote of the General Trattato that it was: the best treatise on arithmetic that appeared in Italy in his century, containing a very full discussion of the numerical operations and the commercial rules of the Italian arithmeticians.

[18] Part IV concerns triangles, regular polygons, the Platonic solids, and Archimedean topics like the quadrature of the circle and circumscribing a cylinder around a sphere.

[19] Tartaglia was proficient with binomial expansions and included many worked examples in Part II of the General Trattato, one a detailed explanation of how to calculate the summands of

In Part IV of the General Trattato he shows by example how to calculate the height of a pyramid on a triangular base, that is, an irregular tetrahedron.

His approach is in some ways a modern one, suggesting by example an algorithm for calculating the height of irregular tetrahedra, but (as usual) he gives no explicit general formula.