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Niccoló Tartaglia

b. Brescia, Italy 1499 or 1500
d. Venice 13 December 1557

Tartaglia died alone and penniless. He began his mathematical studies at an early age and it seems he was for the most part self-taught. He moved to Verona around 1517 where he was employed as a teacher of the abacus. Later he appears to have been put in charge of a school there. In 1534 he moved to Venice where he became a professor of mathematics.

Tartaglia noted in his General Trattato di numeri et misure (General Treatise on number and measure), published in 1556, that Pacioli's solution must be erroneous because it violated common sense. By Pacioli's rule, if A had won but one round and B none, then A would get all. This is obviously unfair and would be substantial cause for litigation.

He therefore proposed that the player with the greater number of points should receive both his stake and a share of the other's which is proportional to the difference of their scores. Again, if Player A has a points and Player B has b, then Player A should receive (n+a-b)/(2n). He gave this rule with some reservation, for he suggested that this is a judicial problem rather than a mathematical one.

Here is the relevant text in both Italian and English in facing columns from the Trattato