# 1911 Encyclopædia Britannica/Tartaglia, Niccolò

**TARTAGLIA,** or Tartalea, **NICCOLÒ** (*c*. 1506-1559), Italian mathematician, was born at Brescia. His childhood was passed in dire poverty. During the sack of Brescia in 1512, he was horribly mutilated by some French soldiers. From these injuries he slowly recovered, but he long continued to stammer in his speech, whence the nickname, adopted by himself, of "Tartaglia." Save for the barest rudiments of reading and writing, he tells us that he had no master; yet we find him at Verona in 1521 an esteemed teacher of mathematics. In 1534 he went to Venice. For Tartaglia's discovery of the solution of cubic equations, and his contests with Antonio Marie Floridas, see Algebra (*History*). In 1548 Tartaglia accepted a situation as professor of Euclid at Brescia, but returned to Venice at the end of eighteen months. He died at Venice in 1559.

*Nuova scienzia*(Venice, 1537). dealt with the theory and practice of gunnery. He found the elevation giving the greatest range to be 45, but failed to demonstrate the correctness of his intuition. Indeed, he. never shook off the erroneous ideas of his time regarding the paths of projectiles, further than to see that no part of them could be a straight line. He nevertheless inaugurated the scientific treatment of the subject. His Quesiti et invenzioni diverse, a collection of the author's replies to questions addressed to him by persons of the most varied conditions, was published in 1546, with a dedication to Henry VIII. of England. Problems' in artillery occupy two out of nine books; the sixth treats of fortification; the ninth gives several examples of the solution of cubic equations. He published in 1551

*Regola generate per sollevare ogni ajfondata nave, intitolata la Travagliata Invenzione*(an allusion to his personal troubles at Brescia), setting forth a method for raising sunken-ships, and describing the diving-bell, then little known in western Europe. He pursued the subject in

*Ragionamenti sopra la Travagliata Invenzione*(May 1551). His largest work,

*Trattato generate di numeri e misure*, is a comprehensive^ mathematical treatise, including arithmetic, geometry, mensuration, and algebra as far as quadratic equations (Venice, 1556, 1560). He published the first Italian translation of Euclid (1543), and the earliest version from the Greek of some of the principal works of Archimedes (1543). These included the tract

*De insidentibus aquae*, of which his Latin now holds the place of the lost Greek text. Tartaglia claimed the invention of the gunner's quadrant.

*Quesili, lib*. vi. p. 74. See also Buoncompagni,

*Intorno ad un testamento inedito di N. Tartaglia*(Milan, 1881); Rossi,

*Elogi di Bresciana illustri*, p. 386. Tartaglia's writings on gunnery were translated into English by Lucar in 1588, and into French by Rieffcl in 1845.