TARTAGLIA, or TARTALEA, NICCOLO (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 . Tartaglia's first printed work, entitled 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 generale per sollevare ogni affondata 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 generale di numeri e misure, is a comprehensive mathematical treatise, including arithmetic, geometry, mensuration, and algebra as far as quadratic equations Venice, 1556, 156o) . 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 . Tartaglia's own account of his early life is contained in his Quesiti, 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 Rieffel in 1845 .