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As any student of art will tell you, one of the chief accomplishments of the Renaissance was the development of perspective in painting--the introduction of spatial perception that led to the legendary beauty and majesty of works by Giotto, Botticelli, and da Vinci. In The Invention of Infinity, Dr. J. V. Field, a noted historian on math and the arts, tells the remarkable story of how the "practical" mathematics of Renaissance artists actually influenced the development of "proper" mathematics--a true story of life imitating art. Here is the fascinating history of the emergence of modern mathematics during the Renaissance, and its intimate relationship with the artisan and artistic traditions of the time. The book covers the period from 1300 to 1650, when craftsmen were educated in "practical mathematics," and when the field of mathematics was gradually taking up a more significant place on the intellectual landscape. Field traces the influence of the mathematics of perspective in the arts, and shows how this led to the invention of a new kind of geometry in the 17th century--the new projective geometry of Desargues--which proved to be a highly significant contribution to the development of modern mathematics. Additionally, the author explores the 14th and 15th-century "abacus" schools popular among merchants and craftsmen, and the contrast between these practical, widely used tools and the abstract arithmetic and geometry taught in the universities of the time, and their application in the theory of music and elementary astronomy. Extensively illustrated with superb color and black and white plates, and including selected extracts from the original mathematical texts, this clear and entertaining account will delight anyone interested in the history of mathematics and art, as well as in the multi-layered social history of the Renaissance.