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INITIATED THE TRANSITION FROM CLASSICAL GREEK GEOMETRY TO MODERN MATHEMATICS. First editions of these two rare and fundamental works on determining centres of gravity - these are fascinating copies with numerous contemporary annotations in an untouched contemporary binding. In these books Valerio transformed the Archimedean 'method of exhaustion' into a series of important theorems "so that for a whole class of convex curves and solids it was no longer necessary to establish results by special methods" (Baron, p. 101). Valerio was thus able to determine for the first time the centres of gravity of a number of 'Archimedean solids,' notably the hemispheroid and hyperboloid "which is undoubtedly one of the most difficult results in classical-Renaissance mathematics" (Napolitani & Saito, p. 108). These works were also important for initiating the transition from classical Greek geometry to modern mathematics (see below) - for example, according to Divizia, De CentroGravitatis anticipated the concept of limit and the integral calculus. Valerio strongly influenced Galileo, through his correspondence and these two books, and he was singled out for praise in the Discorsi, where he is described as 'our greatest geometer, the New Archimedes of our age'. "Valerio introduced important changes and novelties into the mathematics of his time - especially at the methodological level. He opened up a new road which was to be followed by several others: notably, Cavalieri, with his theory of indivisibles, and, above all, Descartes with his geometry of curves. Mathematics, as a result, was totally transformed, and its language and methods have since undergone a revolution" (ibid., p. 74). "Valerio was the first to break with the Greek model of the mathematical object: he introduces, and uses, classes of figures defined by one or more properties, to prove theorems that are more general and productive (in particular Theorem II-32); he invented [sic] the method of exhaustion, codifying in a series of general theorems, the classical technique to establish quantitative relationships between geometric figures . The way to these methods had been opened by Valerio, and Cavalieri proceeded further ahead: but then little remained to be done. The introduction of ars analytica into geometry was to break this wall; it was not so long before Descartes opened a practically infinite new world for mathematicians, by identifying the curves with their equations. It is difficult, however, to imagine Cavalieri and Descartes without Valerio, to imagine their radical innovations without the methodological novelties of De centro gravitatis solidorum . the impact of Valerio's work provoked a crisis in the rigidity of the classical paradigm, and helped to create the conceptual context that was to lead to the birth of modern mathematics" (ibid., pp. 120-3). OCLC lists six copies of De Centro Gravitatis and four of Quadratura Parabolae in US. Provenance: Signature on title 'Ignatis Braccii' (?), possibly Ignatius Braccius, author of Phoenicis effigies in numismatis, et gemma, quae in Museo Gualdino asseruantur (1637). Full page of manuscript remarks in a contemporary hand on front free endpaper discussing the work of Archimedes, Galileo and Valerio on centres of gravity, and numerous marginal annotations in the same hand throughout. "The rediscovery of Greek mathematics, especially of Greek geometry, in the sixteenth century lies at the basis of many of the conceptual revolutions of the following century . The period of rediscovery may be considered to have come to an end in 1575, the year in which both Maurolico and Commandino died. This date marks the beginning of the assimilation phase, an activity which soon became increasingly important. The assimilation of Archimedes involved the completion and the revision of his work; it implied a methodological reflection on the whole subject of geometry of measure and its relationship to mechanics . "Luca Valerio was one of the mo. Seller Inventory # 4695
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