VALERIO, Luca.

De Centro Gravitatis Solidorum Libri Tres...in hac nostra editione, servata ad unguem Auctoris mente, multò correctiores.

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Woodcut printer's device on title & numerous woodcut diagrams in the text. 4 p.l., 260 pp. 4to, cont. limp boards (a little soiled, unimportant marginal dampstaining). Bologna: Heirs of Ducci, 1661. Second edition, combining the De Centro Gravitatis Solidorum and the Quadratura parabola; this edition contains important authorial additions and corrections. These two texts had a considerable influence on Galileo and his studies on motion. Valerio (1552-1618), who had studied under Clavius, met Galileo in Pisa in 1590 and influenced him to renew his studies on the centers of gravity. In 1609 they began an extensive correspondence on problems of motion and mathematics. It was during this time that Galileo was preparing his treatise on motion and mechanics which later became the Discorsi of 1638. "In December 1612, having completed his Sunspot Letters, Galileo considered having the Linceans print his work on centers of gravity of paraboloids, probably in the form of a letter to Luca Valerio. Ensuing correspondence shows that he sent this to Cesi, who in discussing the matter with Valerio found that he was then revising his own book on a similar subject, published in 1603-4. Galileo accordingly gracefully withdrew his work from publication at this time, for which Valerio expressed his gratitude. In fact Valerio did not reprint his book, and Galileo eventually placed his investigations of centers of gravity in an appendix to his own last book in 1638."­Drake, Galileo at Work, p. 202. Valerio's influence on Galileo, through his correspondence and these two books, was enormous, and he was singled out for praise in the Discorsi; where he is described as "our greatest geometer, the New Archimedes of our age." This was high praise indeed, for Valerio was critical of Galileo's Copernicanism and had been expelled from the Accademia dei Lincei in 1616 for his views. "Valerio's De centro gravitatis consists of the application of Archimedean methods to the determination of the volumes and centers of gravity of the various solids of rotation and their segments...Among the mathematicians who studied him and spoke highly of him were Cavalieri, Torricelli, and J. C. de la Faille. He also had a direct influence on Guldin, Gregorius Saint Vincent, and Tacquet."­D.S.B., XIII, pp. 560-61. Fine copy, preserved in a calf-backed box. Ex Bibliotheca Mechanica. M.E. Baron, The Origins of the Infinitesimal Calculus, pp. 101-03. Riccardi, II, 570­"Raro e pregiato." Roberts & Trent, Bibliotheca Mechanica, pp. 332-33.

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• libraire: Jonathan A. Hill, Bookseller, Inc. (USA)