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De componendis gravium momentis dissertatio - Giordano (Vitale) - 1687. 
Angelo Bernabo 1687 - FIRST EDITION, woodcut device on title, diagrams in text, small red ink-stamp, a crowned monogram, at foot of title pp. [viii, including initial blank leaf], 14, [2, blank] (old shelf-mark on initial blank, contemporary vellum over boards, paste-downs and end-leaves foxed, good. A rare treatise on the mechanics and theories of gravitation of Galileo and Torricelli, part of the effort of the 'Galileans' centred on Borelli and Torricelli, and patronised by Queen Christina, to keep the spirit of the new science alive in the decades following Galileo's condemnation and death. De componendis gravium is a reply to the Jesuit Giovanni Francesco Vanni's Specimen de Momentis gravium (Rome, 1684). Vanni attempted to refute the Galilean-Torricellian proposition that the ratio of the components of the weights of a body on an inclined plane and the perpendicular is the same as that of the vertical height and the length of the inclined plane. Giordani demonstrates the correctness of the Galilean-Torricellian proposition by means of four theorems, in which he assumes the Galilean propositions about bodies falling under gravity. Giordani's work was itself the subject of criticism from the Jesuits, to which he responded a year later in Fundamentum doctrinae motus gravium (Rome, 1688). In 1680 Giordano published his Euclide restituto which contains an important contribution to non-Euclidean geometry, the work for which he is best known today: he introduced the geometrical figure now known as a 'Saccheri quadrilateral', after its use by Girolamo Saccheri in his Euclides ab omni naevo vindicatus (Milan, 1733). Giordano met Leibniz in Rome when Leibniz stayed there during his journey through Italy in the years 168990. The two men exchanged letters on the Euclidean definition of a straight line. (Riccardi I 120)
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