TORRICELLI, Evangelista (1608-1647). (Opera geometrica:) De sphaera et solidis sphaeralibus libri duo. -De moto gravium naturaliter descendentium, et proiectorum libri duo. -De dimensione parabolae, solidique hyperbolici problemata duo... cum appendice de dimensione spatij cycloidalis, & cochleae. Florence: Amadoro Massa and Lorenzo de Landis, 1644.
3 parts in one, 4o (231 x 170 mm). General half-title, part 1 title-page with imprint, section titles to parts 2-3, dedication to Grand Duke Ferdinand II de' Medici, part 3 separately signed and paginated and with separate dedication to Prince Leopold de' Medici, imprimatur leaf at end, with blank leaf A6 (part 1), numerous small woodcut diagrams, one full-page engraving, letterpress tables, woodcut head- and tailpieces and initials. (Foxing, browning to last few quires, dampstain to first few leaves, marginal tear to Gg1.) Contemporary speckled paper boards, later(?) morocco lettering-piece, UNCUT, a few quires in part 3 unopened (slight wear at hinges and board edges); modern morocco-backed folding case. Provenance: early rough ink diagrams on front pastedown; 18th-century shelfmark label 2996 on spine.
FIRST EDITION of the only work published during Torricelli's lifetime. A brilliant mathematician, Torricelli was Galileo's assistant and companion during the last two years of the elder scientist's life, and he succeeded Galileo in the post of grand ducal mathematician. In his Opera geometrica, published at the expense of Grand-Duke Ferdinand II, Torricelli elucidated and diffused the difficult geometry of Cavalieri (see lot 359), thereby gaining himself widespread recognition throughout Europe. The first part, compiled around 1641, "studies figures arising through rotation of a regular polygon inscribed in or circumscribed about a circle around one of its axes of symmetry... Torricelli...classifies such rotation solids into six kinds, studies their properties, and presents some new propositions and new metrical relations for the round bodies of elementary geometry... As Torricelli acquired increasing familiarity with the method of indivisibles, he reached the point of surpassing the master -- as Cavalieri himself said" (DSB). In the second section, De moto gravium, Torricelli continued Galileo's study of the parabolic motion of projectiles. The treatise includes several significant contributions to mechanics, the calculus and ballistics. It also "refers to the movement of water in a paragraph so important that Ernst Mach proclaimed Torricelli the founder of hydrodynamics" (DSB). This states "Torricelli's theorem," in which Torricelli determined that the efflux velocity of a jet of liquid spurting from a small hole at the bottom of a vessel is equal to that which a single drop of the liquid would have if it could fall freely in a vacuum from the level of the top of the liquid. Norman 2086.