Opera Geometrica [De sphaera et Solidis Sphaeralibus; De Motu Gravium; De Dimensione Parabolae]

Florence: Amadoro Massa & Lorenzo de Landis, 1644. 1st Edition. Hardcover. Fine. 1st Edition. Hardcover. 4to - over 9¾ - 12" tall. 3 parts in one, 4to. (220x158 mm), [2], [2:blank], [1-2] 3-243 [1], [1-2] 3-115 (i.e. 151) [1] pp., general half-title, part I title with imprint, section titles to parts II & III, dedication to Grand Duke Ferdinand II de' Medici, part III separately signed & paginated with separate dedication to Prince Leopold de' Medici, imprimatur leaf at end, numerous small woodcut diagrams, one full-page engraving, letterpress tables, numerous mispaginations. Internally clean and unspotted, light browning (mainly marginal), contemporary vellum with old ms. mathematical notations on covers. A fine, unsophisticated copy, collated complete. ----

Honeyman VII 2991; Norman 2086; PMM 145; Riccardi II 542; Carli-Favaro 43 (204); Cinti 226 (114). - 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.