GALILEI, Galileo (1564-1642). Discorsi e dimostrazioni matematiche, intorno a due nuove scienze attenenti alla mecanica & i movimenti locali . Leiden: Elzevier Press, 1638.First edition of 'the first modern textbook of physics, a foundation stone in the science of mechanics' (Grolier/Horblit). An unpressed copy in contemporary English binding. Forbidden to publish in Italy due to his heretical support for heliocentrism, Galileo managed to have a manuscript copy of the present work smuggled out of the country to France, from where it was brought to the Elzeviers in Holland. Galileo adopts the dialogue format, as he did in the previous Dialogo (1632; see preceding lot), to introduce his two new sciences: ‘the engineering science of strength of materials and the mathematical science of kinematics’ (DSB). Subject matter includes uniform and accelerated motion, parabolic trajectories, the constitution of matter, the nature of mathematics, the role of experiment and reason in science, the weight of air, the nature of sound and the speed of light, among other things. The Discorsi ‘underlies modern physics not only because it contains the elements of the mathematical treatment of motion, but also because most of the problems that came rather quickly to be seen as problems amenable to physical experiment and mathematical analysis were gathered together in this book with suggestive discussions of their possible solution’ (DSB). ‘Mathematicians and physicists of the later seventeenth century, Isaac Newton among them, rightly supposed that Galileo had begun a new era in the science of mechanics. It was upon his foundations that Huygens, Newton and others were able to erect the frame of the science of dynamics, and to extend its range (with the concept of universal gravitation) to the heavenly bodies’ (PMM). Carli and Favaro 162; Cinti 102; Dibner Heralds of Science 141; Grolier/Horblit 36; Norman 859; PMM 130; Riccardi I, 516.12/1; Roberts & Trent Bibliotheca Mechanica, pp. 129-30; Sparrow Milestones of Science 75; Wellcome 2648; Willems 2648. Quarto (190 x 138mm). Errata leaf at end, printers' woodcut device on title, numerous woodcut illustrations and diagrams in text, woodcut initials, head- and tailpiece (occasional very faint spotting). Contemporary sprinkled sheep ruled in blind, paper spine label lettered in manuscript, red sprinkled edges, probably a Hopetoun binding (scuffed at extremities, small loss at head of spine, pastedowns lifted). Provenance : Earls of Hopetoun (Sir James Hope of Hopetoun [d. c.1661] and successors; sale, Sotheby's, 25 February 1889; bookplate) – Margarethe Braun (her sale, 9 July 2019, lot 268).