Second edition in English of Discorsi e dimonstrazioni matematichè intorno à due nuove scienze, but realistically the earliest obtainable. Widely recognized as “the first modern textbook of physics and the foundation of the [modern] science of mechanics,” Galileo’s Discorsi is a mathematical dialogue on kinematics and a variety of physical problems (including: matter, sound, and light); it also contains philosophical components dealing with the nature of mathematics and the role of experiment and reason in science. The Discorsi replaced the Aristotelean notion of motion with a new one based in inertia and principles derived from falling bodies, projectiles, and the pendulum. “It was upon his [Galileo’s] foundation 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 130. The first translation into English of the work appeared in Vol. II, Part 1 of Thomas Salusbury's Mathematical Collections and Translations in Two Parts. However, nearly all copies of that volume, published in 1665, were consumed in the Great Fire of London in 1666, with only about ten copies of Vol. II, Part I being known to have survived, and only one copy of Vol. II, Part II believed extant. In this copy, the errata, on the verso of p.497, has been neatly scored out in a contemporary hand, and the corrections have been neatly inked at the appropriate places in the text.