This is the first separate English edition of Galileo’s Discourse on Two New Sciences, his masterwork in mathematical physics. The “two new sciences” are tensile strength and motion. The science of motion, or mechanics, includes the parabolic motion of projectiles and Galileo’s law of free fall and the acceleration of falling bodies. The work is in the form of a dialog between three characters: Salviati, Sagredo and Simplicio. The characters discuss tensile strength on the first two days, and mechanics or the physics of motion on the last two days.