Two New SciencesGalileo Galilei
About Two New Sciences
Galileo's last and most mathematical book, written under house arrest after his condemnation by the Inquisition and smuggled out of Italy to be printed in Leiden in 1638. The work returns to the dialogue form of the , with the same three interlocutors (Salviati, Sagredo, and the Aristotelian Simplicio) conversing over four days, but avoids cosmological questions entirely to concentrate on two subjects: the strength of materials and the motion of local bodies.
The first two days treat the resistance of beams and the cohesion of solids, establishing the scaling arguments that explain why animals and machines cannot be indefinitely enlarged. The third and fourth days turn to motion. Galileo demonstrates that all bodies fall with the same acceleration irrespective of weight, that the distance covered in free fall is proportional to the square of the time, that the path of a projectile is a parabola composed of a uniform horizontal motion and a uniformly accelerated vertical one, and that the speed acquired on an inclined plane depends only on the vertical drop.
The founds mathematical physics. The ancient problem of motion, handled qualitatively by Aristotle and the scholastics, becomes a science of quantitative law, derived from idealized thought experiments and tested against measurement. Newton builds directly on its ground.