Galileo and Archimedes on Mechanics

  Galileo's last work, Mathematical Discourses Concerning Two New Sciences, was published in 1632 a few years before his death and contains four dialogues concerned primarily with a discussion of the resistance of matter to breakage, the mechanics of levers, uniform and accelerated motion and the motion of projectiles. He speaks highly of Archimedes' Mechanics which is mathematical in nature and prefers this to Aristotle who mentions the lever in the last book of his Physics (parts 4 and 6). One of the characters in the dialogue, Simplicius, speaks for Aristotle. Another is Salviati, a deceased friend of Galileo, expounds the author's views and the third, Sagredo, another deceased friend of Galileo's, represents an intermediate position.

Archimedes' work On Floating Bodies contains a discussion which is similar to the cryptic passage in Lagrange's Analytical Mechanics in which the lines of the weights meet at the Earth's center of gravity.

Supplemental (Jan 12): Galileo describes the chain as being very nearly a parabola and uses an inverted chain (arch?) in an argument.