In his Two New Sciences (1638), Salviati, widely regarded as Galileo's spokesman, held that all unequal weights would fall with the same finite speed in a vacuum: "In a medium totally devoid of all resistance all bodies would fall with the same speed."[208] Salviati also held that this could be experimentally demonstrated by the comparison of pendulum motions in air with bobs of lead and of cork which had different weights but which were otherwise similar.
Time-squared law
Galileo proposed that a falling body would fall with a uniform acceleration, as long as the resistance of the medium through which it was falling remained negligible, or in the limiting case of its falling through a vacuum.[209][210] He also derived the correct kinematical law for the distance travelled during a uniform acceleration starting from rest—namely, that it is proportional to the square of the elapsed time (d∝t2).[200][211] Galileo expressed the time-squared law using geometrical constructions and mathematically precise words, adhering to the standards of the day. (It remained for others to re-express the law in algebraic terms.)[citation needed]
Inertia
See also: Newton's laws of motion § History
Galileo also concluded that objects retain their velocity in the absence of any impediments to their motion,[212] thereby contradicting the generally accepted Aristotelian hypothesis that a body could only remain in so-called "violent", "unnatural", or "forced" motion so long as an agent of change (the "mover") continued to act on it.[213] Philosophical ideas relating to inertia had been proposed by John Philoponus and Jean Buridan. Galileo stated:[214][215]