The constant ratio that led Galileo from the pendulum law to the law of falling bodies was obtained by his remarkably accurate timings of a pendulum and a fall through distance equal to its length. The ratio has universal significance for the two physical phenomena, as dynamic factors cancel out and leave [mathematical expression], here called "Galileo's constant". Galileo's measurements and calculations are listed in their chronological order, from his working notes on motion preserved at Florence. Exactly ordered, they reveal probable early reflections by Galileo concerning pendulums and air resistance, unpublished by him but of assistance in understanding some statements in his later Discorsi. His discovery of the law of fall required the constant ratio he would not have found without a pendulum timing, something far removed from medieval mean-speed analysis of uniform acceleration
Nuncius A. 2, fasc. 2 (1987), p. 41-54