Summary
Highlights
Galileo's 'Two New Sciences', published in 1638, discusses constant speed and uniform acceleration in its third day. The section on constant speed uses a style similar to Euclid's, defining uniform motion, deriving axioms, and forming theorems. The conclusions, such as a body traveling longer at the same speed covering more distance, are intuitive.
The section on uniform acceleration is more engaging. Galileo defines uniform acceleration as starting from rest and acquiring equal increments of speed in equal time intervals. He presents this through a dramatic scene, similar to Socratic dialogues, where characters debate the definition's accuracy. This narrative style enhances reader interest.
One of Galileo's interlocutors argues that falling objects intuitively gain speed. A brick dropped from different heights demonstrates this: a 10m drop drives a stick further into mud than a 5m drop, while a 1cm drop has no effect. This shows greater velocity and force with longer fall times.
After establishing that falling bodies accelerate, Galileo aims to prove this acceleration is uniform. He conducts an experiment rolling a steel ball down an incline plane, measuring the time taken to travel various distances (full length, 3/4, 1/2, 1/4). Repeated hundreds of times, the experiment revealed that distance traveled is proportional to the square of the time, e.g., 1 foot in 1 second, 4 feet in 2 seconds, 9 feet in 3 seconds.
Galileo's methodology in 'Two New Sciences' clearly positions him as an early proponent of the scientific method. He made observations, formulated hypotheses about natural phenomena, and then performed experiments to validate his conjectures.