What is a parabolic trajectory curve

Galileo's discovery of the parabolic trajectory

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Galileo's discovery of the parabolic trajectory

Galileo did the last part of his last work Discorsi intorno a due nuove scienze (1638) proved that the trajectory of a projectile flying through a resistance-free medium is a parabola. The proof is simple and understandable once it is known that the vertical distance the object falls from rest is proportional to the square of the elapsed time and that the horizontal speed of the body remains the same.

It is certain that Galileo discovered the parabolic trajectory before 1608 and proved it mathematically in early 1609, even though he did not mention it in his printed work until 30 years later. For a science historian, what is interesting about Galileo's discovery is the remarkable amount of experimental scientific methods he used. We take this for granted today, but it wasn't a standard practice in the 17th century.

It is difficult to tell from Galileo's published work how much use he really made of carefully conducted experiments. These, which he actually did, have been repeated over the past few years and have worked very well. However, Galileo did not describe many such experiments and he did not give his results in numerical form, as was common practice among his successors. It was only thanks to his private notes that traces of his experimental data were preserved.

As we have already said, two laws must be known in order to derive a parabolic trajectory. One is the law of free fall, which Galileo discovered in 1604 through a combination of luck and mathematical inference. The other necessary law is a constrained inertia principle; it relates the movement imparted to a body and the behavior of the body as soon as it is freed from the initial impulse.

Such a principle was exactly what Galileo was checking when he discovered the parabolic trajectory. This time luck didn't matter. Galileo's discovery of the parabolic trajectory was a chance find: the discovery of something other than what he was looking for.

The unpublished image manuscript documents one of the experiments that Galileo carried out and during which he discovered the law of the parabolic trajectory in 1608.

Mini dictionary
The free fall = Caduta libera
The movement, en = moto
Here: the body, - = proiettile
The trajectory, en = traiettoria
The speed, en = Velocità