A representation of the motion of a projectile from a gunnery manual of the 1500s. Notice that it appears to be illustrating Tartaglia's demonstration that 45° is the firing angle for maximum distance. 

Beginning in the early 1600s, Galileo had explored the quantitative measurement of trajectories. In the 1632 Dialogue, he wrote: 

"If a perfectly level cannon on a tower were fired parallel to the horizon, it would not matter whether a small charge or a great one were put in, so that the ball would fall 1000 yards away, or 4000, or 6000, or 10000, or more; all these shots would require equal times, and each time would be equal to that which the ball would have taken in going from the mouth of the cannon to the ground if it were allowed to fall straight down without any other impulse."

Notice not only the quantitative measurement and conclusion, but the difference in style from the explanation of flight in Aristotle's Physica:  

 "...the motion begins to cease when the motive force produced in one member no longer causes the next member to be a movent but only causes it to be in motion. The motion of these last two -- of the one as movent and the other as moved -- must cease simultaneously, and with this the whole motion stops."

The later (14th century) Buridan/Oresme theory of 'impetus' added something intrinsic to the moving body to carry it forward, which was exhausted, allowing return to rest.  This did seem to be common sense. 

Galileo disrupted another principle in these motions.  Falling was not steady but accelerating.