 Galileo showed a modern appreciation for the proper relationship between mathematics , theoretical physics , and experimental physics . He understood the parabola , both in terms of conic sections and in terms of the ordinate ( y ) varying as the square of the abscissa ( x ) . Galilei further asserted that the parabola was the theoretically ideal trajectory of a uniformly accelerated projectile in the absence of air resistance or other disturbances . He conceded that there are limits to the validity of this theory , noting on theoretical grounds that a projectile trajectory of a size comparable to that of the Earth could not possibly be a parabola , but he nevertheless maintained that for distances up to the range of the artillery of his day , the deviation of a projectile 's trajectory from a parabola would be only very slight . 
