Artillery cannot be developed without proper notion of reference frame, for example Cartesian one, which is needed in order to properly define notion of a curve given by equation. So before Cartesian reference frame was introduced, and notion of relation between equation of notion and drawn curve was introduced, artillery, and any knowledge working with trajectories was blind and unable to form useful domain of engineering beside some pure empirical rules. In fact it remain in this state long ago after even if mathematics was possible to use equation of motion to develop proper description of trajectory.
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