Christiaan Huygens was the first to prove explicitly that Galileo's argument about ‘natural motion’ is wrong. He replaced this idea through a number of steps. First, he postulated a ‘principle of relativity’ that he supposed to be valid for all motions. He did not introduce this item as an axiom, like a mathematician or a classical philosopher would, but as a summary of what he perceived as the most striking characteristic of motion – without, of course, including some sort of ‘natural motion’ from the start.

From that, he deduced what later came to be called the ‘law of inertia’: free or ‘natural’ motion is motion with a constant velocity, that is, motion in a straight line with constant speed, flatly contradicting Galileo’s assertion about circular motion. Next, he computed geometrically what the difference is between Galileo's two forms of ‘ideal’ motion: the circle and the straight line. In the process he derived the first-ever algebraic equations in theoretical physics, describing the centrifugal acceleration and the oscillation time of the ideal pendulum.

Huygens's main conclusion forms the next step on the path leading from Stevin to modern physics: a curved orbit is an accelerated orbit. An object maintains a constant velocity (fixed speed in a fixed direction) with respect to other objects, unless – through some outside agent to be specified – an acceleration interferes.

But let me start at the beginning. As I have argued above, the primary characteristic of a great scientist is not curiosity, but perceptiveness: the ability to see what others have also seen, but from a different angle. The vision of ‘what motion is’ was vaguely present in some of the writings of Galileo and Descartes, but Huygens provided the clear and definitive formulation. It occurred to him that motion does not mean that an object changes its position in space, but that its position changes relative to other objects in the Universe. The sentence he wrote in his notes reads:

That is two symmetry principles rolled into one. First: nothing changes if you change all positions in space by shifting all positions by the same amount. Second: nothing changes if you add a fixed velocity to all velocities throughout space.