Among Jordanus' demonstrations, one deserves special attention because it does not require the concept of positional gravity, and the principle which it depends upon is not explicitly stated. But on the other hand, this principle shows through so clearly that it is impossible not to recognise it and formulate it in the following way: whatever can lift a weight to a given height can also lift a weight k times heavier to a height k times smaller.
This is the principle which Descartes will take as the foundation of all statics and which, due to Jean Bernoulli, will become the principle of Virtual Displacements.
There is more: we shall see that the current of ideas which carried this principle to Descartes and which had its source in the Elementa of Jordanus, did not suffer any discontinuity in its development. Descartes did, indeed borrow this postulate from the commentators on Jordanus.
Jordanus implicitly appeals to this principle in order to justify the law of equilibrium of the lever.
Therefore, neither the assumed displacement nor a displacement in the opposite direction will take place.
This demonstration of the law of equilibrium of the lever was a great advance over that given by Aristotle and followed later by Thabit ibn Qurra. The latter took as its foundation the axiom of Peripatetic dynamics, the proportionality between force and velocity. The revolution which took place in dynamics in the 16th c was to render it finally void. The former demonstration, on the contrary, brought together the equilibrium of the lever and the equality between the work of the resisting forces. It was the germinal formulation of a principle which was not to see its final and full development until the end of the 18th cent in the Mecanique anylatique of Lagrange.