In all earlier formulations, any departure from uniform motion in a straight line implied the existence of a material impediment to the motion; in the more abstract formulation in the Principia, the existence of an impressed force is implied, with the question of how this force is effected left open.
In a reflection of Malebranche's influence, Berkeley also argued that some Newtonians wrongly attributed genuine causal powers to ordinary material objects through their use of the concept of impressed force; wrongly, because Berkeley firmly rejected the notion that any body could exert any causal power.
Second, with the choice of the third law, the three laws all expressly concern impressed forces: the first law authorizes inferences to the presence of an impressed force on a body, the second, to its magnitude and direction, and the third to the correlative force on the body producing it.
The reason is that in Definition Four in the Principia, which defines an impressed force for the first time, Newton remarks: "This force consists solely in the action and does not remain in a body after the action has ceased".
The idea of an inverse-square law for gravity had been toyed with in England by physicist Robert Hooke, architect Sir Christopher Wren, and astronomer Edmond Halley, but they had been unable to assemble all the necessary concepts the law of attraction, the concept of motion under an impressed force, and the linking mathematics—into a finished product.
Newton's first law reflects Descartes's laws: it is a new version of the principle of inertia, one incorporating the concept of an impressed force.
One important element that becomes clear in his discussion of evidence for the third law — and also in Corollary 2 — is that Newton's impressed force is the same as static force that had been employed in the theory of equilibrium of devices like the level and balance for some time.
This is largely due to the efforts of the pioneering historians of science Pierre Duhem and Anneliese Maier, who saw that Buridan played a key role in the demise of the Aristotelian view of the cosmos.[46] Buridan's major contribution here was to develop and popularize the theory of impetus, or impressed force, to explain projectile motion.
Einstein was intrigued by the fact that the mass that figures in Newton's law of motion, F = ma the mass that measures the resistance of material bodies to being accelerated by an impressed force (inertial mass)—is invariably exactly the same as the mass that determines the extent to which any material body exerts an attractive gravitational force on any other.
Newton has a reply to that kind of view as well: he insists that the phenomena of the motion of the heavenly bodies "follows" solely from gravity itself an impressed force, as we have seen, and therefore an "action"—in accordance with the laws of motion and the law of universal gravitation.
Prong A: To be established is that, although an impressed force is necessary for the generation or alteration of true motion in a body, it is not necessary for the generation of motion relative to other bodies.
