# What in Newton's three laws of motion is original and not a paraphrasing of his predecessors?

The three laws are:

First law: The velocity of a body remains constant unless the body is acted upon by an external force.

Second law: The acceleration a of a body is parallel[disambiguation needed ] and directly proportional to the net force F and inversely proportional to the mass m, i.e., F = ma.

Third law: The mutual forces of action and reaction between two bodies are equal, opposite and collinear.

The first law had already been formulated by some philosophers prior to Newton, Hobbes said in the Leviathan '...[the proposition] that when a thing is in motion it will eternally be in motion unless somewhat else stay it, though the reason be the same (namely that nothing can change itself)...', given his reasoning, I think it safe to mean constant speed and direction, otherwise change is occuring and he explicitly rules that out. I think the same proposition is mentioned in Lucretious's De Rerum Natura.

Are there any antecedents for the second and third law?

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The third law is the original one. The rest are known to contemporaries, although not to philosophers, rather to the scientists. You can see Hooke uses the first and second laws along with Kepler's third law to deduce that gravity is inverse square. – Ron Maimon Jun 13 '12 at 4:40
Thats interesting. I would've suspected the second law to be the original one. Are you saying Hooke was the originator of the second law and the notion of Force? As for the third, isn't there some notion of universal balance (within the philosophical literature), where every action on the moral plane is countered by an opposite one? I'm guessing here, and hope some-one can correct and edify me here. One expects there is more to the story of Gravity than Newton, as far as I remember Hooke approached Newton to ask whether he could prove that an inverse law gives elliptical motion. – Mozibur Ullah Jun 13 '12 at 4:51
But does this mean that the notion of Gravity as a force pulling the Earth towards the Sun also originated with Hooke, or were others involved? – Mozibur Ullah Jun 13 '12 at 4:56
The second law was just common knowledge, as was the first. It probably is due to Galileo and contemporaries, although it took a while to be codified. The laws of motion are not the point of the Principia, they are just the intro. The main point are the special problems. Hooke certainly understood them. Hooke came up with the inverse square law independently of Newton (and before Newton published), and it was pressure from Hooke that led Newton to publish the Principia. Hooke couldn't see that the orbits in an inverse square law would be ellipses, something which Newton had already worked out. – Ron Maimon Jun 13 '12 at 7:55

The first and second laws are not original to Newton, since we know Hooke deduced that gravity must be an inverse square centripetal force in the 1670s without input from Newton. The calculations of centripetal force were then current, and the first and second law naturally follow from Galileo's work on falling bodies.

You can read a lucid discussion of the history in Julian Barbour's "Absolute or relative motion?" Which focuses on this time period. The idea that bodies stay in motion unless acted upon is already floating in the air due to the heliocentric model and the certainty of the rotating Earth.

The third law, however, is new to Newton. He uses it both as a philosophical position and as a way to justify the first and second laws in composite bodies. The third law is essentially a statement of conservation of momentum, and Newton also includes conservation of angular momentum in the first law (as you can see by his example of a spinning body which keeps spinning and moving absent a disturbance).

The third law allows Newton to build up a complete physical science, since he is able to deduce the laws for large bodies assuming laws for the microscopic corpuscules he believed were down below, composing the large bodies. His implicit model for the world is one of atoms interacting by pairwise attractions and repulsions, and asymptotically interacting by gravity. He believes that it is the pairwise nature of the atomic forces that leads to the law of conservation of angular momentum, since there is no change in angular momentum during a pairwise radial attraction/repulsion event.

It is this model that leads him to a corpuscular theory of light, since he cannot bear the idea that matter is one thing and light another.

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The first law

was discovered by Galileo, you can find more details at this link

• Aristotle interpreted the everyday-life experience of his time, which is absolutely valid also today: if we want to keep motion we must sustain it . "He thought that a body was in its natural state when it was at rest, and for the body to move in a straight line at a constant speed an external agent was needed continually to propel it, otherwise it would stop moving."

He did not realize that the motion of objects on the ground and in the air is slowed down by frictional forces: static/kinetic/rolling friction , drag etc.

• Galileo discovered friction during his experiments with balls rolling on inclined planes (1632-1638). He was the first to understand that if motion is not hindered by frictional forces goes on forever. His prose, his charming discursive style, is a nice change from Aristottle. In "Two new sciences" he writes in his note (scolio) to proposition 23, p. 73:

...on a horizontal plane motion is constant and uniform if no cause of acceleration or deceleration intervenes...it is legitimate to expect that any amount of speed in a body in motion is indelibly impressed in it, on condition that every external cause of acceleration or deceleration be removed. This happens only on the horizontal plane...also it follows from this that on such a plane [motion] is eternal ; as a matter of fact if it is constant and uniform it doesn't increase nor decrease, a fortiori it doesn' cease.

He describes the actual phenomenon, what happens, what is true: he does not state it as a law. . The law was stated by Descartes and , later by Newton

The second law

The proportionality between applied force and motion was discovered by Leibniz and was defined mathematically by Coriolis. You can find more details at this link

"... Gottfried Leibniz, as early as 1686, one year before the publication of the Principia, who first affirmed that kinetic energy is proportional to squared velocity (or that velocity is proportional to the square root of energy): $$v \propto \sqrt{V_{viva}} [/m]$$. He called it, a few years later, vis viva = 'a-live' force in contrast with vis mortua = 'dead' force: (Cartesian) momentum (mass/weight * speed: $m *|v|$). This was accompanied by a first formulation of the principle of conservation of kinetic energy, as he noticed that in many mechanical systems of several masses $m_i$ each with velocity $v_i$,

$\sum_{i} m_i v_i^2$

was conserved so long as the masses did not interact. The principle represents an accurate statement of the approximate conservation of kinetic energy in situations where there is no friction or in elastic collisions. Many physicists at that time held that the conservation of momentum, which holds even in systems with friction, as defined by the momentum: $\,\!\sum_{i} m_i v_i$ was the conserved kinetic energy.

....

Thomas Young is thought to have been the first to substitute the terms 'vis viva' and 'potentia motrix' with 'energy' in 1807 (from the Greek word: ἐνέργεια energeia, which had been coined by Aristotle on the stem of ergon = work, energeia = the-state-of-being-at-work). Later (1824-1829) Coriolis introduced the term 'kinetic energy' and this concept (and the consequent theory of conservation of energy) was eventually formalized by Lord Kelvin et al. in the field of thermodynamics....

The third law

was discovered by Huygens, when he studied elastic collisions between spheres. You can find full details at this link.

Huygens also suggested the term 'vis viva' to Leibniz, discovered not only what is called the 'conservation of momentum' in collisions, but the conservation of kinetic energy. He also discovered the quadratic relation between velocity and KE before Leibniz, although it is not certain that Leibniz was aware of that.

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I've removed an inappropriate comment discussion. – David Z Nov 6 '14 at 5:34

Descartes, gave a correct version of the first law (the law of inertia), justified by the constancy of the purposes of God. Galileo (much cited, I believe, as an early proponent of the law of inertia), seems to have been claiming that a body's natural motion is in a circle at constant speed.

As far as I know, Newton invented the second and third laws. Of course the second law is pretty empty (certainly untestable) without other laws (such as Hooke's law for a spring, or Newton's law of gravitation) which relate the force to the relative positions (and possibly velocities) of objects.

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