Introduction
I restored the original title to show how interesting it is that a non-British student (18 at the time) can be more informed than a British physics graduate. He posted this comment:
"The question before this must be whether it was his original or
something like his 1st law, which was a restatement of the
experimental findings of Galileo" – Rijul Gupta Oct 26 '13
He then edited the title and the OP text adding:
"Was it his original finding or was it a restatement of someone
else's, like the first law coming from Galileo?"
This may seem a trivial detail in an answer but it is very important here: he knows that first law wasn't Newton's own (this is sometime acknowledged, though), but he expresses doubts that also third law might not be his own finding, whereas a U.S. academic is skeptical: "...I don't know if there's any evidence that he knew of them beforehand." – Ben Crowell
The historical truth is there, recorded in accessible documents and original texts, if one wants to look for it and is prepared to accept it, even if may be shocking for English eyes. I'll present the original documents, readers can draw their conclusions.
The historical facts
Christiaan Huygens [wiki (1)] was a good-natured, noble generous man, the son of a diplomat who was an advisor to the House of Orange. He was slow to publish his results and discoveries, in the early days his mentor , mathematicians Frans van Schooten was cautious for the sake of his reputation (1), this had the deplorable consequence that his ideas that he naively communicated to his contemporaries were plagiarized. He was too meek, he complained only to friends (even his patent was violated in Egland, France etc.) and therefore his great scientific merits are to date under-evaluated: he found the real law behind 'the conservation of momentum', discovered the formula of kinetic energy, the conservation of KE in elastic collisions, suggested the term 'vis viva' to Leibniz and taught him maths and helped him develop 'calculus', even he never believed in its usefulness.
during the years 1650 - 1666 [Enc. (2)] he lived at home, except for three journeys to Paris and London: an allowance supplied by his father enabled him to devote himself completely to the study of nature
between the years 1652-54, according to his own statements, he developped the theory of collisions in his work (in Latin): "De motu corporum ex percussione" (English translation: Chicago Journals), there is no proof of that, although :"... there are numerous indications that Huygens had established all the propositions and their proofs by 1656 at the latest (see the Avertissement in Oeuvres, Vol. XVI, pp. 3-14, for the evidence) (3, p. 574)
in 1661 he was already famous: in '55 he had discovered the satellite of Saturn (2), in '56 had invented the pendulum clock and in '57 had written his treatise on probability theory (1) . He went to Paris to meet Pascal as "He had been told of recent work in the field by Fermat, Blaise Pascal and Girard Desargues two years earlier" (1).
in May of that year he was in London " "..to observe the planet Mercury transit over the Sun, using the telescope of Richard Reeve in London, together with astronomer Thomas Streete and Reeve himself" (1). He also "..attended meetings in Gresham College, and met Moray, Wallis, and Oldenburg" (2). he told them about his findings and in particular about the theory of collisions". The scholars at Gresham had recently formed the Royal Society Henry Oldenburg (4) was "...one of the foremost intelligencers of Europe of the seventeenth century, with a network of correspondents .. At the foundation of the Royal Society he took on the task of foreign correspondence, as the first Secretary", he was the shady figure (shortly imprisoned as a suspected spy) that recruited scientists all over Europe, trying to entice them with a promise ".. they would be assured undying fame by the preservation of their results in the archives of the RS" and to convince them the could rest assured "that no harm to their discoveries would come about through divulging information in advance of publication" and that at RS each is certain of his due" [(5) p.53, passim]
the Royal Society, it is notorious, when Newton was a member "...in 1699 accused Leibniz of plagiarism. The dispute then broke out in full force in 1711 when the Royal Society proclaimed in a study that it was Newton who was the true discoverer and labelled Leibniz a fraud. This study was cast into doubt when it was later found that Newton himself wrote the study's concluding remarks on Leibniz"
in (June -September) 1663 "Huygens was made a member of the Society" (2), and was invited to London to illustrate his discoveries, in particular on the theory of collisions
in 1668 he was invited by the Society to publish his findings on collisions in the Philosophical Transactions of the Royal Society:"He presented the most important theorems to the Royal Society in 1668, simultaneously with studies by Wren and Wallis" (5 p.543). The Rules of Motion by these two, copied from Huygens' paper, were published while his original work was not. In this dishonest way the Society ensured the primacy of the theory to the English authors and Newton (of course, he can't ignore him altogether) can always cite :"In theoria Wrenni & Hugenii", "together with the third Law, Sir Christ. Wren, Dr. Wallis, and Mr. Huygens", ".. Dr. Wallis, indeed, was something more early in the publication; then followed Sir Christopher Wren, and, lastly, Mr. Huygens"
Huygens was saddened "...and publicly voiced his anger at being disadvantaged by not having his results published (in PT) at the same time as those of the opposite party" [5, p. 53]
in March 1669, having had no satisfaction, he published his paper in French in the Journal des sçavans
immediately after, his original Latin paper was published in the PT of the RS
in 1670, the following year, Huygens had already forgotten his anger and "... seriously ill, chose Francis Vernon to carry out a donation of his papers to the Royal Society in London, should he die." (1). If these historical reports are true, by 1671 (the RS and) Newton was in possess of the complete demonstrations concerning the theory of collisions (by Huygens and Mariotte): in 1669 Newton had already been appointed Lucasian Professor.
in 1670 Edme Mariotte had announced his intention to compose a major work on the impact of bodies. Completed and read to the Academy in 1671, it was published in 1673 as Traité de la percussion ou choc des corps. The first comprehensive treatment of the laws of inelastic and elastic impact and of their application to various physical problems". In order to verify his suppositions, he used " an experimental apparatus consisting of two simple pendulums of equal length, the replaceable bobs (the impacting bodies) of which meet at dead center". Here we found the real inventor of "Newton's 'cradle'. Newton cites Wrenn's experiments and Mariotte's book: ".*.veritas comprobata est a Wrenno ...quod etiam Clarissimus Mariottus libro integro exponere mox dignatus est**" (p. 37), but never Huygens'. Newton affirms that Mariotte had just divulged the findings of the British architect: ".. Wren confirmed the truth of the thing before the Royal Society by the experiment of pendulums, which Mr. Mariotte soon after thought fit to explain in a treatise entirely upon that subject." (p.90)
Huygens was certainly saddened by the fact that Mariotte did not cite him as his source, but did not respond (the silence of the lambs) his nature was so meek that only " seventeen years later, in 1690, when Mariotte was dead, Huygens responded to this slight (see below) by accusing Mariotte of plagiarism. “Mariotte took everything from me,” he protested in a sketch of an introduction to a treatise on impact never completed" (ibidem, you can read about the 'slight'):
Clearly he knew of the work of Wallis, Wren, and Huygens published in the Philosophical Transactions of the Royal Society in 1668; and there are enough striking similarities between Mariotte’s treatise and Huygens’ then unpublished paper on impact (De motu corporum ex percussione, in Oeuvres, XVI) to suggest that he knew the content of the latter, perhaps verbally from Huygens himself* Certainly his colleagues in the Academy recognized Mariotte’s debt to others while they praised the clarity of his presentation. And yet Galileo’s name alone appears in the treatise; Huygens’ in particular is conspicuously absent.
- Since the first meeting in 1661 the RS group had tried to understand the profound meaning of 'conservation of momentum' and even after Huygens sent in his paper in 1668 with the complete list of the rules were not able to interpret them. "In a letter of Feb. 4, 1669, (one month before the delayed publication in RPRS of his submitted paper) Oldenburg "earnestly intreated" Huygens to publish his
theory, but the reply ignored the point. Huygens himself explains his refusal to publish." (3, p. 575) The reason was not, as one might imagine, that he did not want to reveal the theory, but because he wanted to get to the bottom (penitus), to the metaphysical level: "he was concerned to determine the essence and true cause of motion and forces" (ibidem). He mentioned the true principle once, but never wrote it down.
- from 1669 to 1687 Newton tried for 18 more years to figure out the true essence/law of motion, but lacked Huygens' metaphysical insight He tried to be original (as he had done with the 1st law) and produced a 3rd law which is partially in contrast with his own laws. (this will be discussed in a another answer, to separate facts from opinions)
conclusions
This is how Newton found the third law. Is "there enough evidence that he knew of them beforehand"?, I'll leave the answer to the readers, as this post is unpopular just as it is. Certainly if one should decide that
The concept of inertia is indeed useful in two ways. I think your notion of it as a technical promotion of the everyday word "sloth" (without the baggage given it by the Roman Catholic translation of the "deadly sin" Ἀκηδία) as extremely close to the mark. In physics the notion of "inertia" has two, very alike uses:
The first is practical, through a weak form of D'Alembert's principle. The notion arises where we look at a system from an accelerated frame of reference and treat it as a non-accelerated one: to keep the things making up the system "together" and "still" relative to the accelerated frame, we imagine that each of the system components are exerting a force of inertia (in the sense exactly described by Newton in your quote) on the system that tries to "tear it away" from the frame of reference wherein our discourse takes place. This "force" arises from each component's "sloth", i.e. resistance to any change of their state of motion from a non accelerated frame (let's leave aside the term "inertial frame" for this latter notion for now). There has to be something tethering each of the system components to the accelerated frame to resist the "force of inertia" that each of the components exerts in "trying to tear away" from the frame and resume a uniform state of motion. Thus, in designing a centrifugal pump in this way, we would imagine the impellor sitting still, but each of the blades exerts its centrifugal force on the impellor's hub and we thus see that the hub and blades are in a state of tension to resist this centrifugal force and must accordingly be designed so that they may be strong enough to yield this resistance. From a non-accelerated frame, we would simply see the blades making circular paths, and thus we conclude that they are accelerating, so, by Newton II, we know that the hub must be pulling the blades radially, i.e. providing the centripetal force needed to set up this accelerated motion. Sometimes D'Alembert's Principle is thought of simply a re-arrangement of Newton's second law, and thus derivable from the latter, but this is not so as discussed in QMechanic's answer here to the Physics SE question "Deriving D'Alembert's Principle". Moreover, it is indispensable in rotating rigid body problems. In this kind of problem, if we try to work only in non-accelerated frames, Euler's Second Law of Motion becomes highly awkward, because the inertia tensor $I$ of a spinning body is constantly changing relative to a non-rotating frame. It is much easier to fix our frame to the spinning body, thus benefitting from a constant inertia tensor $I$ and live with the inertial forces $\omega\times(I\,\omega)$ in the Euler equations $M = I\, {\rm d}_t \omega + \omega\times(I\,\omega)$
The great theoretical utility of the notion of inertia is as inertial mass: this notion is useful simply by differing from the notion of gravitational mass. Without a clear understanding of the stark differences between these two notions, there could be no discussion of the Equivalence Principle (see Wikipedia page of this name). In this form, the notion of inertia is an indispensable part of the epistemology of the General Theory of Relativity, so I shall now concentrate on talking about this use of the "inertia" notion.
Inertia, Gravitational Coupling and The Equivalence Principle
So now we look at the meaning of the word "mass": it actually has two (and possibly three) in principle distinct meanings:
As "inertia" or "inertial mass" it is a measure of the body's "sloth" or "shove resistance" as discussed above, i.e. inversely proportional to its acceleration under a unit imbalanced force (i.e. inversely proportional to the body's "response" to a standard force). Thus this notion is expressed by the quantity $m_I$ in Newton's second law $\vec{F} = m_I \,\vec{a}$;
As a "coupling constant" describing how strongly a body is influenced by a gravitational field, i.e. how much nett force a unit gravitational field imparts to a body (in the Newtonian notion of gravity). Thus this notion is expressed by the quantity $m_g$ when we say that a small test mass of gravitational mass $m_g$ in a gravitational field $\vec{g}$ feels a force $m_g\,\vec{g}$;
A third possible notion, not really important here, is as a measure of a particle's "stay puttability" as I discuss in my answer to the Physics SE question "Can mass be directly measured without measuring its weight?". This is simply how still a body of a given, standard degree of localisation in space can be made and still conform with the Heisenberg Uncertainty Principle.
Ponder the first two carefully and take heed how much in principle different they are as notions. Without further information, experimental results or postulates, I hope you will agree that there is no possible way whereby these two notions could a priori proven or even guessed to be the same.
The weak equivalence principle asserts that notions 1) and 2) above are the same and, for any body, regardless of its makeup or quantum state, we have $m_I = m_g$ (see my footnote 3). These two are not just alike. They are exactly the same. This is a stunning assertion and it still dazzles me to this day, even though I am fifty years old and first read about it when I was fourteen (I did, however, take a further six years to fully appreciate its significance).
Given their vast conceptual difference as physical notions, any assertion that they are the same must encode real, falsifiable physics about gravitation. For what it means is that any small mass, regardless of makeup or quantum state, with a given initial velocity in a gravitational field must undergo exactly the same motion. This principle has been clearly recognised by many scientists for nearly fifteen hundred years. In the sixth century CE, John Philoponus (see Wiki page of same name) said of experiments potentially falsifying the equivalence principle:
"But this [view of Aristotle that the time taken for a body to fall a given distance is inversely proportional to its weight] is completely erroneous, and our view may be completely corroborated by actual observation more effectively than by any sort of verbal argument. For if you let fall from the same height two weights, one many times heavier than the other you will see that the ratio of the times required for the motion does not depend [solely] on the weights, but that the difference in time is very small."
Galileo certainly knew the equivalence principle and his famous experiment dropping different weight balls from the Tower of Pisa was almost certainly, in reality, done in about 1586 by Simon Stevin dropping balls from the Delft churchtower (see discussion in Equivalence Principle Wiki Page).
Many careful experiments probing the equivalence principle's correctness have been done; amongst the most famous are the Eötvös Experiment (see Wikipedia page of same name) as well as those of Newton (in finding that pendulums of the same length have the same period, independent of length) and by the commander of Apollo 15, David Scott, when he dropped a feather and a hammer from the same height on the Moon to see them both hit the ground at exactly the same time.
So now on to General Theory of Relativity. Einstein was convinced that the Equivalence Principle would lead him to his GTR and from very early on in the piece he kept returning to this principle. The principle shows itself very blatantly in his early works before the full GTR paper of 1916. In:
A. Einstein, "Über den Einfluss der Schwerkraft auf die Ausbreiitung des Lichtes", Annalen der Physik, 35, 1911 English version "On the Influence of Gravitation on the Propagation of Light" is here)
he uses nothing but the equivalence principle very directly and on its own to derive, by very simple and clear arguments, some of the important, readily falsifiable results that would follow from his later 1916 paper:
A. Einstein, "Die Grundlage der allgemeinen Relativitätstheorie", Annalen der Physik, 49, 1916 (English translation, "The Foundation of the General Theory of Relativity" is here)
In the latter paper, indeed in the teaching of GTR, the equivalence principle seems to slip into the background a little (a great deal, in some modern texts) and often the direct assertion of the equivalence of mass notions is overshadowed in modern texts by something like the following statement:
The tangent space to the spacetime manifold solution to the Einstein field equations is Minkowskian
or
Spacetime is locally Minkowskian
or something like this. This is indeed a reasonable, indeed a stronger, statement of the equivalence principle, but it does, in my opinion, need some further explanation. It's at first glance quite different from the Einstein version of the equivalence principle:
The outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime
The way that the equivalence principle is encoded is, in my opinion, some of the reason why inertia is not discussed very much in relativity. The EP is actually part of the building materials for the GTR: the very assertion that spacetime under the influence of "matter" (anything with energy content and thus gravitational mass) is a differentiable, indeed, pseudo-Riemannian manifold fully encodes the EP. So, the mere choice of the geometrical object, before we even contemplate writing down the Einstein Field Equations, or indeed the physics behind them, fully encodes the EP. A manifold is locally like a Euclidean (or, in GTR, flat Minkowskian) space: there are other geometrical objects, notably an Algebraic Variety that we might have chosen to describe the "curvature" of spacetime with and which are more general than manifolds and which do NOT encode the EP. To examine the manifold and why it encodes the EP, I'm going to give my version of the Einstein equivalence principle:
For any chosen, positive precision $\epsilon>0$, there is a magnification $M$ such that if you look at the spacetime manifold with this high enough magnification, you will see a laboratory indistinguishable (to within the chosen precision) from the main cabin of Salviati's Ship
Salviati's ship (see the Wikipedia page for "Galileo's Ship") was, of course, a thought experiment wherein Galileo asserts the impossibility of telling whether or not a ship is moving uniformly by any experiment which does not look to an outside reference. The mere fact that the spacetime manifold has a Tangent Space at every point alone means that if we zoom into the manifold enough so that our little ship takes up a small enough volume in space time, then there exists a frame of reference, that moving along a geodetic line, such that if the ship were stationary in that frame of reference, the Salviati thought experiment would hold. It might (inside a highly curved region like near a black hole) have to be a volume that it is comparable in size to an atomic nucleus, but that's OK in GTR: GTR is a classical theory that does not see the World's granularity: in principle there is always a Salviati ship, even if it is the size of a proton and exists only for $10^{-20}$ seconds. This is a freefall frame, the most general concept of an inertial frame, or a "slothful frame" that describes a (geodesic) flow on spacetime arising in the absence of external forces, and that any accelerated motion relative to that frame requires an unbalanced force. It describes how something moving through spacetime "wants to move" and has a "stubbornness to move thus" and must be compelled by unbalanced force to move differently.
So suppose we are on Salviati's ship, freefalling in a uniform gravitational field and the equivalence principle did not hold, and no frame of reference were Minkowskian (an inertial frame, in Special Relativity). The butterflies, being of a different makeup, might accelerate differently from the waterdrops from the bottle, and the ship's cat, being of very different makeup, would have accelerated relative to the scene and been lost long ago! The whole scene can only stay fixed, with all its constituents staying at the same relative positions, if the equivalence principle holds. Thus we see that the differentiable manifold conception of spacetime can hold only if the equivalence principle is true.
So there is always a local "inertial frame" (I actually like the word "freefall frame" better) in General Relativity. We have come the full circle: for now how do we describe your frame of reference as you sit "stationary" on the Earth's surface reading this? Think about your bottom: you feel it is being pressed by your seat. You conclude that there must be a force pressing you into the seat: our mother tongue has a word for this force: your weight. But this is an inertial force in the sense described at the very beginning of my answer. For it so happens that, in the presence of the Earth, the true inertial frame, the true cabin of the Salviati Ship, as described by GTR, is one beginning stationary relative to you but which is "accelerating" relative to you at $g {\rm m\,s^{-2}}$ towards the centre of the Earth. The matter of your seat must therefore push against you with force $m\,g$ upwards to beget your acceleration relative to the Salviati ship. But, of course, we find it easiest to think in a frame of reference that is stationary relative to our Earthly home. So, in this accelerated frame, we feel the inertia of our bodies as they "try to tear away" and follow their natural, inertial frames.
See Eduardo Guerras Valera's wonderful answer to "How (or why) equivalence principle led to Einstein field equations?" for a fuller description of how Einstein seems to have embedded the EP into the GTR - the modern manifold concept I described was not how people thought about manifolds in Einstein's day, when they thought of them as needfully being curved objects in a higher dimensional Euclidean space. The two conceptions were only shown to be equivalent notions in the 1940s by Hassler Whitney and 1950s by John Nash (the mathematician depicted by Russell Crowe in the film "A Beautiful Mind").
Some theorists believe that the EP is so NONtrivial that its very breakdown (actual experimental falsification) may be the first place where we see in practice the General Theory of Relativity yield to more general, yet to be developed quantum theory of gravity. See the discussion in vnb's answer to the Physics SE question "Does quantum mechanics violate the equivalence principle?". Indeed Paul Davies in his article "Quantum mechanics and the equivalence principle" shows a possible chink: for quantum particles tunnelling to regions in a gravitational field whence they are classical forbidden, the tunnelling depth depends on the particle mass. Also, the problem of whether an electrical charge on the Earth's surface radiates does not seem to be fully resolved. See Ben Crowell's answer to the Physics SE question "Does a constantly accelerating charged particle emit em radiation or not?".
Strictly speaking, all the physics of the Equivalence Principle would be encoded by an assertion that $m_I = \lambda\,m_g$, where $\lambda$ is any constant, so $m_I=m_g$ encodes the EP together with a choice of scaling constant. We choose to define the universal gravitation constant $G$ in Newton's law of gravitation so that $\lambda = 1$. Actually, in General Relativity, in some ways it would make more sense to define $G/(8\pi)$ to be the gravitation constant, in which case the equivalence principle would be $m_I = \sqrt{8\,\pi}\,m_g$.
Best Answer
Newton's 1st and 2nd laws weren't particularly revolutionary or surprising to anyone in the know back then. Hooke had already deduced inverse-square gravitation from Kepler's third law, so he understood the second law. He just could not prove that the bound motion in response to an inverse square attraction is an ellipse.
The source of Newton's second law was Galileo's experiments and thought experiments, especially the principle of Galilean relativity. If you believe that the world is invariant under uniform motion, as Galileo states clearly, then the velocity cannot be a physical response because it isn't invariant, only the acceleration is. Galileo established that gravity produces acceleration, and its no leap from that to the second law.
Newton's third law on the other hand was revolutionary, because it implied conservation of momentum and conservation of angular momentum, and these general principles allow Newton to solve problems. The real juicy parts of the Principia are the specific problems he solves, including the bulge of the Earth due to its rotation, which takes some thinking even now, three centuries later.
EDIT: Real History vs. Physicist's History
The real history of scientific developments is complex, with many people making different contributions of various magnitude. The tendency in pedagogy is to relentlessly simplify, and to credit the results to one or two people, who are sort of a handle on the era. For the early modern era, the go-to folks are Galileo and Newton. But Hooke, Kepler, Huygens, Leibniz and a host of lesser known others made crucial contributions along the way.
This is especially pernicious when you have a figure of such singular genius as Newton. Newton's actual discoveries and contributions are usually too advanced to present to beginning undergraduates, but his stature is immense, so that he is given credit for earlier more trivial results that were folklore at the time.
To repeat the answer here: Newton did not discover the second law of motion. It was well known at the time, it was used by all his contemporaries without comment and without question. The proper credit for the second law belongs almost certainly to the Italians, to Galileo and his contemporaries.
But Newton applied the second law with genius to solve the problem of inverse square motion, to find the tidal friction and precession of the equinoxes, to give the wobbly orbit of the moon (in an approximation), to find the oblateness of the Earth, and the altitude variation of the acceleration of gravity g, to give a nearly quantitative model of the propagation of sound waves, to find the isochronous property of the cycloid, and a host of other contributions which are so brilliant ad so complete in their scope, that he is justly credited as founding the modern science of physics.
But in physics classes, you aren't studying history, and the applications listed above are too advanced for a first course, and Newton did indeed state the second law, so why not just give him credit for inventing it?
Similarly, in mathematics, Newton and Leibniz are given credit for the fundamental theorem of calculus. The proper credit for the fundamental theorem of calculus is to Isaac Barrow, Newton's advisor. Leibniz does not deserve credit at all. The real meat of the calculus however is not the fundamental theorem, but the organizing principles of Taylor expansions and infinitesimal orders, with successive approximations, and differential identities applied in varied settings, like arclength problems. In this, Newton founded the field.
Leibniz gave a second set of organizing principles, based on the infinitesimal calculus of Cavalieri. Cavalieri was Galileo's contemporary in Itali, and he either revived or rediscovered the ideas originally due to Archimedes in "The Method of Mechanical Theorems" (although he might not have had access to this work, which was only definitively rediscovered in the early 20th century. One of the theorems in Archimedes reappear in Kepler's work, suggesting that perhaps the Method was available to these people in an obscure copy in some library, and only became lost at a later date. This is pure speculation on my part. Kepler might have formulated and solved the problem independently of Archimedes. It is hard to tell. The problem is the volume of a cylinder cut off by a prism, related to the problem of two cylinders intersecting at right angles). Cavalieri and Kepler hardly surpassed Archimedes, while Newton went far beyond. Leibniz gave the theory its modern form, and all the formalism of integrals, differentials, product rule, chain rule, and so on are all due to Leibniz and his infinitesimals. Leibniz was also one of the discoverers of the conservation of mechanical energy, although Huygens has his paws on it too, and I don't know the dates.
The mathematicians' early modern history is no better. Again, Newton and Leibniz are given credit for theorems they did not produce, and which were common knowledge.
This type of falsified history sometimes happens today, although the internet makes honest accounting easier. Generally, Witten gets credit for everything, whether he deserves it or not. The social phenomenon was codified by Mermin, who called it "The Matthew principle", from the biblical quote "To those that have, much will be given, and to those that have not, even the little they have will be taken away." The urge to simplify relentlessly reassigns credit to well known figures, taking credit away from lesser known figures.
The way to fight this is to simply cite correctly. This is important, because the mechanism of progress is not apparent from seeing the soup, you have to see how the soup was cooked. Future generations deserve to get the recipe, so that we won't be the only ones who can make soup.