The myth of Newton's apple, did Hipparchus discover Newtons gravity and inverse square law? Michael Lahanas

If I have seen farther it is by standing on the shoulders of giants.
Sir Isaac Newton (1643-1727)

Was Newtons apple in reality Hipparchus of Rhodes, the Greek mathematician? New evidence exists that like Copernicus who did not mention Aristarchus heliocentric model also Newton did not mention the sources of his “revolutionary ideas”. Newton knew the book of Pappus and other books of ancient Greeks. In his last years he even believed that the Greeks had a knowledge that did not survived, according to some statements in the book of Pappus. Newton believed that Descartes analytic method was not superior to the geometric methods of the Greeks. Descartes was convinced that his mathematical discoveries provided a method of doing much simpler calculations. We know that this is correct if we compare the first geometric proofs of Newton with analytic algebraic proofs.

All movement tends to maintenance, or rather all moved bodies continue to move as long as the impression of the force of their motors (original impetus) remains in them.
Principle of Leonardo

Did Newton use Leonardo's words in his first law?

Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.
Sir Isaac Newton, first law of motion

La Rivoluzione Dimenticata (The Forgotten Revolution) Lucio Russo Feltrinelli, Milan, 1996

Heliocentric theories of planetary motions were known long before Hellenistic times, when they were reelaborated by Aristarchus of Samos and then one century later by Hipparchus of Nicea. The point here is the following: Hipparchus was not motivated by purely kinematic purposes as the earlier astronomers were. A dynamical theory of planetary motions based on the attractions of the planets toward the Sun by a force proportional to the inverse square of the distance between planet and Sun was his contribution. Since nothing is left of Hipparchus’s works,the matter is highly debatable. Now an infrequently read work of Plutarch, several parts of the Natural History of Pliny, of the Natural Questions of Seneca, and of the Architecture of Vitruvius, also infrequently read, especially by scientists, clearly show that the cultural elite of the early imperial age (first century A.D.) were fully aware of and convinced of a heliocentric dynamical theory of planetary motions based on the attractions of the planets toward the Sun by a force proportional to the inverse square of the distance between planet and Sun. The inverse square dependence on the distance comes from the assumption that the attraction is propagated along rays emanating from the surfaces of the bodies. The difficulties experienced by those authors in reproducing technical arguments which they did not fully grasp indicate, even more than their indirect references to earlier “learned men”, that they were writing on the basis of earlier sources. An accurate examination of all the extant related literature strongly supports the opinion that the true source must have been Hipparchus. How much of the above was known to Newton?

We learn that Definition 5 (centripetal force) of the Principia is almost the translation of Plutarch’s rendering of the same concept. Likewise, the illustration (Comment after Definition 5) of centrifugal force through the example of the stone put in rotation through a sling is in Plutarch’s De facie. Moreover, in the Scholia12 of the Principia (published only in 1981!) Newton had inserted, without quotation, several chosen passages of De facie, including the full development of the above mentioned ones, in which Plutarch argues that the Moon keeps going along its circular orbit and does not fall on the Earth by compensation between centripetal attraction and centrifugal force. The passage of Seneca in which Plutarch’s theory of the motion of the Moon around the Earth is applied to explain the planetary motions—the center being this time the Sun—also appears, again without quotation, in the fragments, as well as another passage about the motions of the comets in De mundi systemate Liber I. What about the inverse square law? Again in the Scholia Newton gives credit for its discovery to Pythagoras (while in the De mundi systemate Liber I he credits the second king of Rome, the legendary Numa Pompilius, for the introduction of heliocentrism, suggesting, however, that he may have had it from the Egyptians).

Hooke thought of deducing Kepler’s laws out of the inverse square law before Newton and communicated his idea in a letter13 to him. We learn then that the inverse square law can be traced back, through Boulliau, Kepler, Roger Bacon, to the above mentioned Architecture of Vitruvius. The Hellenistic sources were thus forgotten by a kind of “double censorship” mechanism: first by Newton himself and second by his followers, who never published those of his works which could make clear his dependence on them. Voltaire’s invention of the tale of Newton’s apple put the final seal to the matter.

EXTRACT OF MR. DUTEN’S INQUIRY INTO THE ORIGIN OF THE DISCOVERIES ATTRIBUTED TO THE MODERNS

CHAPTER XIII. OF UNIVERSAL GRAVITY, AND CENTRIPETAL AND CENTRIFUGAL FORCE.

Laws of the movement of the planets, according to their distance from the common centre.

It is here the moderns flatter themselves they have a remark able advantage, imagining, that they were the first who discovered the principle of universal gravitation, which they look upon as a truth known to the ancients. It is however easy to make it appear, that they have done nothing but trod in the paths of those ancients. It the moderns have demonstrated the laws of this universal gravitation, and explained them with clearness and precision; but this is all they have done in this respect, and have added nothing.

With the least attention to the knowledge of the ancients, we that they were not unacquainted with universal gravitation; and knew besides, that the circular motion, by which the planets describe their course, is the result of the combination of two moving forces, a rectilinear and a perpendicular, which, united together, form a curve. They knew the reason why these two movements, or contrary forces, retain the planets in their orbs; and have explained themselves on this head, just as the moderns do, excepting only the terms of centripetal and centrifugal; instead of which, however, they used what was altogether equivalent. They also knew the inequality of the course of the planets, ascribing it to’ the variety of their weights reciprocally considered, and of their proportional distances.

I will not expatiate upon Empedocles’ system, in which some have thought the foundation of Newton’s was to be found; imagining, that under the name of love, he intended to initiate a law, or power, which separated the parts of matter, in order to join himself to them, and to which nothing was wanting but the name of attraction. One sees also, that by the name discords be intended to describe another force, which obliged the same parts to recede from one another, and which Newton calls a repelling force. But I leave Empedocles, and pass on’ to passages more deserving notice. The Pythagoreans and Platonics, treating of the creation of the world, perceived the necessity of admitting the force of two powers, viz, projection and gravity, in order to account for the revolution of the planets. Timoeus, speaking of the soul of the world, which puts all nature in motion, says, that God “hath endowed it with two powers, which, in combination, act according to certain numeric proportions.” Plato, who hath followed Timoeus, in his natural philosophy, clearly asserts, that God had impressed upon the planets” a motion which was the most proper for them ; which could be nothing else than the perpendicular motion, which has a tendency to the Centre of the universe, that is, gravity ; and what in this case coincides with it, a lateral impulse, rendering the whole circular. And Diogenes Laertius alluding in all likelihood to this passage of Plato, says, that at the beginning, the bodies of the universe were agitated tumultuously, and with a disorderly movement, but that God afterward regulated their course, by laws natural and proportional. Anaxagoras cited by Diogenes Laertius, being asked what it was that retained the heavenly bodies in their orbit, notwithstanding their gravity ; answered, that” the rapidity of their course preserved them in their stations ; and should the celerity of their motions abate,” the equilibrium of the world being broke, the whole machine would fall to ruin. Plutarch, who knew almost all the shining truths of astronomy, took notice also of the reciprocal energy, which causes the planets to gravitate towards one another; and in explaining what it was that made bodies tend towards the earth, he attributes it “to a reciprocal attraction, whereby all terrestrial bodies have this tendency, and which collects into one the parts constituting the sun and moon, and retains them in their spheres. He afterward applies these particular phenomena to others more general; and “ from what happens in our globe, deduces, according to the same principle, whatever must thence happen respectively in each celestial body ;“ and then considers them in their relative connexions one towards another. He illustrates this general connexion, “by instancing what happens to our moon in its revolution round the earth, comparing it to a stone in a sling, which is impressed by two powers at once; that of projection, which would carry it away, were it not retained by the embrace of the sling; which like the central force, keeps it from wandering, whilst the combination of the two moves it in a circle. In another place, he speaks “of an inherent power in bodies ; that is, in the earth and other planets; of attracting to themselves whatever is within their reach.” It is impossible, not to perceive in all these passages, a plain reference to the centripetal force, which binds the planets to their proper or common centres; and to the centrifugal, which makes them roll in circles at a distance.

We have seen that the ancients attribute to the celestial bodies, a tendency towards one common centre, and a reciprocal attractive power. Lucretius well perceived this truth, though he deduced’ from it a very strange consequence, that the universe had no common centre, but that infinite space was filled with an infinity of worlds like ours; for, says he, if the celestial bodies were all of them carried towards one common centre, and not restrained from that tendency by some exterior active force, they must needs soon diverge towards one another, by virtue of their attractive power, and like bodies tumbling from on high, reunite at the common centre of gravity, and into one infinite, inactive mass. It appears also, that the ancients knew, as well as the moderns the cause of gravitation, which attracted all things, did not reside solely in the centre of the earth. Their ideas were more philosophic; “That this power was diffused through every particle of the terrestrial globe, and compounded of the various energy residing in each.”

It remains to inquire, whether the ancients knew the law by which gravity acts upon the celestial bodies; that it was in an inverse proportion of their quantity of matter, and the square of their distance. Certain it is, that the ancients were not ignorant, that the planets, in their courses observed a constant and invariable pro portion; and that they had different opinions respecting this proportion. Some sought for it in the difference of the quantity of matter contained in the masses, of which they were composed; and others, in the differences of their distances. Lucretius, after Democritus and Aristotle, thought that “ the gravity of bodies was in proportion to the quantity of matter of which they were composed ;“ and the ablest Newtonians, even such as ought to be the most interested to preserve to their master the glory of having first discovered those truths, which are ‘the principal ornaments of his system, have been the first to point at the sources whence they seem to have been drawn. It is true the penetration and sagacity of a Newton, a Gregory, and a Maclauren, were requisite to discover, in the few fragments now remaining, the inverse’ law respecting the squares of the distances, a doctrine which Pythagoras had taught ; but it is no less true, that it was contained in those writings. This the Newtonians acknowledge, and are the first to avail themselves of the authority of Pythagoras, to give weight to their system. Plutarch, of all the philosophers who have spoken of Pythagoras, is he, who, as be had a better opportunity of entering into the ideas of that great man, bath explained them better than any one besides. Pliny, Macrobrius, and Censorinus, have also spoken of the harmony which Pythagoras observed to reign in the course of the planets. Plutarch makes him say, it is probable that the bodies of the planets, their distances, the intervals between their spheres, and the celerity of their courses and revolutions, are not only proportionable among themselves, but to the whole of the universe. And Gregory bath been led to declare, it was evident to any attentive mind, that this great man understood, that the gravitation of the planets towards the sun, was in a reciprocal ratio of their distance from that luminary; and that illustrious modern, followed herein by Maclaurin, makes that ancient philosopher speak thus:

“ A musical string,” says Pythagoras, “yields the very same tone with any other of twice its length, because the tension of the latter, or the force whereby it is extended, is quadruple to that of the former “and the gravity of one planet, is quadruple to that of any other which is at double the distance.” in general, to bring a musical string into unison with one of the same kind, shorter than itself, its tension ought to be increased to Proportion as the square of its length exceeds that of the other ; “ and that the gravity of any planet, may become equal to that of any other nearer the sun, it ought to be increased in proportion as the square of its distance exceeds that of the other.” If, therefore, we should suppose musical strings stretched from the sun to each of the planets, it would be necessary,” in order to bring them all to unison, “to augment or diminish their tensions, in the very same proportion as would be requisite to render the planets themselves equal in gravity.” And this, in all likelihood, gave foundation for the reports, that Pythagoras drew his doctrine of harmony from the spheres.

Before I finish this chapter, 1 must not neglect to insert a passage of Galileo’s, wherein he acknowledges, that he owes to Plato his first idea of the method of determining, how the different degrees of velocity, ought to produce that uniformity of motion discernable in the revolutions of the heavenly bodies. His account is, “Plato being of opinion, that no moveable thing could pass from a state of rest’ to any determinate degree of velocity, so as perpetually and equally to remain in it, without first passing through all the inferior degrees of celerity or retardation; concludes thence, that God, after having created the celestial bodies, determining to assign to each a particular degree of celerity, in which they should always move, impressed upon them, when he drew them from a state of rest, such a force as made them run through their assigned spaces, in that natural and direct way wherein we see the bodies around us pass from rest into motion, by a continual and successive acceleration. And he adds, that having brought them to that degree of motion wherein he intended they should perpetually remain ; he afterward changed the perpendicular into a circular direction, that being the only course that can preserve itself uniform, and make a body without ceasing to keep at an equal distance from its proper centre.” This acknowledgment of Galileo is the more remarkable, as it comes from an inventive genius, who least of any owes his eminence to the aid of the ancients ; for it is the disposition of noble minds to arrogate to themselves as little as possible any merit, but what they have the utmost claim to. Thus do Galileo and Newton, the greatest of all modern philosophers, set an example which will never be imitated but by those of their own class.

References

Review by Sandro Graffi of “ La Rivoluzione Dimenticata” (The Forgotten Revolution) Lucio Russo Feltrinelli, Milan, 1996

Russo Lucio, Levy Silvio (translator), The Forgotten Revolution How Science Was Born in 300 BC and Why it Had to Be Reborn, Springer, 2004, IX, 487 p., ISBN: 3-540-20068-1

Ancient Greece

Medieval Greece / Byzantine Empire

Modern Greece

Cyprus