- Roger Cotes's Preface to the Principia.
Roger Cotes (1682-1716) wrote the Preface to the second edition of Newton's Principia in 1713, from which this extract is taken:
Those who have treated of natural philosophy may be nearly reduced to three classes. Of these some have attributed to the several species of things specific and occult qualities, on which, in a manner unknown, they make the operations of the several bodies to depend. The sum of the doctrine of the Schools derived from Aristotle and the Peripatetics is herein contained. They affirm that the several effects of bodies arise from the particular natures of those bodies. But whence it is that bodies derive those natures they don't tell us; and therefore they tell us nothing. And being entirely employed in giving names to things, and not in searching into things themselves, we may say that they have invented a philosophical way of speaking, but not that they have made known to us true philosophy. ...
There is left then the third class, which profess experimental philosophy. These indeed derive the causes of all things from the most simple principles possible; but then they assume nothing as a principle that is not proved by phenomena. They frame no hypotheses, nor receive them into philosophy otherwise than as questions whose truth may be disputed. They proceed therefore in a twofold method, synthetical and analytical. From some select phenomena they deduce by analysis the forces of nature, and the more simple laws of forces; and from thence by synthesis show the constitution of the rest. This is that incomparably best way of philosophizing, which our renowned author most justly embraced before the rest; and thought alone worthy to be cultivated and adorned by his excellent labours. Of this he has given us a most illustrious example, by the explication of the System of the World, most happily deduced from the Theory of Gravity. That the virtue of gravity was found in all bodies, others suspected, or imagined before him; but he was the only and the first philosopher that could demonstrate it from appearances, and make it a solid foundation to the most noble speculations.
Therefore that we may begin our reasoning from what is most simple and nearest to us, let us consider a little what is the nature of gravity with us on Earth, that we may proceed the more safely when we come to consider it in the heavenly bodies that lie at so vast a distance from us. It is now agreed by all philosophers that all circumterrestrial bodies gravitate towards the Earth. That no bodies really light are to be found is now confirmed by manifold experience. That which is relative levity is not true levity, but apparent only, and arises from the preponderating gravity of the contiguous bodies.
Moreover, as all bodies gravitate towards the Earth, so does the Earth again towards bodies. That the action of gravity is mutual, and equal on both sides, is thus proved. ...
This is the nature of gravity upon Earth; let us now see what it is in the Heavens.
That every body perseveres in its state either of rest, or of moving uniformly in a right line, unless insofar as it is compelled to change that state by forces impressed, is a law of nature universally received by all philosophers. But from thence it follows that bodies which move in curve lines, and are therefore continually going off from the right lines that are tangents to their orbits, are by some continued force retained in those curvilinear paths. Since then the planets move in curvilinear orbits, there must be some force operating by whose repeated actions they are perpetually made to deflect from the tangents. ...
From what has been hitherto said, it is plain that the planets are retained in their orbits by some force perpetually acting upon them; it is plain that that force is always directed towards the centres of their orbits; it is plain that its efficacy is augmented with the nearness to the centre, and diminished with the same; and that it is augmented in the same proportion with which the square of the distance is diminished, and diminished in the same proportion with which the square of the distance is augmented. ...
Because the revolutions of the primary planets about the Sun, and of the secondary about Jupiter and Saturn, are phenomena of the same kind with the revolution of the Moon about the Earth; and because it has been moreover demonstrated that the centripetal forces of the primary planets are directed towards the centre of the Sun, and those of the secondary towards the centres of Jupiter and Saturn, in the same manner as the centripetal force of the Moon is directed towards the centre of the Earth; and since besides, all these forces are reciprocally as the squares of the distances from the centres, in the same manner as the centripetal force of the Moon is as the square of the distance from the Earth; we must of course conclude that the nature of all is the same. Therefore as the Moon gravitates towards the Earth, and the Earth again towards the Moon; so also all the secondary planets will gravitate towards their primary, and the primary planets again towards their secondary; and so all the primary towards the Sun; and the Sun again towards the primary.
Therefore the Sun gravitates towards all the planets, and all the planets towards the Sun. ...
That the attractive virtue of the Sun is propagated on all sides to prodigious distances, and is diffused to every part of the wide space that surrounds it, is most evidently shown by the motion of the comets; which coming from places immensely distant from the Sun, approach very near to it; and sometimes so near, that in their perihelia they almost touch its body. The theory of these bodies was altogether unknown to astronomers, till in our own times our excellent author most happily discovered it, and demonstrated the truth of it by most certain observations. So that it is now apparent that the comets move in conic sections having their foci in the Sun's centre, and by radii drawn to the Sun describe areas proportional to the times. But from these phenomena it is manifest, and mathematically demonstrated, that those forces, by which the comets are retained in their orbits, respect the Sun, and are reciprocally proportional to the squares of the distances from its centre. Therefore the comets gravitate towards the Sun; and therefore the attractive force of the Sun not only acts on the bodies of the planets, placed at given distances and very nearly in the same plane, but reaches also to the comets in the most different parts of the heavens, and at the most different distances. This therefore is the nature of gravitating bodies, to propagate their force at all distances to all other gravitating bodies.
- Bernard de Fontenelle's The Elogium of Sir Isaac Newton.
The following is an extract from Bernard de Fontenelle's The Elogium of Sir Isaac Newton (London, 1728):
The motion of the Moon is the least regular of any of the planets, the most exact tables are sometimes wrong, and she makes certain excursions which could not before be accounted for. Dr Halley, whose profound skill in mathematics has not hindered his being a good poet, says in the Latin verses prefixed to the Principia:
Discimus, hinc tandem qua causa argentea phoebebut that at last she is subdued in this new system: all the irregularities of her course are there shown to proceed from a necessity by which they are foretold. It is difficult to imagine that a system in which they take this form should be no more than a lucky conjecture; especially if we consider this but a small part of a theory, which with the same success comprehends an infinite number of other solutions. The ebbing and flowing of the tide so naturally shows itself to proceed from the operation of the Moon upon the sea, combined with that of the Sun, that the admiration which this phenomenon used to raise in us seems to be lessened by it.
Passibus haud aequis graditur; cur sudita nulli
Hactenus Astronomo numerorum frena recuset.
[That the Moon till then never submitted to the bridle of calculations, nor was ever broke by any Astronomer.]
The second of these two great theories, upon which the Principia chiefly runs, is that of the resistance of mediums to motion, which must enter into the consideration of all the chief phenomena of nature, such as the motions of the celestial bodies, of light and of sound. Sir Isaac, according to his usual method, lays his foundation in the most solid proofs of geometry, he considers all the causes from which resistance can possibly arise; the density of the medium, the swift motion of the body moved, the magnitude of its superficies, and from thence he at last draws conclusions which destroy all the vortices of Descartes, and overturn that immense celestial edifice, which we might have thought immoveable. If the planets move round the Sun in a certain medium whatever it be, in an aetherial matter which fills up the whole, and notwithstanding its being extremely subtle, will yet cause resistance as is demonstrated, when comes it then, that the motions of the planets are not perpetually, nay instantly lessened? But besides this, how can comets traverse those vortices freely every way, sometimes with a tendency absolutely opposite to theirs, without receiving any sensible alteration in their motions, though of never so long a continuance? Whence comes it that these immense torrents whirling round with almost incredible velocity, do not instantly destroy the particular motion of any body, which is but an atom in comparison to them, and why do they not force it to follow their course? The celestial bodies do then move in a vast vacuum, unless their exhalations and the rays of light which together form a thousand different mixtures should mingle a small quantity of matter with the almost infinite immaterial spaces. Thus attraction and vacuum banished from physics by Descartes, and in all appearance for ever, are now brought back again by Sir Isaac Newton, armed with a power entirely new, of which they were thought incapable, and only perhaps a little disguised.
These two great men, whose systems are so opposite, resembled each other in several respects, they were both genius's of the first rank, both born with superior understandings, and fitted for the founding of empires of knowledge. Being excellent geometricians, they both saw the necessity of introducing geometry into physics; for both founded their physics upon discoveries in geometry, which may almost be said of none but themselves. But one of them, taking a bold flight, thought at once to reach the fountain of all things, and by clear and fundamental ideas to make himself master of the first principles; that he might have nothing more left to do, but to descend to the phenomena of nature as to necessary consequences; the other more cautious, or rather more modest, began by taking hold of the known phenomena to climb to unknown principles; resolved to admit them only in such manner as they could be produced by a chain of consequences. The former sets out from what he clearly understands, to find out the causes of what he sees; the latter sets out from what he sees, in order to find out the cause, whether it be clear or obscure. The self-evident principles of the one do not always lead him to the causes of the phenomena as they are; and the phenomena do not always lead the other to principles sufficiently evident. The boundaries which stopped two such men in their pursuits through different roads, were not the boundaries of their understanding, but of human understanding itself.
- Voltaire's On Descartes And Sir Isaac Newton.
The following extract is from Francois-Marie Arouet Voltaire's On Descartes And Sir Isaac Newton in Lettres Écrits de Londres sur les Anglois et Autre Sujets (Basel, 1734):
A Frenchman who arrives in London, will find natural philosophy, like everything else, very much changed there. He had left the world full, and he now finds it empty. In Paris the universe is seen composed of vortices of subtle matter; but nothing like it is seen in London. In France, it is the pressure of the moon that causes the tides of the sea; but in England it is the sea that gravitates towards the moon; so that when you think that the moon should make it flood with us, those gentlemen fancy it should be ebb, which very unfortunately cannot be proved. For to be able to check this, it would have been necessary to have examined the moon and the tides at the very instant of the creation.
You will note further, that the sun, which in France is said to have nothing to do in the affair at all, comes in here for very near a quarter of its assistance. According to your Cartesians, everything is moved by an impulsion, of which we have very little understanding; and according to Sir Isaac Newton, it is by gravitation, the cause of which is no better known to us. In Paris you imagine that the earth is shaped like a melon, or of an oblique figure; in London it has an oblate sphere. A Cartesian declares that light exists in the air; but a Newtonian asserts that it comes from the sun in six and a half minutes. The several operations of your chemistry are performed by acids, alkalis and subtle matter; but attraction dominates even in chemistry among the English.
The very essence of things is totally changed. You fail to agree on the definition of the soul, and also on that of matter. Descartes maintains that the soul is the same thing as thought, and Mr Locke has given a pretty satisfactory proof of the opposite.
Descartes asserts further, that extension alone constitutes matter, but Sir Isaac adds solidity to it. How furiously contradictory are these opinions!
"Non nostrum inter vos tantas componere lites." (Virgil, Eclog. III.)
"'Tis not for us to end such great disputes."
This famous Newton, this destroyer of the Cartesian system, died in March, in the year 1727. His countrymen honoured him in his lifetime, and buried him as though he had been a king who had done well for his people.
The English read with the highest satisfaction, and translated into their own language, the Elogium of Sir Isaac Newton, which M de Fontenelle delivered at the Paris Academy of Sciences. M de Fontenelle presides as judge over philosophers; and the English expected his verdict, as a solemn declaration of the superiority of the English natural philosophy over that of the French. But when it was realised that this gentleman had compared Descartes to Sir Isaac, the whole Royal Society in London rose up in arms. So far from acquiescing with M Fontenelle's judgment, they criticised his discourse. And several (who, however, were not the ablest natural philosophers in that body) even were offended at the comparison; and for no other reason but because Descartes was a Frenchman.
It must be confessed that these two great men differed very much in conduct, in fortune, and in philosophy.
Nature had given Descartes a shining and strong imagination, whence he became a very singular person both in private life and in his way of reasoning. This imagination could not hide itself even in his philosophical works, which are everywhere adorned with very shining, ingenious metaphors and figures. By nature he was almost a poet; and indeed he wrote a piece of poetry to entertain Christina, Queen of Sweden, which however was suppressed in honour to his memory.
He left France purely to seek out the truth, which was then persecuted by the wretched philosophy of the schools. However, he discovered that reason was just as disguised and depraved in the universities of Holland, into which he withdrew, as in his own country. For when the French were condemning the only propositions of his philosophy which were true, he was being persecuted by the supposed philosophers of Holland, who understood him no better; and who, seeing him more closely, hated his person even more, so that he was forced to leave Utrecht.
At last Descartes was snatched from the world in the prime of life in Stockholm. His death was the fault of a bad regimen, and he expired in the midst of some literati who were his enemies, and under the care of a physician to whom he was odious.
The progress of Sir Isaac Newton's life was quite different. He lived happy, and very much honoured in his native land, to the age of eighty-five years.
It was his peculiar good fortune, not only to be born in a country of liberty, but in an age when all scholastic impertinences were banished from the world. Reason alone was cultivated, and mankind could only be his pupil, not his enemy.
One very singular difference in the lives of these two great men is, that Sir Isaac, during the long course of years he enjoyed, was never ruled by any passion, was not subject to the common frailties of mankind, nor ever had any attachments to women - something which I was assured of by the physician and surgeon who attended him in his last moments.
We may admire Sir Isaac Newton on this occasion, but then we must not censure Descartes.
The opinion that generally prevails in England with regard to these new philosophers is, that the latter was a dreamer, and the former a sage.
Very few people in England read Descartes, whose works indeed are now useless. On the other side, but a small number peruse those of Sir Isaac, because to do this the student must be deeply skilled in the mathematics, otherwise those works will be unintelligible to him. But notwithstanding this, these great men are the subject of everyone's discourse. Sir Isaac Newton is allowed every advantage, whilst Descartes is not indulged a single one. According to some, it is to the former that we owe the discovery of a vacuum, that the air is a heavy body, and the invention of telescopes. In a word, Sir Isaac Newton is here as the Hercules of fabulous story, to whom the ignorant ascribed all the feats of ancient heroes.
In a criticism that was made in London of M de Fontenelle's discourse, the writer presumed to assert that Descartes was not a great mathematician. Those who make such a declaration may justly be reproached with beating their own master. Descartes extended the scope of mathematics as far beyond the place where he found it, as Sir Isaac did after him. The former first taught the method of expressing curves by equations. This geometry which, thanks to him, is now common knowledge, was so abstruse in his time, that not so much as one professor would undertake to explain it; and Schooten in Holland, and Fermat in France, were the only men who understood it.
I indeed believe that very few will presume to compare his natural philosophy in any respect with that of Sir Isaac Newton. The former is an essay, the latter a masterpiece.