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Isaac Newton

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I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

Sir Isaac Newton (January 4, 1643 – March 31, 1727 or in Old Style: December 25, 1642 – March 20, 1727) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the greatest mathematicians and physicists and among the most influential scientists of all time. He was a key figure in the philosophical revolution known as the Enlightenment. His book Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687, established classical mechanics. Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for developing infinitesimal calculus.

See also:
Opticks
Philosophiæ Naturalis Principia Mathematica
Religious views of Isaac Newton

Quotes

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Plato is my friend — Aristotle is my friend — but my greatest friend is truth.
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If I have seen further it is by standing on ye sholders of Giants.
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I frame no hypotheses.
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Christ comes as a thief in the night, & it is not for us to know the times & seasons which God hath put into his own breast.
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To explain all nature is too difficult a task for any one man or even for any one age...
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I keep the subject constantly before me, and wait 'till the first dawnings open slowly, by little and little, into a full and clear light.
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I have studied these things — you have not.
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Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.
  • Amicus Plato — amicus Aristoteles — magis amica veritas
    • Plato is my friend — Aristotle is my friend — but my greatest friend is truth.
    • These are notes in Latin that Newton wrote to himself that he titled: Quaestiones Quaedam Philosophicae [Certain Philosophical Questions] (c. 1664)
    • Variant translations: Plato is my friend, Aristotle is my friend, but my best friend is truth.
      Plato is my friend — Aristotle is my friend — truth is a greater friend.
    • This is a variation on a much older adage, which Roger Bacon attributed to Aristotle: Amicus Plato sed magis amica veritas. Bacon was perhaps paraphrasing a statement in the Nicomachean Ethics: Where both are friends, it is right to prefer truth.
  • The best and safest method of philosophizing seems to be, first to enquire diligently into the properties of things, and to establish these properties by experiment, and then to proceed more slowly to hypothesis for the explanation of them. For hypotheses should be employed only in explaining the properties of things, but not assumed in determining them, unless so far as they may furnish experiments.
    • Letter to Ignatius Pardies (1672) Philosophical Transactions of the Royal Society (Feb. 1671/2) as quoted by William L. Harper, Isaac Newton's Scientific Method: Turning Data Into Evidence about Gravity and Cosmology (2011)
  • If I have seen further it is by standing on ye sholders of Giants.
    • Letter to Robert Hooke (15 February 1676) [dated as 5 February 1675 using the Julian calendar with March 25th rather than January 1st as New Years Day, equivalent to 15 February 1676 by Gregorian reckonings.] A facsimile of the original is online at The digital Library. The quotation is 7-8 lines up from the bottom of the first page. The phrase is most famous as an expression of Newton's but he was using a metaphor which in its earliest known form was attributed to Bernard of Chartres by John of Salisbury: "Bernard of Chartres used to say that we [the Moderns] are like dwarves perched on the shoulders of giants [the Ancients], and thus we are able to see more and farther than the latter. And this is not at all because of the acuteness of our sight or the stature of our body, but because we are carried aloft and elevated by the magnitude of the giants." See also: Michael Foster
    • Paraphrases: If I have seen further it is by standing on the shoulders of giants.
      If I have seen further it is only by standing on the shoulders of giants.
  • I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis, and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.
    • Letter to Robert Hooke (15 February 1676) [5 February 1676 (O.S.)]
  • Bullialdus wrote that all force respecting the Sun as its center & depending on matter must be reciprocally in a duplicate ratio of the distance from the center.
  • 1. Fidelity & Allegiance sworn to the King is only such a fidelity and obedience as is due to him by the law of the land; for were that faith and allegiance more than what the law requires, we would swear ourselves slaves, and the King absolute; whereas, by the law, we are free men, notwithstanding those Oaths. 2. When, therefore, the obligation by the law to fidelity and allegiance ceases, that by the Oath also ceases...
    • Letter to Dr. Covel Feb. 21, (1688-9) Thirteen Letters from Sir Isaac Newton to J. Covel, D.D. (1848)
  • It seems to me, that if the matter of our sun and planets and all the matter of the universe, were evenly scattered throughout all the heavens, and every particle had an innate gravity towards all the rest, and the whole of space throughout which this matter was scattered was but finite, the matter on [toward] the outside of this space would, by its gravity, tend towards all the matter on the inside, and, by consequence, fall down into the middle of the whole space, and there compose one great spherical mass. But if the matter was evenly disposed throughout an infinite space it could never convene into one mass; but some of it would convene into one mass and some into another, so as to make an infinite number of great masses, scattered at great distances from one another throughout all that infinite space.
    • Four Letters to Bentley (1692) first letter
  • When I wrote my treatise about our System, I had an eye upon such principles as might work with considering men for the belief of a Deity and nothing can rejoice me more than to find it useful for that purpose. But if I have done the public any service this way, 'tis due to nothing but industry and a patient thought.
    • Newton to Bentley, 10 December 1692 (first letter), The Correspondence of Isaac Newton, ed. H. W. Turnbull (Cambridge: Cambridge University Press, 1961), 3:233. Referenced on p. 383 of Snobelen SD: "The Theology of Isaac Newton’s Principia Mathematica: A Preliminary Survey," pp. 377–412, Neue Zeitschrift für Systematische Theologie und Religionsphilosophie, Volume 52, Issue 4 (Jan 2010)
  • It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact, as it must be, if gravitation in the sense of Epicurus, be essential and inherent in it. And this is one reason why I desired you would not ascribe innate gravity to me. That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left open to the consideration of my readers.
    • Newton to Bentley, 25 February 1692/3, The Correspondence of Isaac Newton, ed. H. W. Turnbull (Cambridge: Cambridge University Press, 1961), 3:253-254. Quoted in: Andrew Janiak, "Newton’s Philosophy", The Stanford Encyclopedia of Philosophy (Fall 2021), ed. Edward N. Zalta
  • I keep the subject constantly before me, and wait 'till the first dawnings open slowly, by little and little, into a full and clear light.
    • Reply upon being asked how he made his discoveries, as quoted in "Biographia Britannica: Or the Lives of the Most Eminent Persons who Have Flourished in Great Britain from the Earliest Ages Down to the Present Times, Volume 5 ", by W. Innys, (1760), p. 3241. Fuller quote:
    • "The mark that seems most of all to distinguish it [the character of his genius] is this, that he himself was the truest judge, and made the justest estimation of it. One day, when one of this friends had said some handsome things of his extraordinary talents, Sir Isaac, in an easy and unaffected way, assured him, that for his own part he was sensible, that whatever he had done worth notice, was owing to a patience of thought, rather than an extraordinary sagacity which he was endowed with above other men. [He begins his first letter to Dr Bentley in 1692, thus, 'When I wrote my treatise about our system, I had an eye upon such principles as might work with considering men for the belief of a Deity, and nothing can rejoice me more than to find it useful for that purpose. But if I have done the public any service this way, it is due to nothing but industry and patient thought.' Four letters, &c. Edit. 1756, 2vo.] I keep the subject constantly before me, and wait ’till the first dawnings open slowly, by little and little, into a full and clear light. And hence we are able to give a very natural account of that unusual kind of horror which he had for all disputes upon these points; a steady unbroken attention was his peculiar felicity, he knew it, and he knew the value of it. In such a situation of mind, controversy must needs be looked upon him as his bane. However, he was at a great distance from being steeped in Philosophy: on the contrary, he could lay aside his thoughts, though engaged in the most intricate researches, when his other affairs required his attendance and, as soon as he had leisure, resume the subject at the point where he left off. This he seems to have done, not so much by any extraordinary strength of memory, as by the force of his inventive faculty, to which every thing opened itself again with ease, if nothing intervened to ruffle him. The readiness of his invention made him not think of putting his memory much to the trial; but this was the offspring of a vigorous intenseness of thought, out of which he was but a common man."
  • In the beginning of the year 1665 I found the method of approximating Series and the Rule for reducing any dignity of any Binomial into such a series. The same year in May I found the method of tangents of Gregory and Slusius, and in November had the direct method of Fluxions, and the next year in January had the Theory of Colours, and in May following I had entrance into the inverse method of Fluxions. And the same year I began to think of gravity extending to the orb of the Moon, and having found out how to estimate the force with which [a] globe revolving within a sphere presses the surface of the sphere, from Kepler's Rule of the periodical times of the Planets being in a sesquialterate proportion of their distances from the centers of their orbs I deduced that the forces which keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve: and thereby compared the force requisite to keep the Moon in her orb with the force of gravity at the surface of the earth, and found them answer pretty nearly. All this was in the two plague years of 1665 and 1666, for in those days I was in the prime of my age for invention, and minded Mathematicks and Philosophy more than at any time since. What Mr Hugens has published since about centrifugal forces I suppose he had before me. At length in the winter between the years 1676 and 1677 I found the Proposition that by a centrifugal force reciprocally as the square of the distance a Planet must revolve in an Ellipsis about the center of the force placed in the lower umbilicus of the Ellipsis and with a radius drawn to that center describe areas proportional to the times. And in the winter between the years 1683 and 1684 this Proposition with the Demonstration was entered in the Register book of the R. Society. And this is the first instance upon record of any Proposition in the higher Geometry found out by the method in dispute. In the year 1689 Mr Leibnitz, endeavouring to rival me, published a Demonstration of the same Proposition upon another supposition, but his Demonstration proved erroneous for want of skill in the method.
  • I have studied these things — you have not.
    • Reported as Newton's response, whenever Edmond Halley would say anything disrespectful of religion, by Sir David Brewster in The Life of Sir Isaac Newton (1831). This has often been quoted in recent years as having been a statement specifically defending Astrology. Newton wrote extensively on the importance of Prophecy, and studied Alchemy, but there is little evidence that he took favourable notice of astrology[1]. In a footnote, Brewster attributes the anecdote to the astronomer Nevil Maskelyne who is said to have passed it on to Oxford professor Stephen Peter Rigaud[2]
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God created everything by number, weight and measure.
  • I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.
    • Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton (1855) by Sir David Brewster (Volume II. Ch. 27). Compare: "As children gath'ring pebbles on the shore", John Milton, Paradise Regained, Book iv. Line 330
  • In default of any other proof, the thumb would convince me of the existence of a God.
    • Attributed to Newton as "A défaut d'autres preuves, le pouce me convaincrait de l'existence de Dieu" in a treatise on palmistry: d'Arpentigny, Stanislas (1856). "IV: Le pouce" (in French). La science de la main (2nd ed.). Paris, France: Coulon-Pineau. p. 53.  A later translation by Edward Heron-Allen renders the phrase as "In default of any other proofs, the thumb would convince me of the existence of God", and acknowledges that it does not seem to appear in any of Newton's works [d'Arpentigny, Casimir Stanislas (1889). "Sub-Section IV: The Thumb" (in English). The Science of the Hand. London, England: Ward, Lock and Co.. p. 138. ]
    • Reported as something said by Newton in a section on palmistry in Charles Dickens's All the Year Round (1864), Vol. 10, p. 346; later found in "The Book of the Hand" (1867) by A R. Craig, S. Low and Marston, p. 51:
"In want of other proofs, the thumb would convince me of the existence of a God; as without the thumb the hand would be a defective and incomplete instrument, so without the moral will, logic, decision, faculties of which the thumb in different degrees offers the different signs, the most fertile and the most brilliant mind would only be a gift without worth. [No closing quotations marks exist to specify the end of the quotation and the beginning of the author's commentary.]
  • We account the Scriptures of God to be the most sublime philosophy. I find more sure remarks of authenticity in the Bible than in any profane history whatever.
    • Anecdote reported by Dr. Robert Smith, late Master of Trinity College, to his student Richard Watson, as something that Newton expressed when he was writing his Commentary On Daniel. In Watson's Apology for the Bible. London 8vo. (1806), p. 57
Sir Isaac Newton had on his table a pile of papers upon which were written calculations that had taken him twenty years to make. One evening, he left the room for a few minutes, and when he came back he found that his little dog "Diamond" had overturned a candle and set fire to the precious papers, of which nothing was left but a heap of ashes.
  • Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.
    • Cited in Rules for methodizing the Apocalypse, Rule 9, from a manuscript published in The Religion of Isaac Newton (1974) by Frank E. Manuel, p. 120, as quoted in Socinianism And Arminianism : Antitrinitarians, Calvinists, And Cultural Exchange in Seventeenth-Century Europe (2005) by Martin Mulsow, Jan Rohls, p. 273.
    • Variant: Truth is ever to be found in the simplicity, and not in the multiplicity and confusion of things.
      • As quoted in God in the Equation: How Einstein Transformed Religion (2002) by Corey S. Powell, p. 29
  • God created everything by number, weight and measure.
    • As quoted in Symmetry in Plants (1998) by Roger V. Jean and Denis Barabé, p. xxxvii, a translation of a Latin phrase he wrote in a student's notebook, elsewhere given as Numero pondere et mensura Deus omnia condidit. This is similar to Latin statements by Thomas Aquinas, and even more ancient statements of the Greek philosopher Pythagoras. See also Wisdom of Solomon 11:20
  • Whence are you certain that ye Ancient of Days is Christ? Does Christ anywhere sit upon ye Throne?
    • He wrote in discussing with John Locke the passage of Daniel 7:9. The Correspondence of Isaac Newton, Vol. III, Letter 362. Cited in The Watchtower magazine, 1977, 4/15, article: Isaac Newton’s Search for God.
  • Who is a liar, saith John, but he that denyeth that Jesus is the Christ? He is Antichrist that denyeth the Father & the Son. And we are authorized also to call him God: for the name of God is in him. Exod. 23.21. And we must believe also that by his incarnation of the Virgin he came in the flesh not in appearance only but really & truly , being in all things made like unto his brethren (Heb. 2 17) for which reason he is called also the son of man.
  • I have that honour for him as to believe that he wrote good sense; and therefore take that sense to be his which is the best.
    • Speaking of the apostle John's writings. Cited in The Watchtower magazine, 1977, 4/15.

Hypothesis explaining the Properties of Light (1675)

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Article sent to Henry Oldenburg in 1675 but not published until Thomas Birch, "History of the Royal Society" (1757) Vol.3 pp. 247, 262, 272; as quoted in Nature (1893) Vol.48 p. 536
  • Were I to assume an hypothesis, it should be this, if propounded more generally, so as not to assume what light is further than that it is something or other capable of exciting vibrations of the ether. First, it is to be assumed that there is an ethereal medium, much of the same constitution as air, but far rarer, subtiller, and more strongly elastic. ...In the second place, it is to be supposed that the ether is a vibrating medium, like air, only the vibrations much more swift and minute; those of air made by a man's ordinary voice succeeding at more than half a foot or a foot distance, but those of ether at a less distance than the hundredth-thousandth part of an inch. And as in air the vibrations are some larger than others, but yet all equally swift... so I suppose the ethereal vibrations differ in bigness but not in swiftness. ...In the fourth place, therefore, I suppose that light is neither ether nor its vibrating motion, but something of a different kind propagated from lucid bodies. They that will may suppose it an aggregate of various peripatetic qualities. Others may suppose it multitudes of unimaginable small and swift corpuscles of various sizes springing from shining bodies at great distances one after the other, but yet without any sensible interval of time. ...To avoid dispute and make this hypothesis general, let every man here take his fancy; only whatever light be, I would suppose it consists of successive rays differing from one another in contingent circumstances, as bigness, force, or vigour, like as the sands on the shore... and, further, I would suppose it diverse from the vibrations of the ether. ...Fifthly, it is to be supposed that light and ether mutually act upon one another. ...æthereal vibrations are therefore the best means by which such a subtile agent as light can shake the gross particles of solid bodies to heat them.
  • And so, supposing that light impinging on a refracting or reflecting ethereal superficies puts it into a vibrating motion, that physical superficies being by the perpetual applause of rays always kept in a vibrating motion, and the ether therein continually expanded and compressed by turns, if a ray of light impinge on it when it is much compressed, I suppose it is then too dense and stiff to let the ray through, and so reflects it; but the rays that impinge on it at other times, when it is either expanded by the interval between two vibrations or not too much compressed and condensed, go through and are refracted.
  • And now to explain colours. I suppose that as bodies excite sounds of various tones and consequently vibrations, in the air of various bignesses, so when rays of light by impinging on the stiff refracting superficies excite vibrations in the ether, these rays excite vibrations of various bignesses... therefore, the ends of the capillamenta of the optic nerve which front or face the retina being such refracting superficies, when the rays impinge on them they must there excite these vibrations, which vibrations (like those of sound in a trumpet) will run along the pores or crystalline pith of the capillamenta through the optic nerves into the sensorium (which light itself cannot do), and there, I suppose, affect the sense with various colours, according to their bigness and mixture—the biggest with the strongest colours, reds and yellows; the least with the weakest, blues and violets; middle with green; and a confusion of all with white, much after the manner, that in the sense of hearing, nature makes use of aereal vibrations of several bignesses to generate sounds of divers tones; for the analogy of nature is to be observed.

Board of Longitude

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  • One [method] is by a Watch to keep time exactly. But, by reason of the motion of the Ship, the Variation of Heat and Cold, Wet and Dry, and the Difference of Gravity in different Latitudes, such a watch hath not yet been made.
    • Written in remarks to the 1714 Longitude committee; quoted in Longitude (1995) by Dava Sobel, p. 52 (i998 edition) ISBN 1-85702-571-7)
  • A good watch may serve to keep a recconing at Sea for some days and to know the time of a Celestial Observ[at]ion: and for this end a good Jewel watch may suffice till a better sort of Watch can be found out. But when the Longitude at sea is once lost, it cannot be found again by any watch.
    • Letter to Josiah Burchett (1721), quoted in Longitude (1995) by Dava Sobel, p. 60

Arithmetica Universalis (1707)

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Joseph Raphson Tr., Universal Arithmetick: Or, A Treatise of Arithmetical Composition and Resolution (1720)

  • Whereas in Arithmetick Questions are only resolv'd by proceeding from given Quantities to the Quantities sought, Algebra proceeds in a retrograde Order, from the Quantities sought as if they were given, to the Quantities given as if they were sought, to the End that we may some Way or other come to a Conclusion or Æquation, from which one may bring out the Quantity sought. And after this Way the most difficult problems are resolv'd, the Resolutions whereof would be sought in vain from only common Arithmetick. Yet Arithmetick in all its Operations is so subservient to Algebra, as that they seem both but to make one perfect Science of Computing; and therefore I will explain them both together.
  • After the same Manner in Geometry, if a Line drawn any certain Way be reckon'd for Affirmative, then a Line drawn the contrary Way may be taken for Negative: As if AB be drawn to the right, and BC to the left; and AB be reckon'd Affirmative, then BC will be Negative; because in the drawing it diminishes AB...
  • The Antients, as we learn from Pappus, in vain endeavour'd at the Trisection of an Angle, and the finding out of two mean Proportionals by a right line and a Circle. Afterwards they began to consider the Properties of several other Lines. as the Conchoid, the Cissoid, and the Conick Sections, and by some of these to solve these Problems. At length, having more throughly examin'd the Matter, and the Conick Sections being receiv'd into Geometry, they distinguish'd Problems into three Kinds: viz. (1.) Into Plane ones, which deriving their Original from Lines on a Plane, may be solv'd by a right Line and a Circle; (2.) Into Solid ones, which were solved by Lines deriving their Original from the Consideration of a Solid, that is, of a Cone; (3.) And Linear ones, to the Solution of which were requir'd Lines more compounded. And according to this Distinction, we are not to solve solid Problems by other Lines than the Conick Sections; especially if no other Lines but right ones, a Circle, and the Conick Sections, must be receiv'd into Geometry. But the Moderns advancing yet much farther, have receiv'd into Geometry all Lines that can be express'd by Æquations, and have distinguish'd, according to the Dimensions of the Æquations, those Lines into Kinds; and have made it a Law, that you are not to construct a Problem by a Line of a superior Kind, that may be constructed by one of an inferior one. In the Contemplation of Lines, and finding out their Properties, I like their Distinction of them into Kinds, according to the Dimensions thy Æquations by which they are defin'd. But it is not the Æquation, but the Description that makes the Curve to be a Geometrical one.
  • The Circle is a Geometrical Line, not because it may be express'd by an Æquation, but because its Description is a Postulate. It is not the Simplicity of the Æquation, but the Easiness of the Description, which is to determine the Choice of our Lines for the Construction of Problems. For the Æquation that expresses a Parabola, is more simple than That that expresses a Circle, and yet the Circle, by reason of its more simple Construction, is admitted before it. The Circle and the Conick Sections, if you regard the Dimension of the Æquations, are of the fame Order, and yet the Circle is not number'd with them in the Construction of Problems, but by reason of its simple Description, is depressed to a lower Order, viz. that of a right Line; so that it is not improper to express that by a Circle that may be expressed by a right Line. But it is a Fault to construct that by the Conick Sections which may be constructed by a Circle. Either therefore you must take your Law and Rule from the Dimensions of Æquations as observ'd in a Circle, and so take away the Distinction between Plane and Solid Problems; or else you must grant, that that Law is not so strictly to be observ'd in Lines of superior Kinds, but that some, by reason of their more simple Description, may be preferr'd to others of the same Order, and may be number'd with Lines of inferior Orders in the Construction of Problems.
  • In Constructions that are equally Geometrical, the most simple are always to be preferr'd. This Law is so universal as to be without Exception. But Algebraick Expressions add nothing to the Simplicity of the Construction; the bare Descriptions of the Lines only are here to be consider'd and these alone were consider'd by those Geometricians who joyn'd a Circle with a right Line. And as these are easy or hard, the Construction becomes easy or hard: And therefore it is foreign to the Nature of the Thing, from any Thing else to establish Laws about Constructions. Either therefore let us, with the Antients, exclude all Lines besides the Circle, and perhaps the Conick Sections, out of Geometry, or admit all, according to the Simplicity of the Description. If the Trochoid were admitted into Geometry, we might, by its Means, divide an Angle in any given Ratio. Would you therefore blame those who should make Use of this Line... and contend that this Line was not defin'd by an Æquition, but that you must make use of such Lines as are defin'd by Æquations?
  • Geometry was invented that we might expeditiously avoid, by drawing Lines, the Tediousness of Computation. Therefore these two Sciences ought not to be confounded. The Antients did so industriously distinguish them from one another, that they never introduc'd Arithmetical Terms into Geometry. And the Moderns, by confounding both, have lost the Simplicity in which all the Elegancy of Geometry consists. Wherefore that is Arithmetically more simple which is determin'd by the more simple Æquations, but that is Geometrically more simple which is determin'd by the more simple drawing of Lines; and in Geometry, that ought to be reckon'd best which is Geometrically most simple. Wherefore, I ought not to be blamed, if with that Prince of Mathematicians, Archimedes and other Antients, I make use of the Conchoid for the Construction of solid Problems.
  • Geometrical Speculations have just as much Elegancy as Simplicity, and deserve just so much praise as they can promise Use.
  • Useful Things, though Mechanical, are justly preferable to useless Speculations in Geometry, as we learn from Pappus.
  • In my Judgment no Lines ought to be admitted into plain Geometry besides the right Line and the Circle.
  • The Ellipse is the most simple of the Conic Sections, most known, and nearest of Kin to a Circle, and easiest describ'd by the Hand in plano. Though many prefer the Parabola before it, for the Simplicity of the Æquation by which it is express'd. But by this Reason the Parabola ought to be preferr'd before the Circle it self, which it never is. Therefore the reasoning from the Simplicity of the Æquation will not hold. The modern Geometers are too fond of the Speculation of Æquations.
  • The Simplicity of Figures depend upon the Simplicity of their Genesis and Ideas, and an Æquation is nothing else than a Description (either Geometrical or Mechanical) by which a Figure is generated and rendered more easy to the Conception.

Geometriae (Treatise on Geometry)

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Disputed

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I can calculate the motions of the heavenly bodies, but not the madness of the people.
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If I had stayed for other people to make my tools and things for me, I had never made anything.
When Sir Isaac Newton was asked about the continuance of the rising of South Sea stock? — He answered, "that he could not calculate the madness of the people."
  • If I had stayed for other people to make my tools and things for me, I had never made anything.
    • This first appears in the Isaac Newton : A Biography (1934), citing unpublished papers by John Conduitt reporting an anecdote of an occasion where Conduitt asked Newton where he obtained the tools to make his reflecting telescope. Newton is said to have laughed and replied, "If I had stayed for other people to make my tools and things for me I had never made anything of it."
  • Atheism is so senseless. When I look at the solar system, I see the earth at the right distance from the sun to receive the proper amounts of heat and light. This did not happen by chance.
    • As quoted in Isaac Newton: Inventor, Scientist, and Teacher (1975) by John Hudson Tiner. "Atheism is so senseless" is a statement Newton made indeed in "A short Schem of the true Religion", but no source for the rest of this statement has been located prior to 1975. Part of this statement might originate as a summation of observations by Colin Maclaurin in his An Account of Sir Isaac Newton's Philosophical Discoveries (1750), Book III, Ch. 5: "On the quantity of watter and density of the sun and planets" : "… the earth … those planets which are nearer the sun are found to be more dense, by which they are enabled to bear the greater heat of the sun. This is the result of our most subtle enquiries into nature, that all things are in the best situations, and disposed by perfect wisdom. If our earth was carried down into the orb of Mercury, our ocean would boil and soon be dissipated into vapour, and dry land would become uninhabitable. If the earth was carried to the orb of Saturn, the ocean would freeze at so great a distance from the sun, and the cold would soon put a period to the life of plants and animals. A much less variation of the earth's distance from the sun than this would depopulate the torrid zone if the earth came nearer the sun, and the temperate zones, if it was carried from the sun. A less heat at Jupiter's distance … might be as fatal … proves on every occasion, the wisdom of the author."


Misattributed

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  • Tact is the knack of making a point without making an enemy.
    • Actually a statement by American advertising executive and author Howard W. Newton (1903–1951); attributions to Isaac are relatively recent, those to Howard date at least to Sylva Vol. 1-3 (1945), p. 57, where it is cited to an earlier publication in Redbook.
    • Variant: Tact is the art of making a point without making an enemy.
  • Les hommes construisent trop de murs et pas assez de ponts.
    • Men build too many walls and not enough bridges.
    • This became widely attributed to Isaac Newton after Dominique Pire ascribed it to "the words of Newton" in his Nobel Lecture, 11 December 1958.[3] Pire refers not to Isaac, but to Joseph Fort Newton, who is widely reported to have said "People are lonely because they build walls instead of bridges." This appears to be paraphrased from a longer passage found in his essays and addresses, The One Great Church: Adventures of Faith (1948), pp. 51–52: "Why are so many people shy, lonely, shut up within themselves, unequal to their tasks, unable to be happy? Because they are inhabited by fear, like the man in the Parable of the Talents, erecting walls around themselves instead of building bridges into the lives of others; shutting out life."

Quotes about Newton

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Kepler succeeded in showing that the planets move along elliptic paths and that the sun lies at a focus of each of these ellipses... Each planet moves so that a straight line drawn to connect it with the sun sweeps out equal areas in equal times. ...The discoveries ...enabled Newton to formulate the laws of mechanics in general and those of gravitation in particular. ...He was able to develop Kepler's laws into a comprehensive physical theory ...~ Peter G. Bergmann.
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His peculiar gift was the power of holding continuously in his mind a purely mental problem until he had seen it through. ~ John Maynard Keynes
Alphabetized by author
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Newton was not the first of the age of reason. He was the last of the magicians… ~ John Maynard Keynes
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Everyone knows Newton as the great scientist. Few remember that he spent half his life muddling with alchemy, looking for the philosopher's stone. That was the pebble by the seashore he really wanted to find. ~ Fritz Leiber
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Nature and Nature's laws lay hid in night:
God said, Let Newton be! — and all was light. ~ Alexander Pope
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Out blaz'd a Newton's soul — and all was light. ~ Aaron Hill

A–F

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  • Newton and Locke are examples of the deep sagacity which may be acquired by long habits of thinking and study.
    • John Adams, in a letter to Abigail Adams (29 October 1775), published Letters of John Adams, Addressed to His Wife, Vol. 1 (1841), ed. Charles Francis Adams, p. 72
  • According to Sir Isaac Newton's Calculations, the last Comet that made its Appearance in 1680, imbib'd so much Heat by its Approaches to the Sun, that it would have been two thousand times hotter than red hot Iron, had it been a Globe of that Metal; and that supposing it as big as the Earth, and at the same Distance from the Sun, it would be fifty thousand Years in cooling, before it recovered its natural Temper. In the like manner, if an Englishman considers the great Ferment into which our Political World is thrown at present, and how intensely it is heated in all its Parts, he cannot suppose that it will cool again in less than three hundred Years. In such a Tract of Time it is possible that the Heats of the present Age may be extinguished, and our several Classes of great Men represented under their proper Characters. Some eminent Historian may then probably arise that will not write recentibus odiis (as Tacitus expresses it) with the Passions and Prejudices of a contemporary Author, but make an impartial Distribution of Fame among the Great Men of the present Age.
  • The greatest scientist who ever lived was Isaac Newton...[about Principia Mathematica] By all odds it's the greatest scientific book ever written or ever will be written, I think.
    • 1990 interview included in Conversations with Isaac Asimov Edited by Carl Freedman (2005)
  • Newton's own motto, "hypotheses non fingo" was, in a sense, disregarded by Newton himself: he rejected hypotheses only where they violated his own "regula philosophandi", that is to say, his principle of their strict parsimony. In terms of present-day methodology, we reject hypotheses as scientifically meaningless if they are incapable even of indirect test; and we reject them as superfluous or as implausible if they are too complex and artificial to conform with well established canons of inductive probability. But freedom of scientific theorizing must be preserved wherever the conditions of meaningfulness and of economy appear to be satisfied.

  • Kepler succeeded in showing that the planets move along elliptic paths and that the sun lies at a focus of each of these ellipses... Each planet moves so that a straight line drawn to connect it with the sun sweeps out equal areas in equal times. ...The discoveries ...enabled Newton to formulate the laws of mechanics in general and those of gravitation in particular. ...He was able to develop Kepler's laws into a comprehensive physical theory only because he managed first to create the necessary mathematical tools... differential and integral calculus, the basic mathematical techniques for dealing with variable quantities, such as the movement of bodies in the course of time. ...[H]e succeeded in drawing from Kepler's empirical laws the principles of motion that applied [to] every instant of time and thus shaped planetary motion into complete orbits.
    • Peter G. Bergmann, The Riddle of Gravitation: From Newton to Einstein to Today's Exciting Theories (1968) pp. 10-11.
  • No monument should stand over [my] grave, only an apple-tree, in memory of the three apples; the two of Eve and Paris, which made hell out of earth, and that of Newton, which elevated the earth again into the circle of heavenly bodies.
  • The landscape has been so totally changed, the ways of thinking have been so deeply affected, that it is very hard to get hold of what it was like before... It is very hard to realize how total a change in outlook he has produced.
    • Hermann Bondi, "Newton and the Twentieth Century—A Personal View" in Let Newton Bel A New Perspective on his Life and Works (1988) R. Flood, J. Fauvel, M. Shortland, R. Wilson p. 241.
  • [T]he life and writings of Sir Isaac Newton abound with the richest counsel. Here the philosopher will learn the art by which alone he can acquire an immortal name. The moralist will trace the lineaments of a character adjusted to all the symmetry of which our imperfect nature is susceptible; and the Christian will contemplate with delight the high-priest of science quitting the study of the material universe,—the scene of his intellectual triumphs,—to investigate with humility and patience the mysteries of his faith.
  • Newton is known for humbly declaring that he had achieved his great breakthroughs by 'standing on the shoulders of giants.' Though this may be true in part, it is largely humbug. Newton was hardly humble, and it would be just as true to say that he achieved greatness by stamping on the shoulders of giants. When others, such as Robert Hooke and Gottfried Leibniz, made breakthroughs in fields he was also researching, Newton fought ferociously to deny them credit for their work.
  • There is a basic incompatibility between any organization and freedom of thought. Suppose Newton had founded a Church of Newtonian Physics and refused to show his formula to anyone who doubted the tenets of Newtonian Physics?
  • The history of mathematics and mechanics for a hundred years subsequent to Newton appears primarily as a period devoted to the assimilation of his work and the application of his laws to more varied types of phenomena. So far as objects were masses, moving in space and time under the impress of forces as he had defined them, their behaviour was now, as a result of his labours, fully explicable in terms of exact mathematics.
  • When Newton saw an apple fall, he found
    In that slight startle from his contemplation ...
    A mode of proving that the earth turn'd round
    In a most natural whirl, called 'gravitation'.
  • My quotations from Newton suggest the motive which induced him to take a stand against the use of hypotheses, namely, the danger of becoming involved in disagreeable controversies. ...Newton could no more dispense with hypotheses in his own cogitations than an eagle can dispense with flight. Nor did Newton succeed in avoiding controversy.
    • Florian Cajori, Explanatory Appendix, Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World (1934) Tr. Andrew Motte, p. 674
  • Opticks was out of harmony with the ideas of 19th-century physics. ...an exposition of the "wrong" (i.e., corpuscular) theory of light,—even though it also contained many of the basic principles of the "correct" (i.e., wave) theory. Not only had Newton erred in his choice... but also he apparently had found no insuperable difficulty in simultaneously embracing features of two opposing theories. ...by adopting a combination of the two theories at once, he had violated one of the major canons of 19th-century physics... Today our point of view is influenced by the theory of photons and matter waves, or the... complementarity of Neils Bohr; and we may read with a new interest Newtons ideas on the interaction of light and matter or his explanation of the corpuscular and undulatory aspects of light.
  • Of the many references to Newton in 18th-century electrical writings only a small number were to the Principia, the greater part by far were to the Opticks. This was true not alone of the electrical writings but also in other fields of experimental enquiry. ...[The Opticks] would allow the reader to roam, with great Newton as his guide, through the major unresolved problems of science and even the relation of the whole world of nature to Him who had created it. ...in the Opticks Newton did not adopt the motto... —Hypotheses non fingo; I frame no hypotheses—but, so to speak, let himself go, allowing his imagination full reign and by far exceeding the bounds of experimental evidence.
  • In the year [1666] he retired again from Cambridge to his mother in Lincolnshire & whilst he was musing in a garden it came into his thought that the power of gravity (which made an apple fall from the tree to the ground) was not limited to a certain distance from the earth, but must extend much farther than was usually thought — Why not as high as the Moon said he to himself, & if so that must influence her motion & perhaps retain her in her orbit. Whereupon he fell a calculating what would be the effect of that supposition being absent from the books & taking the common estimate in use among Geographers & our seamen before Norwood had measured the earth, that to 60 Engish miles were contained in one degree of latitude. His computation did not agree with his Theory and inclined him then to entertain a notion that together with the power of gravity there might be a mixture of that force which the moon would have if it was carried along a vortex, but when the Tract of Picard of the measure of the earth came out shewing that a degree was about 69 1/2 English miles, he began his calculation anew & found it perfectly in agreement to his Theory.
  • [Newton] bought a book of Iudicial Astrology out of a curiosity to see what there was in that science & read in it till he came to a figure of the heavens which he could not understand for want of being acquainted with Trigonometry, & to understand the ground of that bought an English Euclid with an Index of all the problems at the end of it & only turned to two or three which he thought necessary for his purpose & read nothing but the titles of them finding them so easy & self evident that he wondered any body would be at the pains of writing a demonstration of them & laid Euclid aside as a trifling book, & was soon convinced of the vanity & emptiness of the pretended science of Iudicial astrology.
  • Galileo first studied the motion of terrestrial objects, pendulums, free-falling balls, and projectiles. He summarized what he observed in the mathematical language of proportions. And he extrapolated from his experimental data to a great idealization now called the “inertia principle,” which tells us, among other things, that an object projected along an infinite, frictionless plane will continue forever at a constant velocity. His observations were the beginnings of the science of motion we now call “mechanics.”... Newton also invented a mathematical language (the "Fluxions" method, closely related to our present-day calculus) to express his mechanics, but in an odd historical twist, rarely applied that language himself.
    • William H. Cropper, Great Physicists – The Life and Times of Leading Physicists (2001), p. 12: Mechanics historical synopsis
  • But to return to the Newtonian Philosophy: Tho' its Truth is supported by Mathematicks, yet its Physical Discoveries may be communicated without. The great Mr. Locke was the first who became a Newtonian Philosopher without the help of Geometry; for having asked Mr. Huygens, whether all the mathematical Propositions in Sir Isaac's Principia were true, and being told he might depend upon their Certainty; he took them for granted, and carefully examined the Reasonings and Corollaries drawn from them, became Master of all the Physics, and was fully convinc'd of the great Discoveries contained in that Book.
  • Multiple-prism arrays were first introduced by Newton (1704) in his book Opticks. In that visionary volume Newton reported on arrays of nearly isosceles prisms in additive and compensating configurations to control the propagation path and the dispersion of light. Further, he also illustrated slight beam expansion in a single isosceles prism.
    • F. J. Duarte, The Physics of Multiple-Prism Optics in Tunable Laser Optics (2003), p. 57
  • Newton was at heart a Cartesian, using pure thought as Descartes intended, and using it to demolish the Cartesian dogma of vortices.
    • Freeman Dyson, "Birds and Frogs" (Oct. 4, 2008) AMS Einstein Public Lecture in Mathematics, as published in Notices of the AMS, (Feb, 2009). Also published in The Best Writing on Mathematics: 2010 (2011) p. 58.
  • In accordance with Newton's system, physical reality is characterised by concepts of space, time, the material point and force (interaction between material points). Physical events are to be thought of as movements according to law of material points in space. The material point is the only representative of reality in so far as it is subject to change. The concept of the material point is obviously due to observable bodies; one conceived of the material point on the analogy of movable bodies by omitting characteristics of extension, form, spatial locality, and all their 'inner' qualities, retaining only inertia, translation, and the additional concept of force.
  • In order to put his system into mathematical form at all, Newton had to devise the concept of differential quotients and propound the laws of motion in the form of total differential equations—perhaps the greatest advance in thought that a single individual was ever privileged to make.
    • Albert Einstein, "Clerk Maxwell's Influence on the Evolution of the Idea of Physical Reality" Essays in Science (1934)
  • Newton's age has long since passed through the sieve of oblivion, the doubtful striving and suffering of his generation has vanished from our ken; the works of some few great thinkers and artists have remained, to delight and ennoble those who come after us. Newton's discoveries have passed into the stock of accepted knowledge.
  • Newton had other postulates by which he could get the law of angular momentum, but Newtonian laws were wrong. There's no forces, it's all a lot of balony. The particles don't have orbits, and so on.
  • Newton's proof of the law of refraction is based on an erroneous notion that light travels faster in glass than in air, the same error that Descartes had made. This error stems from the fact that both of them thought that light was corpuscular in nature.
    • John Freely, Before Galileo, The Birth of Modern Science in Medieval Europe (2012)

G–L

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  • The history of the apple is too absurd. Whether the apple fell or not, how can any one believe that such a discovery could in that way be accelerated or retarded? Undoubtedly, the occurrence was something of this sort. There comes to Newton a stupid, importunate man, who asks him how he hit upon his great discovery. When Newton had convinced himself what a noodle he had to do with, and wanted to get rid of the man, he told him that an apple fell on his nose; and this made the matter quite clear to the man, and he went away satisfied.
  • It was God who breathed life into matter and inspired its many textures and processes. ...Rather than turn away from what he could not explain, he plunged in more deeply. ...There were forces in nature that he would not be able to understand mechanically, in terms of colliding billiard balls or swirling vortices. They were vital, vegetable, sexual forces—invisible forces of spirit and attraction. Later, it had been Newton, more than any other philosopher, who effectively purged science of the need to resort to such mystical qualities. For now, he needed them.
  • Newton's version of gravity violates common sense. How can one thing tug at another across vast spans of space? ...Newton's formalism nonetheless provided an astonishingly accurate means of calculating the orbits of planets; it was too effective to deny.
  • The prejudice for Sir Isaac has been so great, that it has destroyed the intent of his undertaking, and his books have been a means of hindering that knowledge they were intended to promote. It is a notion every child imbibes almost with his mother's milk, that Sir Isaac Newton has carried philosophy to the highest pitch it is capable of being carried, and established a system of physics upon the solid basis of mathematical demonstration.
    • George Horne, written anonymously in his A Fair, Candid, and Impartial Statement of the Case between Sir Isaac Newton and Mr. Hutchinson (1753)
  • Newton said that he made his discoveries by 'intending' his mind on the subject; no doubt truly. But to equal his success one must have the mind which he 'intended.' Forty lesser men might have intended their minds till they cracked, without any like result. It would be idle either to affirm or to deny that the last half-century has produced men of science of the calibre of Newton. It is sufficient that it can show a few capacities of the first rank, competent not only to deal profitably with the inheritance bequeathed by their scientific forefathers, but to pass on to their successors physical truths of a higher order than any yet reached by the human race. And if they have succeeded as Newton succeeded, it is because they have sought truth as he sought it, with no other object than the finding it.
  • I esteem his [Newton's] understanding and subtlety highly, but I consider that they have been put to ill use in the greater part of this work, where the author studies things of little use or when he builds on the improbable principle of attraction.
    • Christiaan Huygens, writing five years after the appearance of Newton's Principia, as quoted in A. R. Manwell, Mathematics Before Newton (Oxford University Press, 1959), p. 56 – «He [Huygens] said, indeed, that the idea of universal attraction [gravitation] 'appears to me absurd'.»
  • I do not mind at all that [Newton] is not a Cartesian provided he does not offer us suppositions like that of attraction.
    • Christiaan Huygens, letter to Fatio de Duillier (11 July 1687), quoted in René Dugas, Mechanics in the seventeenth century (1958), p. 440
  • ... Newton was harbouring a terrible secret. He believed that the central Christian doctrine of the Trinity was a diabolical fraud and that all of modern Christianity was tainted by its presence. Jesus Christ, the Son of God, was not equal in any sense to God the Father, although he was divine, and was worthy of being worshipped in his own right. Newton did not arrive at these beliefs as a result of pursuing some dilettantish hobby; nor were they the result of studies he pursued at the end of his life. Instead, they lay at the heart of a massive research programme on prophecy and church history that he carried out early in his career. This was at least as strenuous, and, in his eyes, at least as "rational" as his work on physics and mathematics.
  • The room being hung around with a collection of the portraits of remarkable men, among them were those of Bacon, Newton and Locke. Hamilton asked me who they were. I told him they were my trinity of the three greatest men the world had ever produced, naming them. He paused for some time: “the greatest man,” said he, “that ever lived, was Julius Caesar.” Mr. Adams was honest as a politician, as well as a man; Hamilton honest as a man, but, as a politician, believing in the necessity of either force or corruption to govern men.
  • As to the Christian religion, besides the strong evidence which we have for it, there is a balance in its favour from the number of great men who have been convinced of its truth after a serious consideration of the question. Grotius was an acute man, a lawyer, a man accustomed to examine evidence, and he was convinced. Grotius was not a recluse, but a man of the world, who certainly had no bias on the side of religion. Sir Isaac Newton set out an infidel, and came to be a very firm believer.
  • I can venture to affirm, without meaning to pluck a leaf from the never-fading laurels of our immortal Newton, that the whole of his theology, and part of his philosophy, may be found in the Vedas.
    • Sir William Jones, source: Old Diary Laurels 1883–84: The Only Authentic History of the Theosophical Society, Henry Steel Olcott. Quoted from Gewali, Salil (2013). Great Minds on India. New Delhi: Penguin Random House.
  • Do not all charms fly
    At the mere touch of cold philosophy?
    There was an awful rainbow once in heaven:
    We knew her woof, her texture: she is given
    In the dull catalogue of common things.
    Philosophy will clip an Angel's wings,
    Conquer all mysteries by rule of line.
    Empty the haunted air, and gnomed mine—
    Unweave a rainbow    , as it erewhile made
    The tender-person'd Lamia melt into a shade.
    • A response to Newton, over a century after his theory was proposed in Optiks (1714)
    • John Keats, Lamia (1820) Part II, 229-238
  • John Maddox, the editor of Nature... retired in 1995. In August of that year, Maddox wrote an editorial entitled "Is the Principia Publishable Now?" in which he questioned whether or not Newton would get his ideas published today, given the current practice of peer review. Maddox speculates on what a reviewer would have written on receiving the script... He toys with the idea that Huygens (a contemporary... and opponent of Newton's ideas) would have written caustically about the gravitation ideas of Newton—"by what means, pray, does the author fancy that this magic can be contrived over the great distance between the Sun and Jupiter and without the lapse of time?"
    • Al Kelly, Challenging Modern Physics: Questioning Einstein's Relativity (2005)
  • Newton was not the first of the age of reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind that looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago. [...] [H]e looked on the whole universe and all that is in it as a riddle, as a secret which could be read by applying pure thought to certain evidence, certain mystic clues which God had laid about the world to allow a sort of philosopher's treasure hunt to the esoteric brotherhood. He believed that these clues were to be found partly in the evidence of the heavens and in the constitution of elements[...], but also partly in certain papers and traditions handed down by the brethren in an unbroken chain back to the original cryptic revelation in Babylonia.
  • In vulgar modern terms Newton was profoundly neurotic of a not unfamiliar type, but... a most extreme example. His deepest instincts were occult, esoteric, semantic — with profound shrinking from the world, a paralyzing fear of exposing his thoughts, his beliefs, his discoveries, in all nakedness to the inspection and criticism of the world. ...Until the second phase of his life, he was a wrapt, consecrated solitary, pursuing his studies by intense introspection.
    • John Maynard Keynes, "Newton the Man," in The Royal Society Newton Tercentenary Celebrations (1947)
  • His peculiar gift was the power of holding continuously in his mind a purely mental problem until he had seen straight through it. I fancy his pre-eminence is due to his muscles of intuition being the strongest and most enduring with which a man has ever been gifted. ... I believe that Newton could hold a problem in his head for hours and days and weeks until it surrendered to him its secret. Then being a supreme mathematical technician he could dress it up, how you will, for the purposes of exposition, but it was his intuition that was pre-eminently extraordinary.
    • John Maynard Keynes, "Newton the Man," in The Royal Society Newton Tercentenary Celebrations (1947): this starts off with a very similar remark as Keynes had made in Essays in Biography (1933): " His peculiar gift was the power of holding continuously in his mind a purely mental problem until he had seen it through.
  • Isaac Newton’s Philosophae Naturalis Principia Mathematica abstracted time from events, establishing its tractability to scientific calculation. Conceived as pure, absolute duration, without qualities, it conforms perfectly to its mathematical idealization (as the real number line). Since time is already pure, its reality indistinguishable from its formalization, a pure mathematics of change – the calculus – can be applied to physical reality without obstruction. The calculus can exactly describe things as they occur in themselves, without straying, even infinitesimally, from the rigorous dictates of formal intelligence. In this way natural philosophy becomes modern science.
  • When Sir A. Fountaine was at Berlin with Leibnitz in 1701, and at supper with the Queen of Prussia, she asked Leibnitz his opinion of Sir Isaac Newton. Leibnitz said that taking mathematicians from the beginning of the world to the time when Sir Isaac lived, what he had done was much the better half; and added that he had consulted all the learned in Europe upon some difficult points without having any satisfaction, and that when he applied to Sir Isaac, he wrote him in answer by the first post, to do so and so, and then he would find it.
  • The one book that turned out to be perhaps the most influential in guiding Newton's mathematical and scientific thought was none other than Descartes' La Géométrie. Newton read it in 1664 and re-read it several times until "by degrees he made himself master of the whole." ...Not only did analytic geometry pave the way for Newton's founding of calculus... but Newton's inner scientific spirit was truly set ablaze.
  • Newton was really a very valuable man, not onely for his wonderfull skill in Mathematicks but in divinity too and his great knowledge in the scriptures where in I know few his equals.
    • John Locke, quoted in The Cambridge Companion to Newton (edited by I. Bernard Cohen, George E. Smith)

M–R

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  • Newton has... acted contrary to his expressed intention only to investigate actual facts. No one is competent to predicate things about absolute space and absolute motion; they are pure things of thought, pure mental constructs, that cannot be produced in experience. All our principles of mechanics are... experimental knowledge concerning the relative positions and motions of bodies. ...No one is warranted in extending these principles beyond the boundaries of experience. In fact, such an extension is meaningless, as no one possesses the requisite knowledge to make use of it.
  • We shall find it more conducive to scientific progress to recognise, with Newton, the ideas of time and space as distinct, at least in thought, from that of the material system whose relations these ideas serve to co-ordinate.
  • It is an observed fact that bodies of equal mass, placed in the same position relative to the earth, are attracted equally towards the earth whatever they are made of; but this is not a doctrine of abstract dynamics founded on axiomatic principles, but a fact discovered by observation, and verified by the careful experiments of Newton on the times of oscillation of hollow wooden balls suspended by strings of the same length, and containing gold, silver, lead, glass, sand, common salt, wood, water, and wheat. ...measuring the length of a pendulum which swings seconds.
    • James Clerk Maxwell, Matter and Motion (1876)
  • The fact that a magnet draws iron towards it was noticed by the ancients, but no attention was paid to the force with which the iron attracts the magnet. Newton, however, by placing the magnet in one vessel and the iron in another, and floating both vessels in water so as to touch each other, showed experimentally that as neither vessel was able to propel the other along with itself through the water, the attraction of the iron on the magnet must be equal and opposite to that of the magnet on the iron, both being equal to the pressure between the two vessels.
    • James Clerk Maxwell, Matter and Motion (1876)
  • We cannot... regard Newton's statement as an appeal to experience and observation, but rather as a deduction of the third law of motion from the first.
  • At the end of the [19th] century no extension or analogue of the Newtonian gravitation formula has been generally accepted, and it still stands there as almost the only firmly established mathematical relation, expressive of a property of all matter, to which the progress of more than two centuries has added nothing, from which it has taken nothing away.
  • Newton's exegesis merged with a prophetic tradition that helped create during the nineteenth and twentieth centuries the religious and political climates that paved the way for the resettlement of Jews in Palestine – the longed-for vision of the Restoration. Newton would have approved.
    • Benny Peiser, Isaac Newton: “Judaic monotheist of the school of Maimonides” (2007)
  • When I had the honour of his conversation, I endeavoured to learn his thoughts upon mathematical subjects, and something historical concerning his inventions, that I had not been before acquainted with. I found, he had read fewer of the modern mathematicians, than one could have expected; but his own prodigious invention readily supplied him with what he might have an occasion for in the pursuit of any subject he undertook. I have often heard him censure the handling geometrical subjects by algebraic calculations; and his book of Algebra he called by the name of Universal Arithmetic, in opposition to the injudicious title of Geometry, which Des Cartes had given to the treatise, wherein he shews, how the geometer may assist his invention by such kind of computations. He frequently praised Slusius, Barrow and Huygens for not being influenced by the false taste, which then began to prevail. He used to commend the laudable attempt of Hugo de Omerique to restore the ancient analysis, and very much esteemed Apollonius's book De sectione rationis for giving us a clearer notion of that analysis than we had before.
  • The first thoughts, which gave rise to his Principia, he had, when he retired from Cambridge in 1666 on account of the plague. As he sat alone in a garden, he fell into a speculation on the power of gravity; that as this power is not found sensibly diminished at the remotest distance from the centre of the earth to which we can rise, neither at the tops of the loftiest buildings, nor even on the summits of the highest mountains, it appeared to him reasonable to conclude that this power must extend much further than was usually thought: why not as high as the moon? said he to himself.
  • There is a traditional story about Newton: as a young student, he began the study of geometry, as was usual in his time, with the reading of the Elements of Euclid. He read the theorems, saw that they were true, and omitted the proofs. He wondered why anybody should take pains to prove things so evident. Many years later, however, he changed his opinion and praised Euclid. The story may be authentic or not ...
  • Nature and Nature's laws lay hid in night:
    God said, Let Newton be! — and all was light.
    • Alexander Pope, lines written for Newton's monument in Westminster Abbey, as quoted in The Epigrammatists : A Selection from the Epigrammatic Literature of Ancient, Mediæval, and Modern Times (1875) by Henry Philip Dodd, p. 329; a Latin inscription was chosen instead, but this was later inscribed on a marble tablet placed in the room of the manor-house of Woolsthorpe in which Newton was born.
    • Variants:
    • Nature and all her works lay hid in night;
      God said, Let Newton be, and all was light.
    • Nature and nature's laws lay hid in night;
      God said "Let Newton be" and all was light.
    • O'er Nature's laws, God cast the veil of night,
      Out blaz'd a Newton's soul — and all was light.
      • Variant written by Aaron Hill, preserved in Hill's Works (1753), Vol. IV, p. 92; mentioned in The Epigrammatists : A Selection from the Epigrammatic Literature of Ancient, Mediæval, and Modern Times (1875) by Henry Philip Dodd, p. 329
  • Sir Isaac Newton, having perhaps the greatest scientific mind of all time, accepted the books of Book of Daniel and Revelation as revelations from God, being very detailed and accurate representations of the history of the world's dominating kingdoms, and prophesying both the first and second coming of Christ. He understood that the scriptures taught that the true Church of Jesus Christ had been lost, and he awaited three separate future events: 1) the restoration of the gospel by an angel, 2) the re-establishment of the true church, and 3) the rise of a new world kingdom led by the Savior himself, which will crush the kingdoms of the world as the stone pulverized the statue to powder. He saw the whole purpose of these revelations is not to satisfy man's curiosity about the future, but to be a testimony of the foreknowledge of God after they are all fulfilled in the last days. He proposed that the revelations can be understood by discovering rules governing their consistent imagery, but only after they have been fulfilled, unless an interpretation is given with the revelation. Truly Newton's genius was remarkable, and we could learn much from his insights and systematic methods.
  • Were it possible to trace the succession of ideas in the mind of Sir Isaac Newton, during the time that he made his greatest discoveries, I make no doubt but our amazement at the extent of his genius would a little subside. But if, when a man publishes discoveries, he, either through design, or through habit, omit the intermediate steps by which he himself arrived at them; it is no wonder that his speculations confound others... [W]here we see him most in the character of an experimental philosopher, as in his optical inquiries... we may easily conceive that many persons, of equal patience and industry... might have done what he did. And were it possible to see in what manner he was first led to those speculations, the very steps by which he pursued them, the time that he spent in making experiments, and all the unsuccessful and insignificant ones that he made in the course of them; as our pleasure of one kind would be increased, our admiration would probably decrease. Indeed he himself used candidly to acknowledge, that if he had done more than other men, it was owing rather to a habit of patient thinking, than to any thing else. ...[T]he interests of science have suffered by the excessive admiration and wonder, with which several first rate philosophers are considered; and... an opinion of the greater equality of mankind, in point of genius, and powers of understanding, would be of real service in the present age.
  • Dr. Pemberton tells us a that the first thoughts, which gave rise to Newton's Principia, occurred to him when he had retired from Cambridge into Lincolnshire, in 1666, on account of the plague. Voltaire had his information from Mrs. Catharine Barton, Newton's favourite niece, who married Conduitt, a member of the Royal Society, and one of his intimate friends: from having spent a great portion of her life in his society, she was good authority for such an anecdote, and she related that some fruit, falling from a tree, was the accidental cause of this direction to Newton's speculations.

S–Z

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  • Un genio es alguien que descubre que la piedra que cae y la luna que no cae representan un solo y mismo fenómeno.
    • A genius is someone who discovers that the stone that falls and the moon that doesn't fall represent one and the same phenomenon.
    • Variant translation: A genius is someone who discovers that the falling stone and the moon that falls represent one and the same phenomenon.
  • Newton proposed that the particles of the air (we would call them molecules), were motionless in space and were held apart by repulsive forces between them... He assumed that the repulsive force was inversely proportional to the distance between the particles...He showed that, on the basis of this assumption, a collection of static particles in a box would behave exactly as Boyle had found. His model led directly to Boyle's law. Probably the greatest scientist ever, Newton managed to get the right answer from a model that was wrong in every possible way.
    • Brian L. Silver, The Ascent of Science (1998)
  • The weight of a smallish apple is, pleasingly, about 1 newton, or 1 N. ...Newton probably weighed about 700 newtons.
    • Brian L. Silver, The Ascent of Science (1998)
  • The view of space that exists independent of any relationship is called the absolute view. It was Newton's view, but it has been definitely repudiated by the experiments that have verified Einstein's theory of general relativity. ...There are unfortunately not a few good professional physicists who still think about the world as if space and time had an absolute meaning.
  • Despite Newton's belated appreciation of Euclid's geometry, he set it aside as an undergraduate and immediately turned to Descartes' Geometrie, a much more difficult text. Newton read a few pages... and immediately got stuck. ...The second time through, he progressed a page or two further before running into more difficulties. Again, he read it from the beginning, this time getting further still. He continued this process until he mastered Descartes' text. Had Newton mastered Euclid first, Descartes' analytic geometry would have been much easier to understand. Newton later advised others not to make the same mistake.
    But Descartes had ignited Newton's interest in mathematics, an interest that bordered on obsession.
    • Mitch Stokes, Isaac Newton (2010)
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Stukeley's description of Newton's apple (1752) p. 15, Memoirs...
  • After dinner, the weather being warm, we went into the garden, & drank tea under the shade of some apple trees; only he & myself. Amidst other discourse, he told me, he was just in the same situation, as when formerly, the notion of gravitation came into his mind. "Why should that apple always descend perpendicularly to the ground," thought he to him self; occasion'd by the fall of an apple, as he sat in a contemplative mood. "Why should it not go sideways, or upwards? but constantly to the earths centre? Assuredly, the reason is, that the earth draws it. There must be a drawing power in matter. The sum of the drawing power in the matter must be in the earth's center, not in any side of the earth. Therefore does this apple fall perpendicularly or toward the center. If matter thus draws matter; it must be in proportion to its quantity. Therefore the apple draws the earth, as well as the earth draws the apple."
  • By analyzing the measurements of Tycho Brahe, Johannes Kepler established that planetary motions weren't circles but ellipses... Through his telescopes, Galileo saw that the Sun had its perfection tarnished by ugly black spots. And the Moon wasn't a perfect sphere but looked like a place, complete with mountains and giant craters. So why didn't it fall down?
    Isaac Newton finally answered... by exploring... [a radical] idea... that heavenly objects obey the same laws as objects here on Earth. ...Newton ...realized that ...the fate of a horizontally fired cannon ball depends on its speed: it crashes to the ground only if its speed is below some magic value. ...[W]ith ever higher speeds, they'll travel farther ...before landing ...until ...they keep their height over the ground ...constant and never land, merely orbiting ...just like the Moon! Since he knew the strength of gravity near the Earth's surface... he was able to calculate the magic speed... 7.9 kilometers per second. Assuming the Moon... was obeying the same laws... he could similarly predict what speed it needed... Moreover, since the Moon took one month to travel around a circle whose circumference Aristarchos had figured out, Newton already knew its speed... Now he made a remarkable discovery: if he assumed that the force of gravity weakened like the inverse square... then this magical speed that would give the Moon a circular orbit exactly matched its measured speed! He had discovered the law of gravity... applying not merely here on Earth, but in the heavens as well. ...People boldly extrapolated not only to the macrocosmos... but also to the microcosmos, finding that many properties... could be explained by applying Newton's laws of motion to... atoms... The scientific revolution had begun.
    • Max Tegmark, Our Mathematical Universe (2014) pp. 36-38.
  • Newton did not show the cause of the apple falling, but he shewed a similitude between the apple and the stars. By doing so he turned old facts into new knowledge; and was well content if he could bring diverse phenomenon under "two or three Principles of Motion" even "though the Causes of these Principles were not yet discovered."
  • The mechanical philosophy is a case of being victimized by metaphor. I choose Descartes and Newton as excellent examples of metaphysicians of mechanism malgré eux, that is to say, as unconscious victims of the metaphor of the great machine. Together they have founded a church, more powerful than that founded by Peter and Paul, whose dogmas are now so entrenched that anyone who tries to reallocate the facts is guilty of more than heresy.
  • When he [Newton] uttered his Hypotheses non fingo he was saying in a very abbreviated, and hence cryptic way: In induction, I do not invent hypotheses, and in deduction I do not demonstrate from them. More fully, he meant that the inductive side of scientific method has a beginning, a middle, and an end and all must be complete before any deductive system is set up. The beginning consists in '"hinting several things" or making "conjectures" about the causes of phenomena...because they are "plausible consequences" drawn from the facts...they are not derived, like Descartes' conclusions, merely by the Light of Reason or intuition. Although hypothetical in character, Newton did not call them "hypotheses". The middle consists of examining these "hints" and improving them by observations and the tests of experiment. The end is defined by his remark: "and if no exception occur from phenomena, the conclusion may be pronounced generally" and considered "proved" as a "general law of nature". "Afterwards,", the deduction proceeds by assuming the conclusions established as principles, and from them demonstrating the phenomena...The peculiar character of this method, the stress upon experience and the rejection of hypotheses of the Cartesian kind, may be briefly described in Berkeley's words: "It is one thing to arrive at general laws of nature from a contemplation of of the phenomena, and another to frame an hypothesis, and from thence deduce the phenomena (S, 229).
  • The reader will recollect that we are here speaking of the Principia as a mechanical treatise only... As a work on dynamics, its merit is, that it contains a wonderful store of refined and beautiful mathematical artifices, applied to solve all the most general problems which the subject offered. It can hardly be said to contain any new inductive discovery respecting the principles of mechanics; for though Newton's "Axioms or Laws of Motion," which stand at the beginning of the book, are a much clearer and more general statement of the grounds of mechanics than had yet appeared, it can hardly be said that they contain any doctrines which had not been previously stated or taken for granted by other mathematicians.
  • Such, then, is the great Newtonian induction of universal gravitation, and such its history. It is indisputably and incomparably the greatest scientific discovery ever made, whether we look at the advance which it involved, the extent of the truth disclosed, or the fundamental and satisfactory nature of this truth.
  • Due to the genius and labours of Newton almost all the problems presented by the motions of the planets had been mastered. Newton had shown for all time that these motions could be completely accounted for if it were assumed that the same laws of nature, and in particular gravity, operated in the celestial realm as well as in the terrestrial. Although the old Aristotelian distinction between the corrupt earth and the incorruptible heavens was thus finally abandoned, the stellar realm still lay beyond the range of scientific investigation. The natural step, taken by Digges and Bruno, of likening the stars to the sun and scattering them throughout space was still only a step of the imagination.
  • During the Middle Ages the universe was regarded as finite, with the earth at its centre. The idea was abandoned during the Scientific Renaissance, and the universe came to be pictured as an indefinitely large number of stars scattered throughout infinite Euclidean space. This conception appeared to be a necessary consequence of the theory of gravitation; for, as Newton pointed out, a finite material universe in infinite space would tend to concentrate in one massive lump.
    • Gerald James Whitrow, The Structure of the Universe: An Introduction to Cosmology (1949)
  • It is one of the most intriguing facts in the history of science that the two most influential theories concerning the stars—Newton's theory of gravitation and Eddington's theory of stellar construction—were each developed so successfully although Newton was ignorant of the origin of gravitation and Eddington of the origin of stellar energy.
  • He was unhappy with the relativity of motion, even though it is a consequence of his equations, and to escape it he postulated the existence of "absolute" space, with respect to which true rest and motion are defined.
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Silent face, the marble index of a mind for ever voyaging through strange seas of Thought, alone. ~ William Wordsworth
  • And from my pillow, looking forth by light
    Of moon or favouring stars, I could behold
    The antechapel where the statue stood
    Of Newton, with his prism and silent face,
    The marble index of a mind for ever
    Voyaging through strange seas of Thought, alone.
  • Here lies
    Isaac Newton, Knight,
    Who, by a Vigour of Mind almost supernatural,
    First demonstrated
    The Motions and Figures of the Planets,
    The Paths of the Comets, and the Tides of the Ocean.
    He diligently investigated
    The different Refrangibilities of the Rays of Light,
    And the Properties of the Colours to which they give rise.
    An assiduous, sagacious, and faithful Interpreter
    Of Nature, Antiquity, and the Holy Scriptures,
    He asserted his Philosophy of the Majesty of God,
    And exhibited in his conduct the Simplicity of the Gospel.
    Let mortals rejoice
    That there has existed such and so great
    An Ornament of Human Nature    .

See also

[edit]
Philosophy of science
Concepts Analysis • A priori and a posteriori • Causality • Demarcation problem • Fact • Inductive reasoning • Inquiry • Nature • Objectivity • Observation • Paradigm • Problem of induction • Scientific method • Scientific revolution • Scientific theory •
Related topics Alchemy • Epistemology • History of science • Logic • Metaphysics • Pseudoscience • Relationship between religion and science • Sociology of scientific knowledge
Philosophers of science Plato • Aristotle • Stoicism
Averroes • Avicenna • Roger Bacon • William of Ockham
Francis Bacon • Thomas Hobbes • René Descartes • Galileo Galilei • Pierre Gassendi • Isaac Newton • David Hume
Immanuel Kant • Friedrich Schelling • William Whewell • Auguste Comte • John Stuart Mill • Herbert Spencer • Wilhelm Wundt • Charles Sanders Peirce • Henri Poincaré • Pierre Duhem • Rudolf Steiner • Karl Pearson
Alfred North Whitehead • Bertrand Russell • Albert Einstein • Otto Neurath • C. D. Broad • Michael Polanyi • Hans Reichenbach • Rudolf Carnap • Karl Popper • W. V. O. Quine • Thomas Kuhn • Imre Lakatos • Paul Feyerabend • Jürgen Habermas • Ian Hacking • Bas van Fraassen • Larry Laudan • Daniel Dennett
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