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Home > Dictionary of Science Quotations > Scientist Names Index N > Sir Isaac Newton Quotes > Proportion

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Sir Isaac Newton
(25 Dec 1642 - 20 Mar 1727)

English physicist and mathematician who made seminal discoveries in several areas of science, and was the leading scientist of his era.



And thus Nature will be very conformable to her self and very simple, performing all the great Motions of the heavenly Bodies by the Attraction of Gravity which intercedes those Bodies, and almost all the small ones of their Particles by some other attractive and repelling Powers which intercede the Particles. The Vis inertiae is a passive Principle by which Bodies persist in their Motion or Rest, receive Motion in proportion to the Force impressing it, and resist as much as they are resisted. By this Principle alone there never could have been any Motion in the World. Some other Principle was necessary for putting Bodies into Motion; and now they are in Motion, some other Principle is necessary for conserving the Motion.
— Sir Isaac Newton
From Opticks, (1704, 2nd ed. 1718), Book 3, Query 31, 372-3.
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Equations are Expressions of Arithmetical Computation, and properly have no place in Geometry, except as far as Quantities truly Geometrical (that is, Lines, Surfaces, Solids, and Proportions) may be said to be some equal to others. Multiplications, Divisions, and such sort of Computations, are newly received into Geometry, and that unwarily, and contrary to the first Design of this Science. For whosoever considers the Construction of a Problem by a right Line and a Circle, found out by the first Geometricians, will easily perceive that 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 Ancients did so industriously distinguish them from one another, that they never introduced Arithmetical Terms into Geometry. And the Moderns, by confounding both, have lost the Simplicity in which all the Elegance of Geometry consists. Wherefore that is Arithmetically more simple which is determined by the more simple Equation, but that is Geometrically more simple which is determined by the more simple drawing of Lines; and in Geometry, that ought to be reckoned best which is geometrically most simple.
— Sir Isaac Newton
In 'On the Linear Construction of Equations', Universal Arithmetic (1769), Vol. 2, 470.
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I use the word “attraction” here in a general sense for any endeavor whatever of bodies to approach one another, whether that endeavor occurs as a result of the action of the bodies either drawn toward one other or acting on one another by means of spirits emitted or whether it arises from the action of aether or of air or of any medium whatsoever—whether corporeal or incorporeal—in any way impelling toward one another the bodies floating therein. I use the word “impulse” in the same general sense, considering in this treatise not the species of forces and their physical qualities but their quantities and mathematical proportions, as I have explained in the definitions.
— Sir Isaac Newton
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), Book I, Section II, Scholium, 588.
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In the beginning of the year 1665 I found the Method of approximating series & the Rule for reducing any dignity of any Bionomial into such a series. The same year in May I found the method of Tangents of Gregory & Slusius, & in November had the direct method of fluxions & the next year in January had the Theory of Colours & in May following I had entrance into ye inverse method of fluxions. And the same year I began to think of gravity extending to ye orb of the Moon & (having found out how to estimate the force with wch [a] globe revolving within a sphere presses the surface of the sphere) from Keplers rule of the periodic times of the Planets being in sesquialterate proportion of their distances from the center of their Orbs, I deduced that the forces wch keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about wch they revolve: & thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, & found them answer pretty nearly. All this was in the two plague years of 1665-1666. For in those days I was in the prime of my age for invention & minded Mathematicks & Philosophy more then than at any time since.
— Sir Isaac Newton
Quoted in Richard Westfall, Never at Rest: A Biography of Isaac Newton (1980), 143.
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It seems probable to me that God, in the beginning, formed matter in solid, massy, hard, impenetrable, moveable particles, of such sizes and figures, and with such other properties, and in such proportions to space, as most conduced to the end for which He formed them; and that these primitive particles, being solids, are incomparably harder than any porous bodies compounded of them, even so very hard as never to wear or break in pieces; no ordinary power being able to divide what God had made one in the first creation.
— Sir Isaac Newton
From Opticks (1704, 2nd ed., 1718), 375-376.
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Law 2: A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.
— Sir Isaac Newton
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), Axioms, or Laws of Motion, Law 2, 416.
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Thus far I have explained the phenomena of the heavens and of our sea by the force of gravity, but I have not yet assigned a cause to gravity. Indeed, this force arises from some cause that penetrates as far as the centers of the sun and planets without any diminution of its power to act, and that acts not in proportion to the quantity of the surfaces of the particles on which it acts (as mechanical causes are wont to do) but in proportion to the quantity of solid matter, and whose action is extended everywhere to immense distances, always decreasing as the squares of the distances.
— Sir Isaac Newton
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), General Scholium, 943.
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See also:
  • 25 Dec - short biography, births, deaths and events on date of Newton's birth.
  • Isaac Newton - biography from Famous Men of Science (1889)
  • Isaac Newton - Comments on his “Playing on the Seashore” Quote
  • Isaac Newton - “Playing on the Seashore” illustrated quote - Medium 500px.
  • Isaac Newton - “Playing on the Seashore” illustrated quote - Large 800px.
  • Isaac Newton - context of quote “A change in motion” - Medium image (500 x 250 px)
  • Isaac Newton - context of quote “A change in motion” - Large image (800 x 400 px)
  • Isaac Newton - context of quote “In experimental philosophy” - Medium image (500 x 250 px)
  • Isaac Newton - context of quote “In experimental philosophy” - Large image (800 x 400 px)
  • Isaac Newton - context of quote “Standing on the shoulders of giants” - Medium image (500 x 250 px)
  • Isaac Newton - context of quote “Standing on the shoulders of giants” - Large image (800 x 400 px)
  • Isaac Newton - context of quote “Impressed force is the action” - Medium image (500 x 250 px)
  • Isaac Newton - context of quote “Impressed force is the action” - Large image (800 x 400 px)
  • Isaac Newton - context of quote “Inherent force of matter is the power of resisting…” - Medium image (500 x 250 px)
  • Isaac Newton - context of quote “Inherent force of matter is the power of resisting…” - Large image (800 x 400 px)
  • Isaac Newton - context of quote “Plato is my friend” - Medium image (500 x 250 px)
  • Isaac Newton - context of quote “Plato is my friend” - Large image (800 x 400 px)
  • Isaac Newton - context of quote “Colours which appear through the Prism ” - Medium image (500 x 250 px)
  • Isaac Newton - context of quote “Colours which appear through the Prism ” - Large image (800 x 400 px)
  • Isaac Newton - context of quote “Nature does nothing in vain” - Medium image (500 x 250 px)
  • Isaac Newton - context of quote “Nature does nothing in vain” - Large image (800 x 400 px)
  • Isaac Newton - context of quote “No more causes of natural things should be admitted” - Medium image (500 x 250 px)
  • Isaac Newton - context of quote “No more causes of natural things should be admitted” - Large image (800 x 400 px)
  • Isaac Newton - context of quote “Truth is ever to be found in simplicity” - Medium image (500 x 250 px)
  • Isaac Newton - context of quote “Truth is ever to be found in simplicity” - Large image (800 x 400 px)
  • Isaac Newton - context of quote “Every body perseveres in its state of being at rest” - Medium image (500 x 250 px)
  • Isaac Newton - context of quote “Every body perseveres in its state of being at rest” - Large image (800 x 400 px)
  • Isaac Newton - context of quote “God, in the beginning, formed matter” - Medium image (500 x 250 px)
  • Isaac Newton - context of quote “God, in the beginning, formed matter” - Large image (800 x 400 px)
  • Isaac Newton - context of quote “The cause of gravity is what I do not pretend to know” - Medium image (500 x 250 px)
  • Isaac Newton - context of quote “The cause of gravity is what I do not pretend to know” - Large image (800 x 400 px)
  • Sir Isaac Newton’s Apple-Tree - debunking the myth, from Historic Ninepins: A Book of Curiosities by John Timbs (1869)
  • Newton and the Dog - debunking the myth about Newton’s dog Diamond.
  • Booklist for Isaac Newton.

Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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