Philosophiae Naturalis Principia Mathematica. L., 1687; latest edition - L., 1990; rus. lane Academician A. N. Krylov: P., 1915-1916) is the main work of I. Newton, the year of publication of which is considered the year of birth of modern European science. In this work, new definitions of motion, matter, space, time, and force are put forward as the foundations (“principles”, “beginnings”) of scientific knowledge. The entire system is so-called. classical physics appears as the conclusion of all possible consequences from these foundations.

Based on the works of Galileo, Descartes and others, Newton abandons the interpretation of motion given by Aristotle and interprets it not as the process of “returning” the body to its “natural place,” but as a state equivalent in meaning to the state of rest. In this case, the movement is given not an integral (from one point to another), but a differential (at each point) meaning. Time is understood as absolute duration, and space as absolute emptiness. The last definition, from which the principle of long-range action follows, caused fierce disputes between Newton and his contemporaries - Rahn, Hooke, Huygens and others. However, Newton, focusing not on the collision of bodies, but on the interaction of forces, did not need the idea of direct contact, this was the true content of the new dynamics. The work also provides a formulation of the three basic laws of motion and reveals the meaning of dynamics as universal system interactions of atomic forces. The force of inertia is given especially important; it is innate to matter, but we receive information about it only from its manifestations, i.e., based on the interaction of various forces. One of the goals of Principia is to prove the law of universal gravitation, greatest discovery Newton. Newton refuses to clarify the nature of gravity (as well as the nature of inertia), believing that the fact of its existence is sufficient, on the basis of calculations of which “all the phenomena of celestial bodies and the sea” can be explained. “The Principia” had a huge impact on all subsequent development of theoretical science and remained its unshakable foundation for almost two centuries until the discovery of A. Einstein; their laws and formulations are still true for the world of macro-objects and low speeds. The method of principles developed here largely influenced the formation and development of the methodology of science in the 17th and 18th centuries.

The pinnacle of Newton's scientific creativity was precisely this work, after the publication of which he largely moved away from scientific works. The greatness of the author’s plan, which subjected the system of the world to mathematical analysis, and the depth and rigor of the presentation amazed his contemporaries /2/.

Newton's preface (there is also a preface by Cotes, his student) casually sketches out the program mechanical physics: “We propose this work as the mathematical foundations of physics. The whole difficulty of physics, as will be seen, is to recognize the forces of nature from the phenomena of motion, and then to explain other phenomena using these forces (thus, in books 1 and 2, the law of action of central forces is derived from observable phenomena, and in the third, the found law is applied to the description of the world system). It would be desirable to deduce from the principles of mechanics the rest of the phenomena of nature, reasoning in a similar way, for much makes me assume that all these phenomena are determined by certain forces with which the particles of bodies, due to reasons as yet unknown, either tend to each other and interlock in regular figures, or they mutually repel and move away from each other.”

“Principles...” begin with the “Definitions” section, where definitions of the amount of matter, inertial mass, centripetal force and some others are given. This section concludes with a “Teaching,” where the definition of space, time, place, and movement is given. Next comes the section on the axioms of motion, where Newton’s famous 3 laws of mechanics, the laws of motion and the immediate consequences of them are given. Thus, we observe a certain imitation of Euclid’s “Principles...”.

Next, “Beginnings...” is divided into 3 books. The first book is devoted to the theory of gravity and movement in the field of central forces, the second - to the doctrine of environmental resistance. In the third book, Newton outlined the established laws of motion of the planets, the Moon, the satellites of Jupiter and Saturn, gave a dynamic interpretation of the laws, outlined the “method of fluxions,” and showed that the force that attracts a stone to the Earth is no different in nature from the force that keeps the Moon in orbit , and the weakening of attraction is associated only with an increase in distance.

Thanks to Newton, the Universe began to be perceived as a well-oiled clockwork mechanism. The regularity and simplicity of the basic principles that explained all observed phenomena were regarded by Newton as proof of the existence of God: “Such a most graceful conjunction of the Sun, planets and comets could not have happened except by the intention and in the power of a wise and powerful being. This one rules everything not as the soul of the world, but as the ruler of the Universe, and according to his dominion he should be called the Lord God Almighty.”

History of writing

The history of the creation of this work, the most famous in the history of science along with Euclid's Elements, begins in 1682, when the passage of Halley's comet caused a rise in interest in celestial mechanics. Edmond Halley then tried to persuade Newton to publish his “general theory of motion.” Newton refused. He was generally reluctant to be distracted from his research for the painstaking task of publishing scientific works.

In August 1684, Halley came to Cambridge and told Newton that he, Wren and Hooke had discussed how to derive the ellipticity of the orbits of planets from the formula for the law of gravitation, but did not know how to approach the solution. Newton reported that he already had such a proof, and soon sent it to Halley. He immediately appreciated the significance of the result and the method, in November he visited Newton again and this time managed to persuade him to publish his discoveries.

On December 10, 1684, a historical entry appeared in the minutes of the Royal Society:

Mr. Halley... recently saw Mr. Newton in Cambridge, and he showed him an interesting treatise "De motu" [On Motion]. According to the wishes of Mr. Halley, Newton promised to send the said treatise to the Society.

The publication was supposed to be carried out with funds from the Royal Society, but at the beginning of 1686 the Society published a treatise on the history of fish that was not in demand, and thereby depleted its budget. Then Halley announced that he would bear the costs of publication himself. The Society gratefully accepted this generous offer and, as partial compensation, provided Halley with 50 free copies of a treatise on the history of fishes.

Newton's work - perhaps by analogy with the "Principles of Philosophy" ( Principia Philosophiae) Descartes - received the name “Mathematical principles of natural philosophy”, that is, on modern language, "Mathematical foundations of physics".

On April 28, 1686, the first volume of "Mathematical Principles" was presented to the Royal Society. All three volumes, after some editing by the author, were published in 1687. The circulation (about 300 copies) was sold out in 4 years - very quickly for that time. Two copies of this rare edition are kept in Russia; one of them was presented by the Royal Society during the war years (1943) to the USSR Academy of Sciences to celebrate Newton's 300th anniversary. During Newton's lifetime the book went through three editions; With each reissue, Newton made significant additions, improvements and clarifications to the text.

Summary of the work

Both the physical and mathematical level of Newton's work are incomparable with the work of his predecessors. It completely (with the exception of philosophical digressions) lacks Aristotelian or Cartesian metaphysics, with its vague reasoning and vaguely formulated, often far-fetched “first causes” natural phenomena. Newton, for example, does not proclaim that the law of gravity operates in nature, he strictly proves this fact, based on the observed picture of the motion of the planets: from Kepler's first two laws, he deduces that the motion of the planets is controlled by a central force, and from the third law - that attraction is inversely proportional to the square of the distance.

First book

In the first chapter (chapters in the work are called departments) Newton defines basic concepts- mass, force, inertia (“innate force of matter”), momentum, etc. The absoluteness of space and time is postulated, the measure of which does not depend on the position and speed of the observer. Based on these clearly defined concepts, the three laws of Newtonian mechanics are formulated. First given general equations movement, moreover, if Aristotle’s physics argued that the speed of a body depends on driving force, then Newton makes a significant correction: not speed, but acceleration.

Further in Book I, motion in the field of an arbitrary central force is examined in detail. Newton's law of attraction is formulated (with reference to Wren, Hooke and Halley), a strict derivation of all Kepler's laws is given, and hyperbolic and parabolic orbits unknown to Kepler are also described. Newton presented Kepler's third law in a generalized form, taking into account the masses of both bodies.

Chapter X contains the theory of oscillations different types pendulums, including spherical and cycloidal. Next, the attraction of extended (no longer point-like) bodies of spherical or other shapes is examined in detail.

The methods of proof, with rare exceptions, are purely geometric; differential and integral calculus are not explicitly used (probably so as not to multiply the number of critics), although the concepts of limit (“last ratio”) and infinitesimal, with an estimate of the order of smallness, are used in many places.

Second book

Book II is actually devoted to hydromechanics, that is, the movement of bodies on Earth taking into account the resistance of the environment. For example, the oscillations of a pendulum in a resisting medium are studied. Here, in one place (Section II), Newton, as an exception, uses an analytical approach to prove several theorems and proclaims his priority in the discovery of the “method of fluxions” (differential calculus):

In letters which about ten years ago I exchanged with the very skilful mathematician Mr. Leibniz, I informed him that I had a method for determining maxima and minima, drawing tangents and solving similar questions, equally applicable to both rational and rational terms. for irrational ones, and I hid the method by rearranging the letters of the following sentence: “when given an equation containing any number of current quantities, find the fluxions and vice versa.” The most famous man answered me that he also attacked such a method and told me his method, which turned out to be barely different from mine, and then only in terms and outline of formulas.

Third book

Book 3 - world system, mainly celestial mechanics, as well as tidal theory. At the beginning of the book, Newton formulates his version of Occam's razor:

One should not accept in nature other causes than those that are true and sufficient to explain phenomena... Nature does nothing in vain, and it would be in vain for many to do what can be done by fewer. Nature is simple and does not luxury with unnecessary reasons.

This law is then used to describe the motion of planets. The theory of the movement of the Moon and comets and the physical causes of tides are also described in detail. A method is given for determining the mass of the planet, and the mass of the Moon is found from the height of the tides. Explained (with the help of perturbation theory) the anticipation of the equinoxes and irregularities (discrepancies) in the movement of the Moon - both known in antiquity and 7 later established (Tycho Brahe, Flamsteed).

Criticism

The publication of Principia, which laid the foundation for theoretical physics, caused a huge resonance in the scientific world. Along with enthusiastic responses, there were, however, sharp objections, including from famous scientists. Carthusians in Europe attacked her with fierce criticism. The three laws of mechanics did not raise any special objections; the concept of gravity was mainly criticized - a property of an incomprehensible nature, with an unclear source, which acted without a material carrier, through completely empty space. Leibniz, Huygens, Jacob Bernoulli, Cassini rejected gravity and continued to try to explain the motion of the planets by Cartesian vortices or in some other way.

From the correspondence between Leibniz and Huygens:

Leibniz: I don't understand how Newton imagines gravity or attraction. Apparently, in his opinion, this is nothing more than some inexplicable intangible quality.
Huygens: As for the reason for the tides that Newton gives, it does not satisfy me, like all his other theories based on the principle of attraction, which seems ridiculous and absurd to me.

Newton himself preferred not to speak publicly about the nature of gravity, since he had no experimental arguments in favor of the ethereal or other hypothesis, and he did not like to start empty squabbles. Newton confidently rejected the connection between gravity and magnetism suspected by a number of physicists, since the properties of these two phenomena are completely different. In personal correspondence, Newton also admitted the supernatural nature of gravity:

It is incomprehensible that inanimate gross matter could, without the mediation of something immaterial, act and influence other matter without mutual contact, as this should happen if gravity in the sense of Epicurus were essential and innate in matter. To assume that gravity is an essential, inextricable and innate property of matter, so that a body can act on another at any distance in empty space, without the mediation of anything transmitting action and force, this, in my opinion, is such an absurdity that it is inconceivable for anyone. someone who has a sufficient understanding of philosophical subjects.
Gravity must be caused by an agent constantly acting according to certain laws. Whether, however, this agent is material or immaterial, I have left it to my readers to decide.
(From Newton's letter dated February 25, 1693 to Dr. Bentley, author of lectures on the topic "Refutation of Atheism")

Sir Isaac Newton was with me and said that he had prepared 7 pages of additions to his book on light and colors [that is, "Optics"], in a new Latin edition... He had doubts whether he could express the last question like this: " What fills the space free from bodies?” The complete truth is that he believes in the omnipresent Deity in the literal sense. Just as we feel objects when their images reach the brain, so God must feel every thing, always being present with it.
He believes that God is present in space, both free from bodies and where bodies are present. But, considering that such a formulation is too crude, he thinks of writing it like this: “What cause did the ancients attribute to gravity?” He thinks that the ancients considered God to be the cause, and not any body, for every body is already heavy in itself.

Critics also pointed out that the theory of planetary motion based on the law of gravity is insufficiently accurate, especially for the Moon and Mars. Direct measurement of the force of gravity in terrestrial conditions was carried out in 1798 by G. Cavendish using extremely sensitive torsion balances; These experiments completely confirmed Newton's theory.

Place in the history of science

Newton's book was the first work on new physics and at the same time one of the last serious works using old methods mathematical research. All Newton's followers have already used powerful methods mathematical analysis. Throughout the 18th century, analytical celestial mechanics developed intensively, and over time, all the mentioned discrepancies were fully explained by the mutual influence of the planets (Lagrange, Clairaut, Euler and Laplace).

From that moment until the beginning of the 20th century, all Newton's laws were considered immutable. Physicists gradually got used to long-range action, and even tried to attribute it, by analogy, to the electromagnetic field (before the advent of Maxwell's equations). The nature of gravity was revealed only with the advent of Einstein's work on General Relativity, when long-range action finally disappeared from physics.

An asteroid named after Newton's Principia

100 Great Books Demin Valery Nikitich

27. NEWTON “MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY”

27. NEWTON

"MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY"

Newton's book is an unparalleled and unattainable pinnacle of theoretical thought. There has never been anything like this in the history of science. The conclusions formulated in it were the fundamental basis for both the industrial revolution and the scientific, technical and space revolutions that followed it. Machine tools and mechanisms operate “according to Newton,” vehicles move, planes and rockets fly. The Universe itself is structured according to Newton: the laws of gravity determine the well-predictable movement of celestial bodies and objects - planets, stars, meteors, comets.

Actually, the comet, oddly enough, was the reason for writing “Principles” (more precisely, for organizing into a coherent book those ideas that had long occupied the scientist). Halley's Comet, named after the author who studied and thoroughly explained its movement more deeply than others, was what forced Newton to turn the heap (no, a whole mountain) of sheets of paper lying everywhere in his office into one of the unsurpassed masterpieces of scientific thought. The memories of contemporaries miraculously preserved evidence of how this happened.

Edmond Halley, a famous and meticulous astronomer, could not understand in any way the trajectory along which the comet he observed was moving (not to mention the laws governing this movement). He shared his doubts with Newton. He struck him like a thunderbolt with his answer: “I have known this for a long time. The trajectory is an ellipse. The calculations are somewhere among my papers.” It was not possible to find the required sheet of paper in the piles of drafts. And Newton had to write everything again. His absent-mindedness knew no bounds: one day, deep in thought, he dipped his watch into boiling water instead of the egg he intended to boil.

But after a conversation with Halley, Newton dropped everything and sat down to the book. A year and a half of hard work - and humanity was enriched with a creation, the perfection and evidence of which is comparable only with another scientific treatise with a similar name - with Euclid’s “Elements”. This happened a little more than three centuries ago - in 1687. Enormous mental stress led the author to a nervous breakdown; fortunately, it soon passed. In the title of Newton’s work, the word “philosophy” is not an empty phrase: the Universe was not just described, but also comprehended. Although the motto of the great scientist was the famous slogan “I do not invent hypotheses!”, his main work is an example of how to approach the explanation of known and unknown natural phenomena:

The whole difficulty of physics, as will be seen, consists in recognizing the forces of nature from the phenomena of motion, and then using these forces to explain other phenomena. The general proposals set forth in books one and two are intended for this purpose. In the third book we give an example of the above-mentioned application, explaining the system of the world, for here from celestial phenomena, with the help of propositions proven in previous books, the gravitational forces of bodies towards the Sun and individual planets are mathematically deduced. Then, from these forces, also with the help of mathematical propositions, the movements of planets, comets, the Moon and the sea are deduced. It would be desirable to deduce from the principles of mechanics the rest of the phenomena of nature, reasoning in a similar way, for many things force me to assume that all these phenomena are determined by certain forces with which the particles of bodies, due to reasons as yet unknown, either tend to each other and interlock into regular figures, or mutually repel each other. Since these forces are unknown, until now the attempts of philosophers to explain natural phenomena have remained fruitless. I hope, however, that either this method of reasoning, or another, more correct one, will be given some illumination by the reasons presented here.

Newton expresses himself extremely delicately and modestly, although he knew the true value of his discoveries. It was hardly a secret for the scientist that his “Principles” were ahead of his era and at the same time set the direction of science for many centuries to come. Soon this became clear to anyone and everyone. Newton's theory, not without reason, was compared with the act of divine creation in the Bible, using the terminology of Holy Scripture:

This world was shrouded in deep darkness.

Let there be light! And then Newton appeared.

Indeed, “Principia” cannot be called anything other than the Bible of classical mechanics. Here are formulated the basic concepts that to this day adorn any physics textbook. Here, for the first time, clear formulations of the laws of motion (Newton’s famous laws) are given:

Law 1. Every body continues to be maintained in its state of rest or uniform and rectilinear movement, until and as long as it is not forced by applied forces to change this state.

Law II. The change in momentum is proportional to the applied driving force and occurs in the direction of the straight line along which this force acts.

Law III. An action always has an equal and opposite reaction, otherwise the interactions of two bodies on each other are equal and directed in opposite directions.

And there was also the Law of Universal Gravitation. And there was worldwide fame and triumph for the book, originally published in only 250 copies. The author was known as unsociable and a misanthrope, although he corresponded with almost all the famous learned men of Europe. He was distinguished by a difficult and quarrelsome character, was wary of women and did not tolerate competitors. But his services to world science are so great that all this seems insignificant compared to the invaluable contribution made to world civilization. All is forgiven to a genius!

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Mr. Halley... recently saw Mr. Newton in Cambridge, and he showed him an interesting treatise "De motu" [On Motion]. According to the wishes of Mr. Halley, Newton promised to send the said treatise to the Society.

Newton's work - perhaps by analogy with the "Principles of Philosophy" ( Principia Philosophiae) Descartes - was called “Mathematical principles of natural philosophy”, that is, in modern language, “Mathematical foundations of physics”.

In the first chapter, Newton defines the basic concepts - mass, force, inertia (“innate force of matter”), momentum, etc. The absoluteness of space and time is postulated, the measure of which does not depend on the position and speed of the observer. Based on these clearly defined concepts, the three laws of Newtonian mechanics are formulated. For the first time, general equations of motion were given, and if Aristotle’s physics argued that the speed of a body depends on the driving force, then Newton makes a significant correction: not speed, but acceleration.

Page of Newton's Principia with the axioms of mechanics

A page from Newton's Principia

Book 2 is devoted to the movement of bodies on Earth, taking into account the resistance of the environment. Here, in one place (Section II), Newton, as an exception, uses an analytical approach to prove several theorems and proclaims his priority in the discovery of the “method of fluxions” (differential calculus):

In letters which about ten years ago I exchanged with the very skilful mathematician Mr. Leibniz, I informed him that I had a method for determining maxima and minima, drawing tangents and solving similar questions, equally applicable to both rational and rational terms. for irrational ones, and I hid the method by rearranging the letters of the following sentence: “when given an equation containing any number of current quantities, find the fluxions and vice versa.” The most famous man answered me that he also attacked such a method and told me his method, which turned out to be barely different from mine, and then only in terms and outline of formulas.

Book 3 - world system, mainly celestial mechanics, as well as tidal theory. Newton formulates his version of Occam's razor:

One should not accept in nature other causes than those that are true and sufficient to explain phenomena... Nature does nothing in vain, and it would be in vain for many to do what can be done by fewer. Nature is simple and does not luxury with unnecessary reasons.

In accordance with his method, Newton deduces the law of gravity from experimental data on the planets, the Moon and other satellites. To verify that gravity (weight) is proportional to mass, Newton conducted several fairly accurate experiments with pendulums. The theory of the motion of the Moon and comets is presented in detail. Explained (with the help of perturbation theory) the anticipation of the equinoxes and irregularities (discrepancies) in the movement of the Moon - both known in antiquity and 7 later established (Tycho Brahe, Flamsteed). A method is given for determining the mass of the planet, and the mass of the Moon is found from the height of the tides.

Criticism

From the correspondence between Leibniz and Huygens:

Leibniz: I don't understand how Newton imagines gravity or attraction. Apparently, in his opinion, this is nothing more than some inexplicable intangible quality.
Huygens: As for the reason for the tides that Newton gives, it does not satisfy me, like all his other theories based on the principle of attraction, which seems ridiculous and absurd to me.

It is incomprehensible that inanimate crude matter could, without the mediation of something immaterial, act and influence other matter without mutual contact, as this should happen if gravity in the sense of Epicurus were essential and innate in matter. To suppose that gravitation is an essential, inextricable and innate property of matter, so that a body can act on another at any distance in empty space, without the mediation of anything transmitting action and force, this, in my opinion, is such an absurdity that it is inconceivable to anyone. someone who has a sufficient understanding of philosophical subjects. Gravity must be caused by an agent constantly acting according to certain laws. Whether, however, this agent is material or immaterial, I have left it to my readers to decide.
(From Newton's letter dated February 25, 1693 to Dr. Bentley, author of lectures on the topic "Refutation of Atheism")

Sir Isaac Newton was with me and said that he had prepared 7 pages of additions to his book on light and colors [that is, "Optics"], in a new Latin edition... He had doubts whether he could express the last question like this: " What fills the space free from bodies?” The complete truth is that he believes in the omnipresent Deity in the literal sense. Just as we feel objects when their images reach the brain, so God must feel every thing, always being present with it. He believes that God is present in space, both free from bodies and where bodies are present. But, considering that such a formulation is too crude, he thinks of writing it like this: “What cause did the ancients attribute to gravity?” He thinks that the ancients considered God to be the cause, and not any body, for every body is already heavy in itself.

Critics also pointed out that the theory of planetary motion based on the law of gravity is insufficiently accurate, especially for the Moon and Mars.

Place in the history of science

Newton's book was the first work on new physics and at the same time one of the last serious works using old methods of mathematical research. All of Newton's followers already used powerful methods of mathematical analysis. Throughout the 18th century, analytical celestial mechanics developed intensively, and over time, all the mentioned discrepancies were fully explained by the mutual influence of the planets (Lagrange, Clairaut, Euler and Laplace).

Asteroid 2653 Principia (1964) is named after Newton's Principia.

Translations into Russian

Isaac Newton. Mathematical principles of natural philosophy. Translation from Latin and notes by A. N. Krylov. M.: Nauka, 1989. 688 pp. ISBN 5-02-000747-1. Series: Classics of Science.
- Text on math.ru on mccme.ru

Notes

Literature

Antropova V. I. On the geometric method of I. Newton’s “Mathematical Principles of Natural Philosophy” // Historical and mathematical research. - M.: Science, 1966. - No. 17. - P. 205-228.
Bell E.T. Creators of Mathematics. - M.: Education, 1979. - 256 p.
Vavilov S. I. Isaac Newton . - 2nd add. ed.. - M.-L.: Publishing house. USSR Academy of Sciences, 1945.
History of mathematics edited by A. P. Yushkevich in three volumes. Volume 2. Mathematics of the 17th century. M.: Science. 1970.
Kartsev V. P. Newton. - M.: Young Guard, 1987. - (ZhZL).
Kudryavtsev P. S. Course on the history of physics. - M.: Education, 1974.
Spassky B.I. History of Physics. - Ed. 2nd. - M.: graduate School, 1977. - T. 1.

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- “MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY” (Philosophiae Naturalis Principia Mathematica. L., 1687; latest edition L., 1990; Russian translation by academician A. N. Krylov: P., 1915 1916) the main work of I. Newton, year of publication which... ... Philosophical Encyclopedia