Mathematical principles of natural philosophy. Astronomy - Newton

Philosophiae Naturalis Principia Mathematica. L., 1687; latest edition - L., 1990; Russian per. Academician A. N. Krylov: P., 1915-1916) - 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, as the basis ("principles", "beginnings") scientific knowledge new definitions of motion, matter, space, time, force have been put forward. The whole system of the 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 rejects the interpretation of motion given by Aristotle and interprets it not as a process of “returning” a body to its “natural place”, but as a state equivalent in meaning to a 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 - Ren, Hooke, Huygens, etc. However, Newton, focusing not on the collision of bodies, but on the interaction of forces, did not need the idea of ​​direct contact; the true content of the new dynamics. The work also provides a formulation of three basic laws of motion and reveals the meaning of dynamics as a universal system of interaction of atomic forces. The force of inertia is especially important; it is inherent in matter, but we obtain information about it only by its manifestations, that is, on the basis of the interaction of various forces. One of the goals of the Beginnings is to prove the law of universal gravitation, greatest discovery Newton. Newton refuses to clarify the nature of gravitation (as well as the nature of inertia), believing that the fact of its existence is enough, on the basis of which calculations can be explained “all phenomena celestial bodies and the sea. " "Principles" had a tremendous 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 17-18 centuries.

Foreword (9).
Isaac Newton. Mathematical Principles of Natural Philosophy I-VI (1-662).
Alphabetical index (663).
Application
On the Russian translation of Isaac Newton's Mathematical Principles of Natural Philosophy (677).
Author Index (682).

Mathematical principles of natural philosophy (lat.Philosophiae Naturalis Principia Mathematica) is Newton's fundamental work, in which he formulated the law of universal gravitation and Newton's three laws, which laid the foundations classical mechanics.

His Mathematical Principles of Natural Philosophy (Philosophiae naturalis principia mathematica), Optics (Opticks) and De analysi are among the greatest creations of the human mind. Newton's brilliant innovative achievements in science made it possible to explain in exact mathematical language many phenomena of inanimate nature and gave rise to the hope that over time it would be possible to explain all phenomena. Relying on the known facts building a theory describing them mathematically, extracting consequences from the theory and comparing the results obtained with observational and experimental data, he for the first time tried not only to explain physical phenomena, but also to predict them. Having put an end to the confusion of the then theories of light and color, Newton explained the phenomenon of color with his experiments and anticipated modern achievements in the theory of light. The mathematical analysis he created has become one of the most versatile and powerful tools in natural science. For Newton, according to Einstein, “nature was an open book, the writing of which he could read without difficulty. in order like toys. In one person, he combined the experimenter, theorist, the master and - to no less extent - the artist of the word. He appears before us strong, confident and lonely. "

In August 1684, Halley came to Cambridge and told Newton that he and Wren and Hooke had discussed how to derive the ellipticity of the orbits of the 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 record 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 Movement]. According to the will of Mr. Halley, Newton promised to send the said treatise to the Society.

Work on Opus Magnum went on in 1684-1686. According to the recollections of Humphrey Newton, a relative of the scientist and his assistant during these years, at first Newton wrote "Beginnings" in between alchemical experiments, which he focused on, but gradually got carried away and enthusiastically devoted himself to work on the main book of his life.

The publication was supposed to be carried out with funds from the Royal Society, but in early 1686 the Society published an uncalled for treatise on the history of fish, thus draining its budget. Halley then announced that he was covering the publishing costs. The Society gratefully accepted this generous offer and, as partial compensation, provided Halley with 50 copies of a treatise on the history of fish free of charge.

Newton's work - perhaps by analogy with Descartes' "Principles of Philosophy" - was called "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 copyright correction, 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 Academy of Sciences of the USSR to celebrate the 300th anniversary of Newton. During Newton's lifetime, the book went through three editions.

Both the physical and mathematical level of Newton's work are completely 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 contrived "root causes" natural phenomena... Newton, for example, does not proclaim that the law of gravitation operates in nature; he strictly proves this fact based on the observed pattern of planetary motion. Newton's method is the creation of a model of the phenomenon, “without inventing hypotheses,” and then, if there is enough data, the search for its causes. This approach, which was initiated by Galileo, meant the end of the old physics. Mathematical apparatus and general structure Books Newton deliberately built as close as possible to the then standard of scientific rigor - "Principles" of Euclid.

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. Given for the first time general equations motion, moreover, if the physics of Aristotle argued that the speed of the body depends on driving force, then Newton makes a significant correction: not speed, but acceleration.

The author formulated Newton's laws in the following form.
- Every body continues to be held in a state of rest or uniform and straight motion, while and since it is not forced by the applied forces to change this state.
- The change in the momentum is proportional to the applied force and occurs in the direction of the straight line along which this force acts.
- Action is always equal and opposite reaction, otherwise, the interactions of two bodies against each other are equal to each other and directed in opposite directions.

The first law (the law of inertia), in a less clear-cut form, was published by Galileo. It should be noted that Galileo allowed free movement not only in a straight line, but also in a circle (apparently, for astronomical reasons). Galileo also formulated the most important principle of relativity, which Newton did not include in his axioms, because for mechanical processes this principle is a direct consequence of the equations of dynamics. In addition, Newton considered space and time as absolute concepts, the same for the entire Universe, and clearly indicated this in his "Principles".

Newton also gave strict definitions of such physical concepts as momentum (not quite clearly used by Descartes) and force. The rule of vector addition of forces is indicated. The concept of mass is introduced into physics as a measure of inertia and, at the same time, gravitational properties (earlier physicists used the concept of weight).

Later in Book I, the motion in the field of an arbitrary central force is considered in detail. The Newtonian law of attraction is formulated (with reference to Wren, Hooke and Halley), a rigorous derivation of all Kepler's laws is given, and hyperbolic and parabolic orbits unknown to Kepler are described.

Methods of proof, with rare exceptions - purely geometric, differential and integral calculus are clearly not applied (probably, in order not to multiply the number of critics), although the concepts of the limit ("last relation") and infinitesimal, with an estimate of the order of smallness, are used in many places.

Book 2 is devoted to the motion 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 I exchanged about ten years ago with a very skillful mathematician, Mr. Leibniz, I informed him that I had a method for determining the maximums and for the irrational, and I hid the method by rearranging the letters of the following sentence: "when an equation is given containing any number of current quantities, find fluxions and vice versa." The most famous husband answered me that he also attacked such a method and told me his method, which turned out to be hardly different from mine, and then only in terms and in the outline of formulas.

Book 3 is the system of the world, mainly celestial mechanics, and also the theory of tides. Newton formulates his own version of Occam's Razor:

Nature should not accept other causes beyond those that are true and sufficient to explain the phenomena ... Nature does nothing in vain, but it would be in vain to do to many what can be done less. Nature is simple and not luxurious with unnecessary reasons.

In accordance with his method, Newton deduces the law of gravitation from experimental data on the planets, the moon and other satellites. To test that the force of 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 equinoxes and irregularities (discrepancies) in the motion of the Moon - both known in antiquity and 7 later established (Tycho Brahe, Flamsteed). A method for determining the mass of the planet is given, and the mass of the Moon is found from the height of the tides.

Newton's famous apple tree

Newton I. Mathematical Principles of Natural Philosophy.
Scientific publication.
Edited by L.S. Polak.
Translation from Latin and comments by A.N. Krylov.
Foreword by L.S. Polak.
(Moscow: Nauka, 1989. - Classics of Science)

Publishing house annotation:
"Elements" by I. Newton is one of the greatest works in the history of natural science. This essay laid the foundations of mechanics, physics and astronomy, it formulated a program for the development of these areas of science, which remained decisive for more than a century and a half.
This edition is a facsimile reproduction of I. Newton's book translated from Latin and with commentary by Academician A.N. Krylov. The book also includes a subject index compiled by I. Newton and published in Russian for the first time.
The book is intended for a wide range of specialists in the field natural sciences, as well as readers interested in the history of science.

Everything that suits you, about the universe, suits
And me. Nothing too early or too early for me
late if it is timely for you. Everything,
what your watch brings, O nature, is a good fruit.
Everything is from you, everything is in you, everything is in you.
Marcus Aurelius

It is easy to do what is difficult for
others have talent; genius does what
which is beyond the power of talent.
Henri-Frederic Amiel

Build nature, its law lurked in the eternal darkness,
And God said: "Appear, Newton!" - and immediately the light
spilled.
Alexander Pope

School years make all people on our planet Newtonians. Almost with mother's milk, we absorb into our spiritual flesh the three axioms of Newton, his space and time, his law of universal gravitation and much, much more. And only then thermodynamics, statistical mechanics, the theory of elementary particles, to one degree or another, change the image of the world familiar to us - the Newtonian image, deepening, expanding, clarifying and still preserving it as a starting point, as an approximate picture of the macrocosm of human existence.

It is not without reason that Newton's "Principles", offered to our reader, caused a radical reconstruction of earthly and celestial science, mechanics, physics, cosmology, cosmogony, and were the beginning of the tremendous progress of natural science in the 17th-20th centuries. It is no coincidence that Lagrange called "Beginnings" "the greatest work of the human mind."

The discovery of the law of universal gravitation was preceded in England by a period of exciting searches, in which the greatest mathematicians, astronomers, physicists of that era participated: Hooke, the constant opponent and opponent of Newton, Halley, his enthusiastic admirer, Wren, a great architect and scientist. In 1684 the three of them meet in London and discuss the question of the motion of bodies under the influence of the force of gravity; here Hooke declares that he already has a solution, but he postpones the message about it. Time passes, and Halley notices that Mr. Hooke is "not as good as his words", and asks Newton with the question: what should be the orbit of a body moving around the center of attraction under the action of a force inversely proportional to the square of the distance? Newton immediately replies that it is, of course, an ellipse and that he has already mastered the solution of the problem since 1679. From this moment, Newton's intense work began, leading to the creation of the "Principles".

We know from the vast number of currently published manuscripts and letters of Newton that he was an extremely conscientious person and rewrote the same passage five or six times until he was completely satisfied with what was written. Nevertheless, The Beginnings is a difficult book and requires a lot of work from the reader to understand it. It is not for nothing that there is something like a historical anecdote. Cambridge students, meeting Newton, said: "Here comes a man who wrote a book in which neither he himself nor anyone else understands anything."

Knowledge of the science of that time and the works of his contemporaries can be seen from the analysis of the composition of Newton's library (he, apparently, did not acquire books that he did not read). It contains 2,100 volumes, including 169 on alchemy and chemistry, 178 on mathematics and physics, 538 on natural sciences, 477 on theology, 149 in classical antiquity. This reflects a wide range of Newton's scientific and religious interests, his deep erudition in natural science, mathematics, philosophy, theology, ancient history. In addition, it is possible to establish the sources of his methodology and views that were far from generally accepted for that time.

During the years of creating the great book for Newton, new physics and the physical picture of the world, the mathematical cognizability of the cosmos as a whole and the solvability of particular problems, the alchemical idea of ​​the unity of the micro- and macrocosm, the omnipotent creator of moving matter that exists and persists in space and time ... The reader will see all the deepest content of the "Elements", having mastered the geometric methods that Newton uses (one should not at the same time forget that Newton and Leibniz independently discovered the mathematical analysis of the infinitesimal). Here we note that much in the "Elements" is, as it were, disguised (for example, Newton owned the method of variations of arbitrary constants of elliptical motion, and the equations that Lagrange subsequently gave were apparently anticipated by Newton and applied by him to solving problems in the theory of the motion of the Moon ). He combined with his theory of gravitation what was empirically developed in the past centuries. Newton himself wrote that what he achieved, "... he owes only diligence and persistent thought."

Versatility discovered by Newton the dynamic system was a surprise to his contemporaries and it took more than a dozen years until it became the true dominant of scientific creativity in Europe.

The work, entitled "Mathematical Principles of Natural Philosophy" by the author, consists of three books. The first "On the Motion of Bodies" was completed on April 28, 1686, and on the same day it was presented to the Royal Society of London. Then the second book was written, bearing the same name, and, finally, the third "On the system of the world", in the creation of which Newton was very afraid of delays on the part of "the impudent and vexatious lady of philosophy" (in the then sense of the word). However, everything worked out (however, not without help, according to Newton, "the wittiest and in all areas of the learned husband of E. Halley"). In the middle of the summer of 1687, Principles were published.

It is not by chance that Newton called his great work "Mathematical Principles". Mathematics for him was the main tool in physical research. The exposition in "Beginnings" is carried out by the geometric method, the translation of which into the language mathematical analysis(discovered at the same time by Newton and Leibniz) is realized with the preservation of the ideological structure of the "Elements" and with the strengthening of their heuristic activity already in the 18th century.

But Newton never, as the reader will see, lost touch with experiment, and this is his strength. His amazing art in setting up experiments laid the foundations for experimental research of the modern type - let the reader cast a glance not only at the Beginnings, but also at Newton's Optics and even at his enormous alchemical works.

The great work of Newton, who created an entire epoch in the development of natural science, and the revolution made by him, should not be regarded as the result of the linear development of earlier ideas. If he had predecessors in the development and application of the first two axioms of motion, then the third law completely belongs to Newton; so far no one has been able to indicate them. But without the third law of dynamics, the grandiose picture of the universe, drawn in the "Elements" and representing the triumph of Newton's new universality, which united earthly and celestial mechanics, would not be complete.

As you know, Newton formulated the law of gravitation (the inverse square law), which determines the motion of celestial bodies in classical space, before he wrote "Beginnings", having successfully applied it to the analysis of attraction between the Sun and the planets. However, only according to its third law, gravity could no longer be considered as some kind of isolated property inherent in the central body of the solar system. It should be inherent in the Moon, every planet, comet and star in the Universe - a thought that is probably one of the deepest that ever came to the human mind.

Voltaire in his "Philosophical Letters", work on which he began in late 1727 - early 1728, while in England, and completed, returning to his homeland at the end of 1732, was the first on the continent of Europe to extol both Newton himself and Newtonianism. The French Judicial Chamber ("Parliament") immediately condemned this book to be burned as a book "seductive, contrary to religion, good morals and respect for the authorities."

In it, in particular, Voltaire writes: "... the greatest was Isaac Newton; ... for if true greatness consists in receiving a powerful talent from heaven and using it for self-education and enlightenment of others, then a person like Mr. Newton, barely seen once in ten centuries, is really great, while all ... politicians and conquerors, without whom not a single century has been, are usually nothing more than eminent villains. we honor those who control their minds with the power of their truth, but not those who create slaves by violence; those who have cognized the Universe, and not those who disfigured it. "

Newtonian science still occupies special place- many of the values, concepts and laws formulated in it are used to this day, are elements of the modern scientific picture of the world and serve as the basis for the development of numerous technologies, having withstood the transformations and changes that have occurred in natural science since the time of Newton.

Of course, since the creation of Principia, the formulation of classical dynamics after the works of Euler, Lagrange, Hamilton, Poincaré and other scientists has undergone significant changes. She became clearer, enriched. In addition, they have undergone a critical revision and detailed analysis of the limits of its applicability (theory of relativity, quanta, black holes, etc.).

In conclusion, it is necessary to emphasize the truly innumerable confirmations of the provisions developed by Newton in the "Principles". Over the past decades, they have received a decisive "cosmic" proof: it is enough to recall the precision experiments set up with the help of artificial earth satellites and which confirmed Newton's equations with high accuracy. The world is one: "Nature is very in agreement and is similar in itself."

The present, third edition of the translation of "Elements" into Russian (the first two have long become a bibliographic rarity) is supposed to consist of two parts. The first is a facsimile edition of the translation made by A.N. Krylov and provided with his notes. The translation was published in 1936. in the form of t. VII of his "Works". There is also a subject index attached to the third (last lifetime) edition of Newton's book; the index has not previously been translated into Russian. In addition, the publication includes a note on the history of translation of the "Elements" into Russian and a personal index.

The second part will contain translations of Newton's preparatory materials for the Beginnings, published over the past decades, excerpts from his letters relating to the problems raised in the Beginnings, and articles that aim to clarify the place and meaning of the Beginnings in all of Newton's work. , in the history of world science; will also give a picture of the time and circumstances of the creation of "Elements", their prehistory, assimilation, development and criticism by the scientific community in the 18th-20th centuries, their penetration into Russia and their role in the development of natural science and technology in our country. The second part also contains a bibliography of Newton's works, a list of the main Newtonian literature and the necessary reference apparatus.

L.S.Polak

Newton's "Principles of Natural Philosophy" constitute the unshakable foundation of Mechanics, Theoretical Astronomy and Physics. Lagrange called this work "the greatest of the works of the human mind," so the benefits that anyone can derive from the study of this work is self-evident.

During the life of the author, Newton's work was published three times: in 1686, 1713 and 1725. Then there were five or six more editions in Latin. The last of these Latin editions was performed in Glasgow in 1871 under the tutelage of W. Thomson (Lord Kelvin) and H. Blackburn.

All these Latin editions now constitute a kind of rarity, at the same time the ancient form of formulas adopted in them and the old mathematical language introduce an extra difficulty for the present reader in the study of Newton's work.

On the English language The Principles were translated, one might say, with subscript precision by Mott and published in 1727; in addition, there is a French translation of them, performed by the Marquis Duchatelet with notes by Clairaut, published in 1759, and, finally, German translation WolFersa, published in 1871.

Already by the time of publication it is clear that English and French translations are also rare. Wolfers's translation is inaccurate in places, and it is noticeable that the translator did not clearly understand the author's idea, moreover, the notes with which he provided his translation are in places erroneous.

The Latin language is inaccessible to most of the students of our Maritime Academy, therefore, in order to make it easier for them to get acquainted with the primary source of many of the knowledge he communicated and so that, when mentioning Newton's name, those who wish could find his true words, proofs and reasoning related to this issue, I decided to perform Russian translation of Newton's "Principles of Natural Philosophy". I adhered to the Latin text of the 1871 edition and, having translated it almost interlinearly at first, I repeatedly reread and corrected this translation so that, while accurately preserving not only the meaning of the original, but also the very words of the author,

to achieve the correctness and smoothness of the Russian language and avoid the use of Latin words like: impulse, effect, fact, etc., which do not become Russian from writing them in Russian letters. Then, for even more thorough cleaning, I rewrote this translation myself to prepare it for publication.

Newton leads almost all of his reasoning and proofs geometrically, from the words of his preface to the first edition it is clear what importance he attached to the accuracy of the drawing. In the edition of Thomson and Blackburn this accuracy is observed, I tried to comply with it in the Russian translation; for this I redrawn all the drawings in ink on a doubled scale, and re-compiled some of them myself, strictly following their full compliance with the text. With these drawings made by myself, the cliches were made by photo-zincography in half.

Certain passages of the text in terms of the brevity of the presentation or the peculiarities of the mathematical techniques that were at that time required some explanations and interpretations, all these interpretations are placed in the text itself in the notes, just as in the Latin three-volume edition of the Jesuits Leser and Jacquier in 1760. Only a note to Proposition LXVI due to its considerable volume, it was referred to the end of the first book.

Those passages of the original, which, due to the peculiarities of the Latin language, allowed different interpretations, are given in the notes and in Latin, and I explain the reasons that made me stop at one or another interpretation of them.

The Head and the Conference of the Academy acknowledged that the placement of the Russian translation of Newton's "Principles" in Izvestia of the Marine Academy corresponds to the purpose of this publication, and I consider it my duty to bring GI Shulgin and the Conference of the Academy deep gratitude for the confidence in my work.

A. Krylov,
Professor Emeritus
Marine Academy.

Since the ancients, according to Pappus, gave great importance mechanics in the study of nature, then the newest authors, discarding substances and hidden properties, try to subordinate the phenomena of nature to the laws of mathematics.

This essay refers to the careful development of the applications of mathematics to physics.

The ancients viewed mechanics in two ways: how rational(speculative), developed by hard evidence, and how practical... Practical mechanics includes all crafts and industries, called mechanical, from which it got its name and the most Mechanics.

Since the artisans are content in their work with only a small degree of accuracy, the opinion was formed that mechanics is so different from geometry, that everything that is quite accurate belongs to geometry, less accurate belongs to mechanics. But errors do not lie in the craft or art itself, but belong to the performer of the work: whoever works with less precision is the worst mechanic, and if anyone could perform a product with the most perfect precision, he would be the best of all mechanics.

However, the very drawing of straight lines and circles, which serves as the basis of geometry, in essence refers to mechanics. Geometry doesn't teach how draw these lines, but assumes (postulates) the feasibility of these constructions. It is also assumed that those who begin the study of geometry have already learned how to accurately draw circles and straight lines; in geometry it is shown only how different questions and problems are solved by drawing these lines. Drawing a line and a circle in itself is also a task, but not a geometric one. The solution to this problem is borrowed from mechanics, geometry teaches only the use of these solutions. Geometry is glorified for the fact that having borrowed so few basic principles from outside, it achieves so much.

So geometry is based on mechanical practice and is nothing but that part general mechanics, which expounds and proves the art of accurate measurement. But so in crafts and industries, for the most part it is necessary to deal with the movement of bodies, then usually everything that concerns only magnitude is referred to geometry, all that concerns movement - to mechanics.

In this sense rational mechanics there is the doctrine of the movements produced by whatever forces, and the forces required to produce any movements, precisely stated and proven.

The ancients developed this part of mechanics only in the form of the doctrine of five machines used in crafts; Moreover, even gravity (since this is not an effort made by the hands) was considered by them not as a force, but only as weights moved by the said machines. But we, arguing not about crafts, but about the doctrine of nature, and therefore, not about the efforts made by hands, but about the forces of nature, will mainly deal with what relates to gravity, lightness, elastic force, resistance of liquids and to similar attractive or pressing forces. Therefore, 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 by the phenomena of motion, and then by these forces to explain the rest of the phenomena. For this purpose, the general proposals set forth in books one and two are intended. In the third book, we give an example of the above application, explaining the system of the world, because here from celestial phenomena, with the help of sentences proven in previous books, the forces of gravity of bodies to the Sun and individual planets are mathematically derived. Then, according to these forces, also with the help of mathematical sentences, the motions of the planets, comets, the moon and the sea are deduced. It would be desirable to deduce from the principles of mechanics and other natural phenomena by reasoning in the same way, for much makes me suppose that all these phenomena are caused by some forces with which the particles of bodies, due to reasons as yet unknown, or tend to each other and interlock in the correct figures , or they mutually repel and move away from each other. Since these forces are unknown, until now the attempts of philosophers to explain the phenomena of nature have remained fruitless. I hope, however, that either for this mode of reasoning, or for another more correct one, the reasons given here will provide some illumination.

Edmund Halley, the most ingenious and in all fields of science, assisted in the publication of this work, who not only corrected the typographic proofs and took care of making drawings, but even at his insistence I started the publication itself. Having received from me evidence of the orbits of celestial bodies, he incessantly insisted that I report them to the Royal Society, which then, with its benevolent attention and solicitude, made me think about releasing them. After that I started researching the inequalities of the moon's motion, then I tried to make another application related to: the laws and measurement of gravitational forces and others; to the study of the type of paths described by bodies under the influence of attraction, following any law; to the movement of many bodies relative to each other; to the movement of bodies in a resisting environment; to the forces, densities and movements of the medium; to the study of the orbits of comets, and to similar questions; as a result, I postponed the publication until another time, in order to process and publish all this together.

Everything related to the movement of the moon (as not perfect) is summarized in the corollaries of Proposition LXVI, so as not to resort to separate proofs and to complex methods that do not correspond to the importance of the subject, and also so as not to interrupt the sequence of other sentences. Something that I found later, I preferred to insert, perhaps in less suitable places rather than re-numbering sentences and links. I most earnestly ask that everything stated here be read with benevolence and that the shortcomings in such a difficult subject should not be condemned, but supplemented with new works and research by readers.

Isa Newton.

Newtonian philosophy, a new, so long-desired edition, now largely revised and supplemented, we present to you, my benevolent reader. You can see the main content of this most famous work in the attached tables of contents, while additions and changes are indicated to you in the author's preface. It remains only to add something about the very method of this philosophy.

Those who tried to explain physics can generally be attributed to three categories. First of all, there are special hidden qualities attributed to various objects, from which it is not known how, in their opinion, the interaction of individual bodies should have occurred. This was the essence of scholastic teachings, originating from Aristotle and peripatetics... They argued that individual actions of bodies occur due to the peculiarities of their very nature, what these features are, they did not teach that, therefore, in essence, they did not teach anything. Thus, everything was reduced to the name of individual objects, and not to the very essence of the matter, and we can say that they created a philosophical language, and not philosophy itself.

Others, discarding the useless heap of words, hoped to use their labor more profitably. They argued that all matter in the universe is homogeneous and that all the difference in species seen in bodies occurs in some of the simplest and understandable properties of the particles that make up the body. Rising, thus, from the simpler to the more complex, they would be right if they in fact ascribed to these primary particles only the very properties that nature endowed them with, and not any other. But in fact, they give themselves the right to admit what unknown types and sizes of particles they want, their indefinite positions and movements, as well as invent various imperceptible liquids that freely penetrate through the pores of bodies and possess omnipotent subtlety and hidden movements.

Thus, they indulge in fantasies, neglecting the true essence of things, which, of course, cannot be found by deceptive assumptions, when it can hardly be investigated with the help of the most accurate observations. Borrowing the grounds for their reasoning from hypotheses, even if everything further was developed by them in the most accurate way on the basis of the laws of mechanics, would create a very elegant and beautiful fable, but still only a fable.

The third category remains - those who are followers of experimental philosophy (that is, the experimental method in the study of natural phenomena). They also strive to deduce the causes of all things from possibly simple beginnings, but they do not accept anything as a beginning as soon as that which is confirmed by the occurring phenomena. They do not invent hypotheses and do not introduce them into Physics except in the form of assumptions, whose validity is subject to investigation. Thus, they use two methods - analytical and synthetic. They derive the forces of nature and the simplest laws of their action analytically from some selected phenomena, and then synthetically obtain the laws of other phenomena. This one is the one The best way studies of nature and is adopted primarily in front of the rest of our most famous author. It was only to this method that he considered worthy to apply his labors for its improvement and development. He also gave the most famous example of the application of this method, deriving in the happiest way an explanation of the system of the world from the theory of gravitation. Already others have assumed or suspected the existence of gravitation as a general property of bodies, but only he was the first and one of all who was able to prove the existence of gravitation on the basis of occurring phenomena and put it in the basis of the most sublime research.

I, of course, know persons with prominent names who, suffering from some prejudices, are reluctant to agree with this new beginning and give preference to the unknown over the firmly established. I do not mean to harm their fame, but I just want to outline everything in a nutshell, so that you yourself, a benevolent reader, can form a fair judgment about this matter.

Newton Isaac

Great English mathematician, physicist and astronomer, creator of classical mechanics. Born in Woolsthorpe, Lincolnshire, the son of a farmer. Studied at Trinity College, Cambridge University; in 1667 he became a bachelor, in 1668 - a master. In 1669 he took the Lukasov Chair of Mathematics, becoming a professor of mathematics and optics at Trinity College. In the early 1670s. made a reflector telescope, for which he was awarded the election to the Royal Society of London (1672). In 1687, his book "Mathematical Principles of Natural Philosophy" was published, which laid the foundation for all mathematical natural science. In 1696 he received the post of curator of the Mint and moved from Cambridge to London; under his leadership, a tremendous amount of work was done to re-coin the entire English coin. In 1700 he was appointed director of the Mint. Since 1703 - President of the Royal Society of London.

Isaac Newton became one of the founders modern physics... He formulated the basic laws of mechanics and in fact created a unified program for describing all physical phenomena based on mechanics; discovered the law of universal gravitation; explained the motion of the planets around the Sun and the Moon around the Earth, as well as the tides in the oceans; laid the foundations of mechanics continuous media, acoustics and physical optics; developed differential and integral calculus, color theory and many other mathematical and physical theories. Mathematics for him was the main tool in physical research; he emphasized that mathematics is essentially a part of natural science. IN last years life I. Newton devoted a lot of time to theology, as well as ancient and biblical history; he studied the Bible by scientific methodology, using astronomical calculations related to solar eclipses, linguistic analysis etc.

Title page of Newton's "Beginnings"

The history of the creation of this work, the most famous in the history of science along with the "Principles" of Euclid, begins in 1682, when the passage of Halley's comet caused a rise in interest in celestial mechanics. Edmond Halley 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 work of publishing scientific papers.

Newton's Beginnings page with the axioms of mechanics

Later in Book I, the motion in the field of an arbitrary central force is considered in detail. The Newtonian law of attraction is formulated (with reference to Wren, Hooke and Halley), a rigorous derivation of all Kepler's laws is given, and hyperbolic and parabolic orbits unknown to Kepler are described.

Page from Newton's Beginnings

Methods of proof, with rare exceptions - purely geometric, differential and integral calculus are clearly not applied (probably, in order not to multiply the number of critics), although the concepts of the limit ("last relation") and infinitesimal, with an estimate of the order of smallness, are used in many places.

Book 2 is devoted to the motion 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 I exchanged about ten years ago with a very skillful mathematician, Mr. Leibniz, I informed him that I had a method for determining the maximums and for the irrational, and I hid the method by rearranging the letters of the following sentence: "when an equation is given containing any number of current quantities, find fluxions and vice versa." The most famous husband answered me that he also attacked such a method and told me his method, which turned out to be hardly different from mine, and then only in terms and in the outline of formulas.

Book 3 is the system of the world, mainly celestial mechanics, and also the theory of tides. Newton formulates his own version of Occam's Razor:

Nature should not accept other causes beyond those that are true and sufficient to explain the phenomena ... Nature does nothing in vain, but it would be in vain to do to many what can be done less. Nature is simple and not luxurious with unnecessary reasons.

Criticism

The publication of "Principles", which laid the foundation for theoretical physics, caused a huge resonance in the scientific world. During Newton's lifetime, the book went through three editions.

Along with enthusiastic responses, there were, however, strong objections, including from well-known scientists. The Carthusians in Europe lashed out at her with fierce criticism. Three laws of mechanics did not raise any special objections, mainly the concept of gravitation was criticized - properties of an incomprehensible nature, with an obscure source, which acted without a material carrier, through a completely empty space. Leibniz, Huygens, Jacob Bernoulli, Cassini rejected gravitation and tried as before to explain the motion of the planets by Cartesian vortices or in some other way.

From the correspondence between Leibniz and Huygens:

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

Newton himself preferred not to speak publicly about the nature of gravitation, since he did not have experimental arguments in favor of an ethereal or other hypothesis, and he did not like to start empty skirmishes. In addition, Newton admitted the supernatural nature of gravitation:

It is inconceivable that inanimate gross matter could, without the medium of anything immaterial, act and influence other matter without mutual contact, as it should have happened if gravity in the sense of Epicurus was essential and innate in matter. To assume that gravity is an essential, indissoluble and innate property of matter, so that a body can act on another at any distance in empty space, without the medium of anything transmitting action and force, this, in my opinion, is such an absurdity that is inconceivable for someone who knows enough to understand philosophical subjects. Gravity must be caused by an agent constantly acting according to certain laws. Whether, however, this agent is tangible or intangible, I left it to my readers to decide.

(From a letter from Newton dated February 25, 1693 to Dr. Bentley, author of the lectures on the "Refutation of Atheism")

Sir Isaac Newton was with me and said that he had prepared 7 pages of addenda to his book on light and colors [that is, to Optics], in a new Latin edition... He had doubts whether he could express the last question like this: "What is the space that is free of bodies filled with?" The complete truth is that he literally believes in an omnipresent Deity. Just as we feel objects when their images reach the brain, so God should feel every thing, always being present with it. He believes that God is present in space, both free of bodies and where bodies are present. But, considering that such a formulation is too crude, he thinks to write it like this: "What reason 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 gravitation is not accurate enough, especially for the Moon and Mars.

Newton's book was the first work on new physics and at the same time one of the last serious works using the old methods of mathematical research. All of Newton's followers had already used powerful methods of calculus. Throughout the 18th century, analytical celestial mechanics developed intensively, and over time, all the above-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 unshakable. Physicists gradually got used to long-range action, and even tried to attribute it, by analogy, electromagnetic field(before the appearance of Maxwell's equations). The nature of gravitation was revealed only with the appearance of Einstein's works on the General Theory of Relativity, when long-range action finally disappeared from physics.

Literature

• Isaac Newton, Mathematical principles of natural philosophy. Translation from Latin and notes by A. N. Krylov. M., Science, 1989, 688 with ISBN 5-02-000747-1
• Spassky B.I.... History of Physics. M., " graduate School", 1977.

• History of Mathematics, edited by A.P. Yushkevich in three volumes, Moscow: Nauka.

• Bell E. T. The creators of mathematics. Moscow: Education, 1979.
• Vavilov S.I. Isaac Newton. 2nd revised edition. M.-L .: Ed. USSR Academy of Sciences, 1945

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See what "Newton's Beginnings" is in other dictionaries:

Three laws underlying the so-called. classic mechanics or Newtonian mechanics. Formulated by I. Newton (1687). The first law: “Every body continues to be held in its state of rest or uniform and rectilinear motion, as long as and since ... ... Physical encyclopedia

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It is proposed to rename this page to Beginnings. Explanation of the reasons and discussion on the Wikipedia page: To rename / August 29, 2012. Perhaps its current name does not correspond to the norms of the modern Russian language and / or the rules ... ... Wikipedia

It is proposed to rename this page to Beginnings (values). Explanation of the reasons and discussion on the Wikipedia page: Towards renaming / August 29, 2012. Perhaps its current name does not correspond to the norms of the modern Russian language and / or ... ... Wikipedia

Three laws underlying the so-called. classical mechanics (see Mechanics). Formulated by I. Newton (1687). The first law: “Every body continues to be held in its state of rest or uniform and rectilinear motion, until ... ... Great Soviet Encyclopedia

Mr. Halley ... recently saw Mr. Newton in Cambridge, and he showed him an interesting treatise "De motu" [On Movement]. According to the will 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 in early 1686 the Society published an uncalled for treatise on the history of fish, thus draining its budget. Halley then announced that he was covering the publishing costs. The Society gratefully accepted this generous offer and, as partial compensation, provided Halley with 50 copies of a treatise on the history of fish free of charge.

Newton's work - perhaps by analogy with the "Principles of Philosophy" ( Principia Philosophiae) Descartes - received the name "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 are given, and if the physics of Aristotle asserted that the speed of a body depends on the driving force, then Newton makes a significant correction: not speed, but acceleration.

Newton's Beginnings page with the axioms of mechanics

Later in Book I, the motion in the field of an arbitrary central force is considered in detail. The Newtonian law of attraction is formulated (with reference to Wren, Hooke and Halley), a rigorous derivation of all Kepler's laws is given, and hyperbolic and parabolic orbits unknown to Kepler are described.

Page from Newton's Beginnings

Methods of proof, with rare exceptions - purely geometric, differential and integral calculus are clearly not applied (probably, in order not to multiply the number of critics), although the concepts of the limit ("last relation") and infinitesimal, with an estimate of the order of smallness, are used in many places.

Book 2 is devoted to the motion 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 I exchanged about ten years ago with a very skillful mathematician, Mr. Leibniz, I informed him that I had a method for determining the maximums and for the irrational, and I hid the method by rearranging the letters of the following sentence: "when an equation is given containing any number of current quantities, find fluxions and vice versa." The most famous husband answered me that he also attacked such a method and told me his method, which turned out to be hardly different from mine, and then only in terms and in the outline of formulas.

Book 3 is the system of the world, mainly celestial mechanics, and also the theory of tides. Newton formulates his own version of Occam's Razor:

Nature should not accept other causes beyond those that are true and sufficient to explain the phenomena ... Nature does nothing in vain, but it would be in vain to do to many what can be done less. Nature is simple and not luxurious with unnecessary reasons.

In accordance with his method, Newton deduces the law of gravitation from experimental data on the planets, the moon and other satellites. To test that the force of 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 equinoxes and irregularities (discrepancies) in the motion of the Moon - both known in antiquity and 7 later established (Tycho Brahe, Flamsteed). A method for determining the mass of the planet is given, and the mass of the Moon is found from the height of the tides.

Criticism

The publication of "Principles", which laid the foundation for theoretical physics, caused a huge resonance in the scientific world. Along with enthusiastic responses, there were, however, strong objections, including from well-known scientists. The Carthusians in Europe lashed out at her with fierce criticism. Three laws of mechanics did not raise any special objections, mainly the concept of gravitation was criticized - properties of an incomprehensible nature, with an obscure source, which acted without a material carrier, through a completely empty space. Leibniz, Huygens, Jacob Bernoulli, Cassini rejected gravitation and tried, as before, to explain the motion of the planets by Cartesian vortices or in some other way.

From the correspondence between Leibniz and Huygens:

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

Newton himself preferred not to speak publicly about the nature of gravitation, since he did not have experimental arguments in favor of an ethereal or other hypothesis, and he did not like to start empty skirmishes. In addition, Newton admitted the supernatural nature of gravitation:

It is inconceivable that inanimate gross matter could, without the medium of anything immaterial, act and influence other matter without mutual contact, as it should have happened if gravity in the sense of Epicurus was essential and innate in matter. To assume that gravity is an essential, indissoluble and innate property of matter, so that a body can act on another at any distance in empty space, without the medium of anything transmitting action and force, this, in my opinion, is such an absurdity that is inconceivable for someone who knows enough to understand philosophical subjects. Gravity must be caused by an agent constantly acting according to certain laws. Whether, however, this agent is tangible or intangible, it is up to my readers to decide.

(From a letter from Newton dated February 25, 1693 to Dr. Bentley, author of the lectures on the "Refutation of Atheism")

Sir Isaac Newton was with me and said that he had prepared 7 pages of addenda to his book on light and colors [that is, to Optics], in a new Latin edition ... He had doubts if he could express the last question like this: What is the space that is free of bodies filled with? " The complete truth is that he literally believes in an omnipresent Deity. Just as we feel objects when their images reach the brain, so God should feel every thing, always being present with it. He believes that God is present in space, both free of bodies and where bodies are present. But, considering that such a formulation is too crude, he thinks to write it like this: "What reason 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 gravitation is not accurate enough, 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 the old methods of mathematical research. All of Newton's followers had already used powerful methods of calculus. Throughout the 18th century, analytical celestial mechanics developed intensively, and over time, all the above-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 unshakable. Physicists gradually got used to long-range action, and even tried to attribute it, by analogy, to the electromagnetic field (before the appearance of Maxwell's equations). The nature of gravitation was revealed only with the appearance of Einstein's works on the General Theory of Relativity, when long-range action finally disappeared from physics.

The asteroid 2653 Principia (1964) is named in honor of Newton's Beginnings.

Russian translations

• Isaac Newton. Mathematical principles of natural philosophy. Translation from Latin and notes by A. N. Krylov. Moscow: Nauka, 1989.688 pp. ISBN 5-02-000747-1. Series: Classics of Science.
  • Text on math.ru on mccme.ru

Notes (edit)

Literature

• Antropova V.I. O geometric method"Mathematical Principles of Natural Philosophy" by I. Newton // Historical and mathematical research... - M .: Nauka, 1966. - No. 17. - S. 205-228.
• Bell E. T. The creators of mathematics. - M .: Education, 1979 .-- 256 p.
• Vavilov S.I. Isaac Newton . - 2nd add. ed .. - M.-L .: Publishing house. Academy of Sciences of the USSR, 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. History of Physics Course. - M .: Education, 1974.
• Spassky B.I. History of Physics. - Ed. 2nd. - M .: Higher school, 1977 .-- T. 1.

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See what "Mathematical Principles of Natural Philosophy" is in other dictionaries:

- “MATHEMATICAL BEGINNINGS OF NATURAL PHILOSOPHY” (Philosophiae Naturalis Principia Mathematica. L., 1687; last 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