Philosophiæ Naturalis Principia Mathematica

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PhilosophiÃÆ'Â| Naturalis Principia Mathematica (Latin for the Mathematical Principles of Natural Philosophy ), often referred to simply as Principia , is a work in three books by Isaac Newton, in Latin, first published July 5, 1687. After annotating and correcting a personal copy of the first edition, Newton published two further editions, in 1713 and 1726. The < i> Principia declared Newton's laws of motion, forming the basis of classical mechanics; Newton's universal law of gravity; and Kepler's planetary law derivation (first empirically obtained by Kepler).

Principia is considered to be one of the most important works in the history of science.

The French mathematical physicist Alexis Clairaut judged in 1747: "The famous book of the Principles of Mathematics of Natural Philosophy marks the age of the great revolution in physics.The method followed by the famous writer Sir Newton... spreading the mathematical light on science that up to the moment it remains in the dark of conjectures and hypotheses. "

A more recent assessment is that while Newton's theory of acceptance is indirect, by the end of the century after publication in 1687, "no one can deny that" (from Principia ) "a science has emerged that, at least in some things, so far more than ever before, he stands alone as a major example of science in general. "

In formulating his physical theory, Newton developed and used the mathematical method now included in the field of calculus. But the language of calculus as we know it is largely absent from the Principia ; Newton provides ample evidence in the geometric form of infinitesimal calculus, based on the limit of the ratio of the disappearance of small geometric quantities. In a revised conclusion to Principia, Newton used his famous expression, the non-finger hypothesis ("I am not formulating the General Scholium hypothesis ").

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Contents

Goals and topics covered include

In the preface to Principia , Newton writes:

[...] Rational Mechanics will be the science of motion resulting from any power, and the power required to produce any movement, is proposed accurately and shown [...] And therefore we offer this work as a mathematical principle of his philosophy.. For all philosophical difficulties it seems to consist in this - from the movement phenomena to investigate the forces of Nature, and then from these forces to demonstrate other phenomena [...]

The Principia primarily deals with large movable bodies, initially under a variety of hypothetical conditions and laws of force in both media which do not reject and reject, thus offering the criteria for deciding, by observation, to which the law of force operates within observable phenomena. It attempts to mask the hypothetical movement or possibilities of celestial bodies and from ground projectiles. It explores the difficult problem of motion disturbed by various interesting forces. His third and final book deals with the interpretation of observations about the movement of planets and their satellites.

It shows:

• how the observations of astronomy prove the law of inverse squared gravity (with high accuracy according to Newton's time standards);
• offers a relative mass estimate for known giant planets and for Earth and the Sun;
• defines the very slow motion of the Sun relative to the solar system's barycenter;
• shows how the theory of gravity can explain the irregularities in the motion of the Moon;
• identifies oblateness of Earth figure;
• contributes roughly to the ocean waves including the phenomenon of spring and seawater by the disturbing (and varying) gravitational attraction of the Sun and the Moon in the waters of the Earth;
• describes the equinoxes precession as the effect of the gravitational attraction of the Moon on the Earth's equatorial bulge; and
• provides theoretical basis for various phenomena about the comet and its elongated and almost parabolic orbit.

The opening section of Principia contains, in a revised and extended form, almost all content of the 1684 Newton channel De motu corporum in gyrum .

The Principia begins with "Definitions" and "Axioms or Laws of Motion", and continues in three books:

Book 1, De motu corporum

Book 1, subtitle De motu corporum ( On body motion ) concerns movement without any media that refuse. It opens with the mathematical exposition "first and last ratio method", the geometric shape of the infinitesimal calculus.

The second section establishes the relationship between the centripetal forces and the laws of the area now known as Kepler's second law (Proposition 1-3), and links the circular velocity and radius of curvature to radial force (Proposition 4), and the relationship between the various centripetal forces. as the inverse-square distance to the center and the orbit of conic-sectional forms (Proposition 5-10).

Proposition 11-31 defines motion properties in eccentric-conical form paths including ellipses, and their relationship to the central-inverse-focused force directed to the focus, and incorporates Newton's theorem of the oval (lemma 28).

Proposition 43-45 is a demonstration that is in an eccentric orbit under the centripetal force in which the apse can move, the orientation of the stable and immobile line is an inverse square law indicator.

Book 1 contains some evidence with little connection to real-world dynamics. But there are also parts with applications that reach far into the solar system and the universe:

Proposition 57-69 deals with "gestures drawn from each other by centripetal force". This section is of major importance for its application to the solar system, and includes Proposition 66 along with 22 consequences: here Newton takes the first steps in the definition and the study of the three major bodily movement issues subject to their mutually annoying gravity attraction, name and fame (among other reasons, because of its great difficulty) as a matter of three bodies.

Proposition 70-84 relates to the pulling power of the ball body. This section contains Newton's evidence that an enormous symmetrical object attracts other bodies outside of itself as if all its mass is concentrated in its center. This fundamental result, called the Shell theorem, allows the inverse-square law of gravity to be applied to a real solar system approaching a very close approximation.

Book 2

Part of the original contents planned for the first book is divided into the second book, which mostly concerns the motion through the media refuse. Just as Newton examined the consequences of the different law of attraction in Book 1, here he examined different laws of resistance; thus Part 1 discusses resistance in direct proportion to speed, and Part 2 continues to examine the implications of resistance equivalent to the square of velocity. Book 2 also discusses the hydrostatic (in Section 5 ) and the properties of the compressible fluid. The effect of air resistance on the pendulum is studied in Section 6 , along with Newton's report on his experiments, to try to find some characteristics of the air resistance in reality by observing the pendulum movement under different conditions. Newton compares the resistance offered by the media to ball motions with different properties (material, weight, size). In Section 8, he takes the rule to determine the velocity of the waves in the liquid and relates them to density and condensation (Proposition 48: this will be very important in acoustics). He considers that this rule applies equally to light and sound and estimates that the sound speed is about 1088 feet per second and can increase depending on the amount of water in the air.

Less than Book 2 has stood the test of time from Books 1 and 3, and it has been said that Book 2 is largely written with the aim of refuting Descartes's theory of having wide acceptance before Newton's work (and for some time after). According to the Cartesian theory of vortices, planetary motion is produced by a whirlpool of fluid that fills interplanetary space and brings the planets with them. Newton writes at the end of book 2, the conclusion that the vortical hypothesis is completely contrary to astronomical phenomena, and does not explain it so much that it confuses them.

Book 3, De mundi systemate

Book 3, subtitle De mundi systemate ( On the world system ), is an explanation of many consequences of universal gravitation, especially its consequences for astronomy. It builds on the proposition of the preceding book, and applies it to a further specificity than in Book 1 with the motions observed in the solar system. Here (introduced by Proposition 22, and continues in Proposition 25-35) developed several features and deviations of the orbital motion of the Moon, especially its variations. Newton lists the astronomical observations he relies on, and gradually establishes that the inverse square law of gravity holds true for the solar system, beginning with the Jupiter satellite and occurring gradually to show that law is a universal application. He also gave begins on the Lemma 4 and Proposition 40 comet motion theories, of which much data came from John Flamsteed and Edmond Halley, and contributed waves, attempting a quantitative estimate of the contributions of the Sun and the Moon to the ups and downs. movement; and offers the first theory of precession equinox. Book 3 also considers harmonic oscillators in three dimensions, and motion in the law of arbitrary forces.

In Book 3 Newton also clarified his heliocentric view of the solar system, modified in a somewhat modern way, since already in the mid-1680s he recognized the "sun divergence" from the center of gravity of the solar system. For Newton, "the common center of gravity of the Earth, the Sun, and all Planets must be respected as the Center of the World," and that this center "is resting, or moving forward uniformly in the correct line." Newton rejected the second alternative after adopting the position that "the center of the world's system is immovable", which "is recognized by all, while some hold that the Earth, the other, that the Sun has fixed it. Newton estimates Sun's mass ratio: Jupiter and Sun: Saturn, and suggests that this places the center of the Sun usually farther from the center of general gravity, but only slightly, the most distance "will hardly amount to a solar diameter".

Comments on Principia

The sequence of definitions used in the dynamics setting in Principia can be recognized in many textbooks today. Newton first defined the definition of mass

The quantity of matter is that which arises simultaneously of density and magnitude. The body twice as dense in double the space is quadruple quantity. This quantity I specify by body name or mass.

It is then used to determine the "quantity of motion" (the momentum of today is called), and the principle of inertia in which the mass replaces the previous Cartesian idea of ​​intrinsic forces. This then sets the stage for the introduction of forces through the momentum of the body changes. Surprisingly, for today's readers, the exposition seems to be false in dimension, since Newton does not introduce the time dimension in the rate of quantity change.

He defines space and time "not because they are known to everyone". Instead, he defines "true" time and space as "absolute" and explains:

It is only I who must observe, that the vulgar considers the numbers below no other idea than the relationship they bring to the obvious objects. And it would be easier to distinguish it to be absolute and relative, true and real, mathematical and general. [...] not the absolute place and movement, we use the relative; and that without the discomfort in common affairs; but in philosophical discussion, we must step back from our senses, and consider things themselves, different from what is only a clear measure of them.

For some modern readers, it may appear that a number of currently recognized dynamic quantities are used in Principia but not named. The mathematical aspects of the first two books are so clearly consistent that they are easily accepted; for example, Locke asked Huygens if he could trust the mathematical evidence, and was convinced of the truth.

However, the concept of an attractive force acting on a distance receives a colder response. In his note, Newton writes that the inverse square law appears naturally because of the structure of matter. However, he revoked this sentence in a published version, where he stated that the motion of the planet is consistent with the inverse square law, but refuses to speculate on the origin of the law. Huygens and Leibniz noted that the law was incompatible with the idea of ​​ether. From the point of view of Cartesians, therefore, this is the wrong theory. Newton's defense has been adopted by many famous physicists - he points out that the mathematical form of the theory must be true because it explains the data, and he refuses to speculate further on the nature of gravity. The many phenomena that can be set by theory so impressive that young "philosophers" soon adopted the methods and language of the Principia .

Rules of Reasoning in Philosophy

Perhaps to reduce the risk of public misunderstanding, Newton was included at the beginning of Book 3 (in the second edition (1713) and third (1726)) section entitled "The Rule of Reasoning in Philosophy." In the four rules, when they came to finally stand in the 1726 edition, Newton effectively offered a methodology to deal with unknown phenomena in nature and reached an explanation for them. The four Rules of the 1726 edition are executed as follows (omitting some commentary annotations that follow each):

Rule 1: We have to admit there is no more natural causes than the two are true and enough to explain their appearance.

Rule 2: Therefore for the same natural effect we must, as far as possible, establish the same cause.

Rule 3: The quality of the body, which does not recognize the intensification or forgiveness of degrees, and which is found to belong to all bodies within the range of our experiments, should be respected by the universal qualities of all bodies.

Rule 4: In experimental philosophy we have to look at the propositions summed up by the general induction of phenomena as accurate or nearly correct, not holding back the opposite hypotheses that might be imagined, until such time as other phenomena occur, where they can either be made more accurately, or can be excluded.

The Rules section for this philosophy is followed by a list of 'Phenomena', which listed a number of observations mainly astronomy, which Newton used as the basis for later conclusions, as if adopting a series of fact consensus from his time astronomers.

Both 'Rules' and 'Phenomena' evolved from one edition of the Principia to the next. Rule 4 appears in the third edition (1726); Rule 1-3 comes as a 'Rule' in the second edition (1713), and their predecessors were also present in the first edition of 1687, but there they have a different title: they are not given as 'Rules', but not in the first edition (1687) the predecessor of the then three 'Rules', and most of the later 'Phenomenon', all incorporated under one heading 'Hypothesis' (where the third item is the predecessor of the weight revision which gives the Rule then 3).

From this textual evolution, it appears that Newton wanted by the title 'Rule' and 'Phenomenon' later to clarify for the readers his views on the role that these statements would play.

In the third edition (1726) of Principia , Newton describes each rule in an alternative way and/or provides an example to support what the rule claims. The first rule is described as the economic principle of the philosophers. The second rule states that if one of the causes is given to natural effects, then the same cause as far as possible should be established for the natural effects of the same kind: for example respiration in humans and animals, fires at home and in the Sun, or light reflections whether it occurs terrestrial or from planets. Broad explanations are given from the third rule, regarding the quality of the body, and Newton discusses here generalizations of observations, with warnings against crush makeovers contrary to experiments, and the use of rules to illustrate the observations of gravity and space..

Isaac Newton's statement of four rules revolutionized the investigation of phenomena. With these rules, Newton can in principle begin to deal with all the unsolved mysteries in the world today. He was able to use his new analytical method to replace Aristotle, and he was able to use his method to transform and update Galileo's experimental methods. The re-creation of the Galileo method has never changed significantly and basically, scientists are using it today.

General Scholium

The General Scholium is the closing essay added to the second edition, 1713 (and changed in the third edition, 1726). This is not to be confused with General Scholium at the end of Book 2, Section 6, which discusses experiments and pendulum resistance due to air, water, and other liquids.

Here Newton uses his famous expression Hypotheses non fingo , "I formulate no hypothesis", in response to criticism of the first edition of the Principia . ( 'Fingo' is sometimes now translated 'pretend' rather than the traditional 'frame'.) Newton's gravitational pull, the invisible power capable of acting over great distances, has led to his criticism introduce "occult agencies" into science. Newton firmly rejected such criticism and wrote that it is enough that the phenomenon implies gravitational pull, as they do; but the phenomenon does not so far indicate the cause of this gravity, and it is unnecessary and inappropriate to frame the hypothesis of things not implied by phenomena: such a hypothesis "has no place in experimental philosophy", in contrast to the precise way in which " a particular proposition is inferred from the phenomenon and subsequently given in general by induction ".

Newton also underlined his criticism of the theory of the vortex of planetary motion, Descartes, indicating its incompatibility with the highly eccentric orbit of comets, which brought them "through all parts of the sky with indifference".

Newton also gave a theological argument. From the world system, it concludes the existence of God, in line with what is sometimes called the argument of intelligent design or purpose. It has been argued that Newton gave "oblique arguments for the unitarian conception of God and the implicit attack on the doctrine of the Trinity", but General Scholium does not seem to be saying specifically about these things.

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Write and publish

Halley and Newton's early stimulus

In January 1684, Edmond Halley, Christopher Wren, and Robert Hooke had a conversation in which Hooke confessed not only to have the law of the inverse square, but also all laws of planetary motion. Wren was unsure, Hooke did not produce any claimed derivation although others gave him time to do so, and Halley, who could lower the inverse square law for a limited circular case (by replacing Kepler's relationship into Huygens's formula for centrifugal force) but failing to get a general relationship, decided to ask Newton.

Halley's visit to Newton in 1684 resulted from Halley's argument about planetary motion with Wren and Hooke, and they seem to have given Newton an incentive and spurred on developing and writing what became Philosophiae Naturalis Principia Mathematica. Halley at the time was a Fellow and a member of the Royal Society Council in London (a position which in 1686 he resigned to become a Community Paid Officer). Halley's visit to Newton at Cambridge in 1684 may have occurred in August. When Halley asked Newton's opinion of the planetary issue discussed earlier that year between Halley, Hooke and Wren, Newton surprised Halley by saying that he had made a derivative some time ago; but he could not find the newspaper. (The matching account of this meeting comes from Halley and Abraham De Moivre which Newton justified.) Halley then had to wait for Newton to 'find' the result, but in November 1684 Newton sent a version of Halley which was reinforced from whatever previous work Newton had done on this issue. This takes the form of a 9-page manuscript, De motu corporum in gyrum ( From gestures in orbit ): the title is displayed on some surviving copies, though the original (missing) is possible without title.

The Newton Treaty De motu corporum in gyrum , which he sent to Halley at the end of 1684, came from what is now known as the three laws of Kepler, assuming the law of the inverse square, and generalizing the result into a conic. part. It also extends the methodology by adding solutions of problems on body movement through medium resisting. The contents of De motu were so passionate about Halley by their mathematical and physical originality and the widespread implications for the theory of astronomy that he soon went to visit Newton again, in November 1684, to ask Newton to let the People's Kingdom have more such work. The results of their meeting clearly helped to stimulate Newton with the enthusiasm needed to take an investigation into further math problems in this field of physical sciences, and he did so in a highly concentrated period of work that lasted at least until mid-1686.

Newton's attention to his work in general, and for his project during this time, is indicated by later memories of the secretary and copyist of the period, Humphrey Newton. The story tells about Isaac Newton's absorption in his lessons, how he sometimes forgets his food, or his sleep, or his clothing state, and how when he walks in his garden he occasionally rushes back to his room with some new ones. thinking, not even waiting to sit down before starting to write it down. Other evidence also indicates Newton's absorption at Principia: Newton for many years continues to program regular chemistry or alchemy experiments, and he usually keeps a record of dates from them, but for a timeframe from May 1684 to April 1686, the Notebook Newton's chemistry has no entries at all. So it seems that Newton ignores the activities he usually dedicates, and does very little for more than a year and a half, but concentrates on developing and writing what his great work is.

The first of three constituent books was sent to Halley for the printer in the spring of 1686, and the other two books were rather late. The complete work, published by Halley at its own financial risk, appeared in July 1687. Newton has also communicated to Flamsteed with Flamsteed, and during the composition period he exchanged several letters with Flamsteed on observational data on planets , ultimately recognizing the contribution of Flamsteed in the published version of Principia in 1687.

Initial version

The process of writing the first edition of the Principia through several stages and drafts: some parts of the original material still survive, while others are lost except for fragments and cross-references in other documents.

The surviving material shows that Newton (until some time in 1685) compiled his book as a two-volume work. The first volume is titled De motu corporum, Liber primus , with its contents which then appears in extended form as Book 1 of Principia .

A fair-copy draft of the second volume of Newton planned for De Motu corporum, Liber secundus survived, the settlement dated around the summer of 1685. This included the application of the results of Liber primus to Earth , The Moon, the waves, the solar system, and the universe; in this case it has many of the same goals as the last 3 Books of Principia , but is written much less formal and more readable.

It is unknown why Newton changed his mind radically about the final form of what had become a readable narrative in De Motu corporum, Liber secundus in 1685, but he began again from the new, more rigorous. , and a less accessible mathematical style, eventually produced Book 3 of the Principia as we know it. Newton flatly admits that this style change is deliberate when he writes that he has (first) compiled this book "in popular methods, which may be read by many," but to "prevent discord" by readers who can not "rule out prejudice [ ir] ", he has" reduced "it into a form of proposition (by mathematical means) to be read by them alone, which first makes themselves master the principles set forth in previous books." The last book 3 also contains additions some important important quantitative results that Newton arrived for a while, especially about the theory of comet movements, and some of the disruption of the Moon's movements.

The result is numbered Book 3 of the Principia rather than Book 2, because in the meantime, the draft of Liberusus has grown and Newton has divided it into two books. The new and final 2 book is closely linked to body movement through rejecting media.

But the secundus of 1685 is still readable today. Even after it was replaced by Book 3 of the Principia , it was fully completed, in more than one manuscript. After Newton's death in 1727, the relatively easy character of his writings encouraged the publication of an English translation in 1728 (by unknown persons, not authorized by Newton's heirs). It appears under the English heading of A Treatise of the World of System. It has some changes relative to Newton's 1685 script, mostly to remove cross-references that use obsolete numbering to cite propositions from the first draft of Book 1 of the Principia . Newton's heirs soon published a Latin version that they had, also in 1728, under the new (new) De Mundi Systemate title, changed to update cross references, quotations and diagrams to the final edition of > Principia , making it look as if it had been written by Newton after the Principia , than before. The System of the World is popular to stimulate two revisions (with similar changes as in Latin printing), second edition (1731), and reprinted 'corrected' second edition (1740).

The role of Halley as a publisher

The first text of three books of the Principia was presented to the Royal Society at the close of April 1686. Hooke made some priority claims (but failed to prove it), causing some delays. When Hooke's claim was discovered by Newton, who resented the dispute, Newton threatened to appeal and suppress Book 3 as a whole, but Halley, showing considerable diplomatic skill, wisely persuaded Newton to withdraw his threat and let him advance to publicity. Samuel Pepys, as President, gave imprimatur on June 30, 1686, licensing a book for publication. The Society has just spent its book budget on History of Fishes, and the publication costs are borne by Edmund Halley (who later acted as the publisher of the Philosophical Transactions of the Royal Society): the book it appeared in the summer of 1687.

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Historical context

Beginning of the Scientific Revolution

Nicolaus Copernicus has moved the Earth away from the center of the universe with a heliocentric theory which he presents evidence in his book De Revolutionibus orbium coelestium ( In the celestial sphere revolution ) published in 1543. This structure is completed when Johannes Kepler wrote a new Astronomia nova ( Astronomy ) in 1609, established evidence that planets move in elliptical orbits with the sun at one focus, and the planets do not move with a constant velocity along this orbit. Instead, their velocity varies so that the line connecting the center of the sun and the planet sweeps the same area at the same time. For both of these laws he added a third of a decade later, in his book Harmonices Mundi ( Harmony of the world ). This law sets the proportionality between the third force of the planet's characteristic distance from the sun and the square throughout the year.

The foundations of modern dynamics are set out in the Galileo book Dialogo sopra i due massimi sistemi del mondo ( Dialog on two main world systems ) in which the idea of ​​inertia is implied and used. In addition, Galileo's experiments with sloping fields have resulted in precise mathematical relationships between elapsed time and acceleration, speed or distance for uniform and uniform body movement.

Descartes' book of 1644 Principles of philosophy states that the body can act on one another only through contact: a principle that encourages people, among themselves, to hypothesize universal media as carriers of interactions such as light and gravity - aether. Newton was criticized for seemingly introducing forces acting at a distance without medium. Not until the development of particle theory is Descartes's idea proved when it is possible to describe all interactions, such as strong, weak, and electromagnetic fundamental interactions, using the mediation of the measuring boson and gravity through hypothesized gravity. Although he is mistaken in his treatment of circular movements, this effort is more useful in the short run when he leads others to identify circular motions as a matter raised by the principle of inertia. Christiaan Huygens solved this problem in the 1650s and published it later in 1673 in his book Horologium oscillatorium sive de motu pendulorum .

Newton's Role

Newton had studied these books, or, in some cases, secondary sources based on them, and made notes entitled Quaestiones quaedam philosophicae during his days as a scholar. During this period (1664-1666) he created the base of calculus, and conducted the first experiments in color optics. At this time, the proof that white light is a combination of primary colors (found through prismatic) replaces the prevailing color theory and receives a very favorable response, and causes bitter disputes with Robert Hooke and others, forcing him to sharpen his ideas. to the point where he had compiled part of his later book Opticks in the 1670s in response. The work of calculus is shown in various papers and letters, including two for Leibniz. He became a fellow of the Royal Society and the second Lucasian Math Professor (succeeded Isaac Barrow) at Trinity College, Cambridge.

Newton's early work on motion

In the 1660s Newton studied the colliding body movements, and concluded that the mass centers of the two colliding bodies remained uniformed. Surviving manuscripts of the 1660s also show Newton's interest in planetary motion and that in 1669 he has shown, for the circular case of planetary motion, that the force he calls 'the effort to recede' (now called the centrifugal force) has an inverse-quadratic relationship with distance from the center. After 1679-1680 correspondence with Hooke, described below, Newton adopted a language of inward or centripetal force. According to Newtonian scholar, J Bruce Brackenridge, although much has been made about changes in language and differences in viewpoint, such as between centrifugal or centripetal force, actual calculations and actual evidence remain the same. They also involve a combination of tangential and radial displacements, which Newton made in the 1660s. The difference between centrifugal and centripetal point of view, although a significant change in perspective, does not alter the analysis. Newton also clearly states the concept of linear inertia in the 1660s: because Newton is indebted to the work of Descartes published 1644.

Controversy with Hooke

Hooke published his ideas about gravity in the 1660s and again in 1674. He proposed the principle of gravitational pull in Micrographia 1665, in the 1666 lectures of the Royal Society of Gravity, and again in 1674, when he published his ideas on the World System in a somewhat evolving form, in addition to the Attempts to Prove the Motion of the Earth from Observation . Hooke clearly postulates the joint attraction between the Sun and the planet, in a way that increases with closeness to the body of interest, along with the principle of linear inertia. Hooke's statement until 1674 does not mention, however, that the inverse square law applies or may apply to this attraction. Hooke's gravity is also not yet universal, though closer to universality more closely than the previous hypothesis. Hooke also does not provide any accompanying evidence or mathematical demonstrations. In these two aspects, Hooke declared in 1674: "Now, these few degrees of gravity have not been experimentally tested" (showing that he does not yet know what laws might be followed by gravity); and for all of his proposals: "Here I am only a clue at the moment", "have myself a lot of other things in the hands I first combined, and therefore can not attend well" (ie, "Demanding this Investigation").

In November 1679, Hooke began the exchange of letters with Newton, in which the full text is now published. Hooke told Newton that Hooke had been appointed to manage the correspondence of the Royal Society, and hoped to hear from members about their research, or their views on the research of others; and as if to arouse Newton's interest, he asks what Newton thinks about things, gives the entire list, mentions "combining the movements of the sky of the planets of direct movement by tangent and the movement of interest toward the central body," and "my hypothesis of law or the cause of springinesse, "and then a new hypothesis from Paris on planetary motion (which Hooke describes at length), and then attempts to undertake or improve the national survey, the difference in latitude between London and Cambridge, and other items. Newton's answer offers "fansy of my own" about terrestrial experiments (not proposals about space movement) that might detect Earth's motion, using the body first hung in the air and then falling to let it fall. The main point is to show how Newton thinks the falling body can experimentally reveal the Earth's motion with its direction of deviation from the vertical, but it goes hypothetically to consider how its motion can continue if the solid Earth has not been in the way (in the spiral path to the center). Hooke disagreed with Newton's idea of ​​how the body would keep moving. A short correspondence developed, and towards the end of Hooke, writing on January 6, 1680 to Newton, communicated "his assumption... that Attraction is always in double proportion to the Distance from the Reciprocall Center, and Consequently that Speed ​​would be in unparalleled proportion to Fascination and Consequences as Kepler Considers Reciprocall to Distance. "(Hooke's conclusion about the speed is not true.)

In 1686, when the first book of Newton Principia was presented to the Royal Society, Hooke claimed that Newton had obtained from him the "idea" of the "Gravity drop rule, which became reciprocally as the square of the distance from the Center". At the same time (according to Edmond Halley's contemporary report) Hooke agrees that the "Therby-produced Curve Demonstration" is entirely Newton's.

The recent assessment of the early history of the inverse square law is that "in the late 1660s," the assumption of "the inverse proportion between gravity and squared distance is somewhat common and has been put forward by a number of different people to be different." reason. "Newton himself has pointed out in the 1660s that for planetary motions under circular assumptions, forces in the radial direction have square-squared connections with a distance from the center Newton, faced in May 1686 with Hooke's claim on the inverse square law, denies that Hooke would be credited as the author of the idea, giving reasons including previous work quotes by others before Hooke.Newton also firmly claims that even if it happens that he has first heard the inverse square proportions of Hooke, which he does, he will still have some the right to it in view of its development and mathematical demonstrations, allowing observations to be relied upon as evidence of its accuracy, while Hooke, without mathematical demonstrations and evidence supporting the supposition, can only guess (according to Newton) that it is roughly valid "at great distances from the center ".

The background described above shows there is a basis for Newton to refuse to bring down the inverse square law of Hooke. On the other hand, Newton does accept and admit, in all editions of the Principia , that Hooke (but not exclusively Hooke) separately values ​​the inverse square law in the solar system. Newton recognizes Wren, Hooke and Halley in this connection in Scholium to Proposition 4 in Book 1. Newton also acknowledges to Halley that his correspondence with Hooke in 1679-80 has revived his inactive interest in astronomical matters, but that does not mean, according to Newton, that Hooke had told Newton something new or original: "but I am not grateful to him for any light in the business, but only because of the diversion he gave me from my other studies to think about these things "for his dogmatization in writing as if he had found movement in the Ellipsis, which made me inclined to try it...".) Newton's exciting interest in astronomy received further stimulus with the advent of comets in the winter of 1680/1681, at where he corresponded with John Flamsteed.

In 1759, several decades after the deaths of Newton and Hooke, Alexis Clairaut, the leading mathematical astronomer in his field in the field of gravity studies, made his judgment after reviewing what Hooke published about gravity. "One should not think that this idea... of Hooke diminishes Newton's glory", writes Clairaut; "The Hooke example" works "to show what the distance is between the ogled truth and the demonstrated truth".

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Location of initial edition copy

Since only between 250 and 400 copies were printed by the Royal Society, the first edition is very rare. Some collections of rare books containing first editions and other early copies of Newton Principia Mathematica , include:

• The Cambridge University Library has a copy of the first edition of Newton himself, with handwritten notes for the second edition.
• Earl Gregg Swem Library at College of William & amp; Mary has the first edition of the Principia. Inside is a record in Latin by an unidentified hand.
• The collection of Frederick E. Brasch Newton and Newtoniana at Stanford University also has the first edition of the Principia.
• The first edition is part of the Crawford Collection, housed in the Royal Observatory, Edinburgh.
• The Uppsala University Library has a copy of the first edition, stolen in 1960 and returned to the library in 2009.
• Folger Shakespeare Library in Washington, D.C. has the first edition, as well as the second edition of 1713 edition.
• The Huntington library in San Marino, California has a personal copy of Isaac Newton, with annotations in Newton's own hands.
• Martin Bodmer's library stores a copy of the original edition that Leibniz owns. In it, we can see handwritten notes by Leibniz, especially about the controversy over who first compiled the calculus (though he published it later, Newton argues that he developed it earlier).
• The St Andrews University Library houses both variants of the first edition, as well as copies of 1713 and 1726 editions.

In 2016, the first edition sold for $ 3.7 million.

The facsimile edition (based on the 3rd edition of 1726 but with variant readings from previous editions and important annotations) was published in 1972 by Alexandre Koyrà © Å © and I. Bernard Cohen.

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Next edition

Two later editions were published by Newton:

Second edition, 1713

Newton had been urged to create a new edition of the Principia since the early 1690s, in part because copy of the first edition had become extremely rare and expensive in the years following 1687. Newton referred to his plan. for the second edition in correspondence with Flamsteed in November 1694: Newton also kept an annotated copy of the first edition specifically related to the interleaves he could record for revision; these two copies survived: but he had not yet finalized the revision in 1708, and the two would-be editors, Newton almost severed ties with one, Nicolas Fatio de Duillier, and the other, David Gregory apparently never met Newton's Agreement and was also seriously ill, died later in the year 1708. Nevertheless, the reason for accumulating not delaying the new edition is much longer. Richard Bentley, master of Trinity College, persuaded Newton to allow him to do a second edition, and in June 1708 Bentley wrote to Newton with the first sheet of specimen prints, at the same time expressing the (unmet) hope that Newton had made. progress towards completion of the revision. It seems that Bentley later realized that the editor was technically too difficult for him, and with Newton's approval he appointed Roger Cotes, Plumian's astronomy professor at Trinity, to brief him for him as a sort of deputy (but Bentley still makes regulatory publications and has financial and profit responsibilities). Correspondence 1709-1713 shows Cotes reporting to two masters, Bentley and Newton, and managing (and often correcting) a series of major and important revisions that Newton sometimes can not give his full attention. Under the weight of Cotes' effort, but was hampered by a priority dispute between Newton and Leibniz, and by problems at Mint, Cotes was able to announce his publication to Newton on 30 June 1713. Bentley sent Newton only six copies of the presentation; Cotes are not paid; Newton eliminated the confession to Cotes.

Among those who gave Newton the correction for the Second Edition were: Firmin Abauzit, Roger Cotes and David Gregory. However, Newton omitted some thanks to some of the priority disputes. John Flamsteed, Royal Astronomer, suffers this specifically.

The Second Edition is the basis of the first edition printed abroad, which appeared in Amsterdam in 1714.

Third edition, 1726

The third edition was published March 25, 1726, under the supervision of Henry Pemberton, M.D., a man with the greatest skill in these matters... ; Pemberton later said that this recognition was more valuable to him than two hundred guinea honors from Newton.

Annotations and other editions

In 1739-42, two French priests, PÃÆ'¨res Thomas LeSeur and FranÃÆ'§ois Jacquier (of the Minim order, but sometimes mistakenly identified as Jesuits), were produced with the help of J.L. Calandrini a very annotated version of the Principia in the 3rd edition of 1726. Sometimes this is called the Jesuit edition: it is widely used, and reprinted more than once in Scotland during the 19th century.

ÃÆ' â € ° milie du ChÃÆ' Â ¢ telet also makes the Newtonian translation of Principia into French. Unlike LeSeur and the Jacquier edition, his book is a complete translation of Newton's three books and their prefaces. He also included a Comment section where he combined the three books into a clearer and easier to understand summary. He belonged to the analytical section in which he applied the new mathematical calculus to Newton's most controversial theory. Previously, geometry was the standard mathematical used to analyze theory. Translation Du ChÃÆ' Â ¢ telet is the only complete one that has been done in French and the translation remains the standard French translation to this day.

English translation

Two full English translations of Newton's

Principia have appeared, both based on the 3rd edition of Newton in 1726.

The first, from 1729, by Andrew Motte, is portrayed by the Newtonian scholar I. Bernard Cohen (in 1968) as "still has tremendous value in conveying to us the taste of Newton's words in their own time, and that is generally true to original: clear, and well written ". Version 1729 is the basis for several publications, often incorporating revisions, including the widely used modern English version of 1934, which appears under the name of the editorial Florian Cajori (though completed and published only a few years after his death). Cohen points out ways in which the 1829 terminology and punctuation of the 1729 translation may be confusing to modern readers, but he also made harsh criticisms of the modernized modernized version of English in 1934, and suggests that revisions have been made without pay attention to the original. , also pointed out a big mistake "which gives a final boost to our decision to produce an entirely new translation".

The second full English translation, into modern English, is the work resulting from this decision by collaborating with I. Bernard Cohen, Anne Whitman and Julia Budenz; it was published in 1999 with a guide by way of introduction.

William H. Donahue has published a translation of the main argument of the work, published in 1996, along with the expansion of the included evidence and many comments. This book was developed as a textbook for the class at St. John's College and the purpose of this translation is to be faithful to the Latin text.

Praise

In 2014, the British astronaut Tim Peake named his upcoming mission to the International Space Station Principia after the book, in "the honor of Britain's greatest scientist". The Peake Principia team was launched on December 15, 2015 on board the Soyuz TMA-19M.

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See also

• Atomism
• Newton's Philosophical Elements

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References

Further reading

• Alexandre Koyrà ©  ©, Newtonian Study (London: Chapman and Hall, 1965).
• I. Bernard Cohen, Introduction to Newton's Principia (Harvard University Press, 1971).
• Richard S. Westfall, Strength in Newtonian physics; science dynamics in the seventeenth century (New York: American Elsevier, 1971).
• S. Chandrasekhar, Principia Newton for general readers (New York: Oxford University Press, 1995).
• Guicciardini, N., 2005, "Philosophia Naturalis..." in Grattan-Guinness, I., ed., Landmark Writing in Western Mathematics . Elsevier: 59-87.
• Andrew Janiak, Newton as a Philosopher (Cambridge University Press, 2008).
• FranÃÆ'§ois De Gandt, Forced and geometry in Principia Newton trans. Curtis Wilson (Princeton, NJ: Princeton University Press, c1995).
• Steffen Ducheyne, Main Business Philosophy of Nature: Isaac Newton's Philosophical Methodology (Dordrecht e.a.: Springer, 2012).
• John Herivel, Background of Principia Newton; a study of Newton's dynamic research in 1664-84 (Oxford, Clarendon Press, 1965).
• Brian Ellis, "The Origin and Nature of Newton's Law of Attraction" in Beyond the Edge of Certainty , ed. R. G. Colodny. (Pittsburgh: University of Pittsburgh Press, 1965), 29-68.
• E.A. Burtt, Metaphysical Foundation of Modern Science (Garden City, NY: Doubleday and Company, 1954).
• Colin Pask, Magnificent Principia: Exploring Isaac Newton's Work (New York: Prometheus Books, 2013).

External links

Latin version

First edition (1687)

• Trinity College Library, Cambridge High-resolution digital version of Newton's first edition copy, with annotations.
• Cambridge University, Cambridge Digital Library A high resolution digital version of Newton's own first edition copy, inserted with a blank page for annotations and corrections.
• 1687: Newton Principia , first edition (1687, in Latin). High resolution presentation from copies of Gunnerus Library.
• 1687: Newton Principia , first edition (1687, in Latin).
• The Gutenberg Project.
• ETH-Bibliothek ZÃÆ'¼rich.
• PhilosophiÃÆ'Â| Naturalis Principia Mathematica From Rare Books and Special Collection Divisions at the Library of Congress

Second edition (1713)

• ETH-Bibliothek ZÃÆ'¼rich.
• ETH-Bibliothek ZÃÆ'¼rich (reprint of Amsterdam that was hijacked in 1723).

Third edition (1726)

• ETH-Bibliothek ZÃÆ'¼rich.

Later Latin edition

• Principia (in Latin, annotated). 1833 Glasgow reprints (volume 1) with Book 1 and 2 Latin editions annexed by Leseur, Jacquier and Calandrini 1739-42 (described above).
• Archive.org (1871 reprint edition 1726)

English translation

• Andrew Motte, 1729, the first English translation of the third edition (1726)
  • WikiSource, Partial
  • Google Books, vol.1 with Book 1.
  • Google Books, vol.2 with Books 2 and 3. (Book 3 begins at p.200.) (Google Metadata mislabeled this vol.1).
  • Partial HTML
• Robert Thorpe's 1802 Translation
• N. W. Chittenden, ed., 1846 "American Edition" English version partly modernized, mostly Motte translation of 1729.
  • Wikisource
  • Archive # 1
  • Archive # 2
  • eBooks @ Adelaide eBooks @ Adelaide
• Percival Frost 1863 translation with Archive.org interpolation
• Florian Cajori 1934 modernization 1729 Motte and 1802 Thorpe translation
• Ian Bruce has made a complete translation of the third edition, with notes, on his website.

More links

• David R. Wilkins of School of Mathematics at Trinity College, Dublin has transcribed sections into TeX and METAPOST and created the source, and the.pdf format is available in Extracts from Isaac Newton's Work

Source of the article : Wikipedia