المبادئ الرياضية للفلسفة الطبيعية

Philosophiæ Naturalis Principia Mathematica
Prinicipia-title.png
Title page of Principia, first edition (1686/1687)
العنوان الأصلي Philosophiæ Naturalis Principia Mathematica
اللغة اللاتينية
تاريخ النشر
1687
نـُشـِر بالعربية
1728

Philosophiæ Naturalis Principia Mathematica, Latin for "Mathematical Principles of Natural Philosophy"، وكثيراً ما يشار إليه ببساطة Principia، هو عمل في ثلاث كتب بقلم إسحاق نيوتن، باللاتينية، نُشر لأول مرة في 5 يوليو 1687.[1][2] After annotating and correcting his personal copy of the first edition,[3] Newton also published two further editions, in 1713 and 1726.[4] The Principia states Newton's laws of motion, forming the foundation of classical mechanics, also Newton's law of universal gravitation, and a derivation of Kepler's laws of planetary motion (which Kepler first obtained empirically). The Principia is "justly regarded as one of the most important works in the history of science".[5]

The French mathematical physicist Alexis Clairaut assessed it in 1747: "The famous book of mathematical Principles of natural Philosophy marked the epoch of a great revolution in physics. The method followed by its illustrious author Sir Newton ... spread the light of mathematics on a science which up to then had remained in the darkness of conjectures and hypotheses."[6] A more recent assessment has been that while acceptance of Newton's theories was not immediate, by the end of a century after publication in 1687, "no one could deny that" (out of the Principia) "a science had emerged that, at least in certain respects, so far exceeded anything that had ever gone before that it stood alone as the ultimate exemplar of science generally."[7]

In formulating his physical theories, Newton developed and used mathematical methods now included in the field of calculus. But the language of calculus as we know it was largely absent from the Principia; Newton gave many of his proofs in a geometric form of infinitesimal calculus, based on limits of ratios of vanishing small geometric quantities.[8] In a revised conclusion to the Principia (see General Scholium), Newton used his expression that became famous, Hypotheses non fingo ("I contrive no hypotheses"[9]).

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تمهيد

خاض نيوتن في الكثير من الشؤون العلمية، كما نعرف، وأكد مراراً وتكراراً مركزية الانسان في الكون، وعارض ديكارت في بعض أهم نظرياته، وأكمل عمل كبلر وگاليليو. ووضع الكثير من الكتب والدراسات، ولكن يبقى كتابه «المبادئ الرياضية للفلسفة الطبيعية»، أهم مؤلفاته، لأنه تمكن من أن يلخص في أجزائه الثلاثة أفكاره وتجاربه الكثيرة، ويثبت الكثير من القوانين والقواعد. صحيح ان معظم هذه كانت معروفة ومدروسة منذ الاغريق، وأن عصر النهضة عاد وطوّرها معقلناً إياها، غير ان جهد نيوتن كان اضافة مهمة اليها، وقوننة لها. ولعلنا لا نكون مبالغين إن قلنا أن واحداً من أهم اسهامات نيوتن كان تبسيط تلك القوانين التي كانت قلة في زمنه والأزمان السابقة عليه قادرة على فهمها. وبالتالي كان المجتمع ككل عاجزاً عن تصور حقيقتها. والعالم هيغنز نفسه، الذي عاصر نيوتن، وكان من ألمع الأذهان في زمنه كان لا يفتأ، قبل شروحات نيوتن، يقول إن نظرية الجاذبية ليست أكثر من هراء.


المحتويات

الهدف المعلن والمواضيع المغطاة

Sir Isaac Newton (1643–1727) author of the Principia

In the preface of the Principia, Newton wrote[10]

[...] Rational Mechanics will be the science of motions resulting from any forces whatsoever, and of the forces required to produce any motions, accurately proposed and demonstrated [...] And therefore we offer this work as mathematical principles of philosophy. For all the difficulty of philosophy seems to consist in this—from the phenomena of motions to investigate the forces of Nature, and then from these forces to demonstrate the other phenomena [...]


وضع اسحاق نيوتن كتابه «المبادئ الرياضية للفلسفة الطبيعية» منتصف ثمانينات القرن السابع عشر، ونشره في لندن في العام 1687، ليعتبر منذ ذلك الحين «واحداً من أكثر الأعمال العلمية عبقرية في التاريخ الانساني». والكتاب، كما أشرنا، يتألف من ثلاثة أجزاء تسبقها مقدمة للمؤلف، يشن فيها هجوماً عنيفاً ضد خواء الدراسات الاكاديمية، مقترحاً انه في كتابه سيطبّق الحسابات الرياضية على دراسة الظواهر الطبيعية. وفي الجزءين الأول والثاني من الكتاب، راح يمعن، على ما يعرض ج. د. برنال صاحب كتاب «العلم في التاريخ»، في تحليل الكثير من الأمور والظواهر والقوانين، الى جانب دراسته المعمقة لقوانين حركة الكواكب. وكان «هدفه الأساس»، وفق برنال «اثبات أو شرح كيف ان الجاذبية الأرضية تستطيع المحافظة على نظام الكون» وهو «أراد ان يوضح ذلك ليس من طريق الفلسفة القديمة ولكن بطريقته الكمية الفيزيائية الجديدة». ويرى برنال ان على نيوتن، للوصول الى ذلك، أن ينجز واجبين: أولهما «هدم كل الأفكار الفلسفية القديمة والحديثة»، وثانيهما «إقرار افكاره ليس فقط لصحتها، ولكن لأنها الأكثر موثوقية في عملية عقلنة الظواهر المختلفة». ويؤكد برنال هنا ان «نظرية الجاذبية الأرضية» التي «اكتشفها» نيوتن و «انجازاته الأخرى في العلوم الفلكية تمثل آخر الحلقات في سيرورة إضفاء الصورة التي رسمها ارسطو للكون، تلك السيرورة التي بدأ كوبرينكوس في رسمها. وهكذا، بعدما كانت الصورة الأولية تحدثنا عن أن الكواكب تتحرك بفضل «محرك الأول أو بالملائكة بأمر من الخالق»، صارت الصورة الجديدة صورة سيرورة «ميكانيكية تصل تبعاً لقوانين طبيعية لا تحتاج الى قوى دائمة ولكن تحتاج الى العناية الإلهية لخلقها ودورانها في أفلاكها». وهكذا تمكن نيوتن في التفاف ذكي من أن يترك «الباب مفتوحاً» لضرورة وجود العناية الإلهية من أجل استقرار النظام الفلكي». ومن الملاحظ ان ذلك الفكر «التصالحي» - وفق بعض الدارسين - جاء في وقت انتهت فيه «المرحلة الهدامة لعصري النهضة والإصلاح، وبدأت مرحلة وفاق وتراضٍ بين الدين والعلم».

The opening sections of the Principia contain, in revised and extended form, nearly[11] all of the content of Newton's 1684 tract De motu corporum in gyrum.

The Principia begins with 'Definitions'[12] and 'Axioms or Laws of Motion'[13] and continues in three books:


هذا بالنسبة الى الفكر الذي يسيطر على الجزئين الأولين من الكتاب، أما في الجزء الثالث فإنه يتوصل الى الاستنتاجات الفلسفية، ومن هنا يسمي الجزء «أنظمة العالم». وفيه يجدد المبادئ الفلسفية الأربعة التي ينبغي ان يستلهمها، في رأيه كل بحث وعمل في مجال العلوم الفيزيائية. وهكذا نجده هنا مُطبّقاً على نظام العالم، المبادئ الفلسفية التي حددها في مقدمة الجزء الأول. وهذا ما يجعل مؤرخي العلم يقولون ان «على رغم ان أعظم اكتشافات نيوتن هو اكتشافه قوانين الجاذبية الأرضية، انطلاقاً من دراسة ديناميكية حركة الكواكب، إلا ان اثره الأكبر في العلم هو في ايجاده الطرق العملية التي استخدمها لتحقيق نتائج. فحساب التفاضل والتكامل، الذي أوصله الى ذروته، أعطى العالم طريقة عملية للانتقال من التغير الكمي للأشياء الى الكم نفسه والعكس بالعكس، كما قدم الطرق الرياضية الدقيقة الموصلة الى حل المسائل الفيزيائية. وهو إذ وضع قوانين الحركة التي لم تربط الحركة بالقوة فقط، بل ربطت القوة بتغير الحركة أيضاً، قضى نهائياً على البديهيات القديمة التي كانت تعتقد ان القوة ضرورية لاستمرار الحركة من دون اعتبار لدور الاحتكاك» (برنال).

Book 1, De motu corporum

Book 1, subtitled De motu corporum (On the motion of bodies) concerns motion in the absence of any resisting medium. It opens with a mathematical exposition of "the method of first and last ratios",[14] a geometrical form of infinitesimal calculus.[8]

Newton's proof of Kepler's second law, as described in the book. If an instantaneous centripetal force (red arrow) is considered on the planet during its orbit, the area of the triangles defined by the path of the planet will be the same. This is true for any fixed time interval. When the interval tends to zero, the force can be considered continuous. (Click image for a detailed description).


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الكتاب الأول، De motu corporum

Book 1, subtitled De motu corporum (On the motion of bodies) concerns motion in the absence of any resisting medium. It opens with a mathematical exposition of "the method of first and last ratios",[15] a geometrical form of infinitesimal calculus.[8]

Newton's proof of Kepler's second law, as described in the book. If an instantaneous centripetal force (red arrow) is considered on the planet during its orbit, the area of the triangles defined by the path of the planet will be the same. This is true for any fixed time interval. When the interval tends to zero, the force can be considered continuous. (Click image for a detailed description).


الكتاب الثالث، De mundi systemate

Book 3, subtitled De mundi systemate (On the system of the world) is an exposition of many consequences of universal gravitation, especially its consequences for astronomy. It builds upon the propositions of the previous books, and applies them with further specificity than in Book 1 to the motions observed in the solar system. Here (introduced by Proposition 22,[16] and continuing in Propositions 25–35[17]) are developed several of the features and irregularities of the orbital motion of the Moon, especially the variation. Newton lists the astronomical observations on which he relies,[18] and establishes in a stepwise manner that the inverse square law of mutual gravitation applies to solar system bodies, starting with the satellites of Jupiter[19] and going on by stages to show that the law is of universal application.[20] He also gives starting at Lemma 4[21] and Proposition 40[22]) the theory of the motions of comets, for which much data came from John Flamsteed and Edmond Halley, and accounts for the tides,[23] attempting quantitative estimates of the contributions of the Sun[24] and Moon[25] to the tidal motions; and offers the first theory of the precession of the equinoxes.[26] Book 3 also considers the harmonic oscillator in three dimensions, and motion in arbitrary force laws.


Commentary on the Principia

The sequence of definitions used in setting up dynamics in the Principia is recognisable in many textbooks today. Newton first set out the definition of mass6

The quantity of matter is that which arises conjointly from its density and magnitude. A body twice as dense in double the space is quadruple in quantity. This quantity I designate by the name of body or of mass.


Rules of Reasoning in Philosophy

Perhaps to reduce the risk of public misunderstanding, Newton included at the beginning of Book 3 (in the second (1713) and third (1726) editions) a section entitled "Rules of Reasoning in Philosophy." In the four rules, as they came finally to stand in the 1726 edition, Newton effectively offers a methodology for handling unknown phenomena in nature and reaching towards explanations for them. The four Rules of the 1726 edition run as follows (omitting some explanatory comments that follow each):

Rule 1: We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.

Rule 2: Therefore to the same natural effects we must, as far as possible, assign the same causes.

Rule 3: The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.

Rule 4: In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, not withstanding any contrary hypothesis that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.

This section of Rules for philosophy is followed by a listing of 'Phenomena', in which are listed a number of mainly astronomical observations, that Newton used as the basis for inferences later on, as if adopting a consensus set of facts from the astronomers of his time.

Both the 'Rules' and the 'Phenomena' evolved from one edition of the Principia to the next. Rule 4 made its appearance in the third (1726) edition; Rules 1–3 were present as 'Rules' in the second (1713) edition, and predecessors of them were also present in the first edition of 1687, but there they had a different heading: they were not given as 'Rules', but rather in the first (1687) edition the predecessors of the three later 'Rules', and of most of the later 'Phenomena', were all lumped together under a single heading 'Hypotheses' (in which the third item was the predecessor of a heavy revision that gave the later Rule 3).

From this textual evolution, it appears that Newton wanted by the later headings 'Rules' and 'Phenomena' to clarify for his readers his view of the roles to be played by these various statements.

In the third (1726) edition of the Principia, Newton explains each rule in an alternative way and/or gives an example to back up what the rule is claiming. The first rule is explained as a philosophers' principle of economy. The second rule states that if one cause is assigned to a natural effect, then the same cause so far as possible must be assigned to natural effects of the same kind: for example respiration in humans and in animals, fires in the home and in the Sun, or the reflection of light whether it occurs terrestrially or from the planets. An extensive explanation is given of the third rule, concerning the qualities of bodies, and Newton discusses here the generalisation of observational results, with a caution against making up fancies contrary to experiments, and use of the rules to illustrate the observation of gravity and space.

Isaac Newton’s statement of the four rules revolutionised the investigation of phenomena. With these rules, Newton could in principle begin to address all of the world’s present unsolved mysteries. He was able to use his new analytical method to replace that of Aristotle, and he was able to use his method to tweak and update Galileo’s experimental method. The re-creation of Galileo's method has never been significantly changed and in its substance, scientists use it today.[بحاجة لمصدر]


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General Scholium

The General Scholium is a concluding essay added to the second edition, 1713 (and amended in the third edition, 1726).[27] It is not to be confused with the General Scholium at the end of Book 2, Section 6, which discusses his pendulum experiments and resistance due to air, water, and other fluids.

Here Newton used what became his famous expression Hypotheses non fingo, "I contrive no hypotheses",[9] in response to criticisms of the first edition of the Principia. ('Fingo' is sometimes nowadays translated 'feign' rather than the traditional 'frame'.) Newton's gravitational attraction, an invisible force able to act over vast distances, had led to criticism that he had introduced "occult agencies" into science.[28] Newton firmly rejected such criticisms and wrote that it was enough that the phenomena implied gravitational attraction, as they did; but the phenomena did not so far indicate the cause of this gravity, and it was both unnecessary and improper to frame hypotheses of things not implied by the phenomena: such hypotheses "have no place in experimental philosophy", in contrast to the proper way in which "particular propositions are inferr'd from the phenomena and afterwards rendered general by induction".[29]

Newton also underlined his criticism of the vortex theory of planetary motions, of Descartes, pointing to its incompatibility with the highly eccentric orbits of comets, which carry them "through all parts of the heavens indifferently".

الكتابة والنشر

Halley and Newton's initial stimulus

في يناير 1684، هالي ورن وهوك had a conversation in which Hooke claimed to not only have derived the inverse-square law, but also all the laws of planetary motion. Wren was unconvinced, Hooke did not produce the claimed derivation although the others gave him time to do it, and Halley, who could derive the inverse-square law for the restricted circular case (by substituting Kepler's relation into Huygens' formula for the centrifugal force) but failed to derive the relation generally, resolved to ask Newton.[30]

النسخة المبدئية

Newton's own first edition copy of his Principia, with handwritten corrections for the second edition.

The process of writing that first edition of the Principia went through several stages and drafts: some parts of the preliminary materials still survive, others are lost except for fragments and cross-references in other documents.[31]


السياق التاريخي

بداية الثورة العلمية

Nicolaus Copernicus (1473–1543) was the first person to formulate a comprehensive heliocentric (or Sun-centered) model of the universe

Nicolaus Copernicus had moved the Earth away from the center of the universe with the heliocentric theory for which he presented evidence in his book De revolutionibus orbium coelestium (On the revolutions of the heavenly spheres) published in 1543. The structure was completed when Johannes Kepler wrote the book Astronomia nova (A new astronomy) in 1609, setting out the evidence that planets move in elliptical orbits with the sun at one focus, and that planets do not move with constant speed along this orbit. Rather, their speed varies so that the line joining the centres of the sun and a planet sweeps out equal areas in equal times. To these two laws he added a third a decade later, in his book Harmonices Mundi (Harmonies of the world). This law sets out a proportionality between the third power of the characteristic distance of a planet from the sun and the square of the length of its year.

Italian physicist Galileo Galilei (1564–1642), a champion of the Copernican model of the universe and an enormously influential figure in the history of kinematics and classical mechanics

The foundation of modern dynamics was set out in Galileo's book Dialogo sopra i due massimi sistemi del mondo (Dialogue on the two main world systems) where the notion of inertia was implicit and used. In addition, Galileo's experiments with inclined planes had yielded precise mathematical relations between elapsed time and acceleration, velocity or distance for uniform and uniformly accelerated motion of bodies.

Controversy with Hooke

Imaginary portrait of English polymath Robert Hooke (1635–1703).

Hooke published his ideas about gravitation in the 1660s and again in 1674. He argued for an attracting principle of gravitation in Micrographia of 1665, in a 1666 Royal Society lecture On gravity, and again in 1674, when he published his ideas about the System of the World in somewhat developed form, as an addition to An Attempt to Prove the Motion of the Earth from Observations.[32] Hooke clearly postulated mutual attractions between the Sun and planets, in a way that increased with nearness to the attracting body, along with a principle of linear inertia. Hooke's statements up to 1674 made no mention, however, that an inverse square law applies or might apply to these attractions. Hooke's gravitation was also not yet universal, though it approached universality more closely than previous hypotheses.[33] Hooke also did not provide accompanying evidence or mathematical demonstration. On these two aspects, Hooke stated in 1674: "Now what these several degrees [of gravitational attraction] are I have not yet experimentally verified" (indicating that he did not yet know what law the gravitation might follow); and as to his whole proposal: "This I only hint at present", "having my self many other things in hand which I would first compleat, and therefore cannot so well attend it" (i.e., "prosecuting this Inquiry").[32]


مواقع النسخ

A page from the Principia

Several national rare-book collections contain original copies of Newton's Principia Mathematica, including:

الترجمات الإنگليزية

Two full English translations of Newton's 'Principia' have appeared, both based on Newton's 3rd edition of 1726.

Homages

British astronaut Tim Peake named his 2014 mission to the International Space Station Principia after the book, in "honour of Britain's greatest scientist".[35]

انظر أيضاً

هناك كتاب ، Isaac Newton، في معرفة الكتب.


المراجع

  1. ^ Among versions of the Principia online: [1].
  2. ^ Volume 1 of the 1729 English translation is available as an online scan; limited parts of the 1729 translation (misidentified as based on the 1687 edition) have also been transcribed online.
  3. ^ Newton, Isaac. "Philosophiæ Naturalis Principia Mathematica (Newton's personally annotated 1st edition)".
  4. ^ [In Latin] Isaac Newton's Philosophiae Naturalis Principia Mathematica: the Third edition (1726) with variant readings, assembled and ed. by Alexandre Koyré and I Bernard Cohen with the assistance of Anne Whitman (Cambridge, MA, 1972, Harvard UP)
  5. ^ J M Steele, University of Toronto, (review online from Canadian Association of Physicists) of N Guicciardini's "Reading the Principia: The Debate on Newton’s Mathematical Methods for Natural Philosophy from 1687 to 1736" (Cambridge UP, 1999), a book which also states (summary before title page) that the "Principia" "is considered one of the masterpieces in the history of science".
  6. ^ (in French) Alexis Clairaut, "Du systeme du monde, dans les principes de la gravitation universelle", in "Histoires (& Memoires) de l'Academie Royale des Sciences" for 1745 (published 1749), at p.329 (according to a note on p.329, Clairaut's paper was read at a session of November 1747).
  7. ^ G E Smith, "Newton's Philosophiae Naturalis Principia Mathematica", The Stanford Encyclopedia of Philosophy (Winter 2008 Edition), E N Zalta (ed.).
  8. ^ أ ب ت The content of infinitesimal calculus in the 'Principia' was recognized both in Newton's lifetime and later, among others by the Marquis de l'Hospital, whose 1696 book "Analyse des infiniment petits" (Infinitesimal analysis) stated in its preface, about the 'Principia', that 'nearly all of it is of this calculus' ('lequel est presque tout de ce calcul'). See also D T Whiteside (1970), "The mathematical principles underlying Newton's Principia Mathematica", Journal for the History of Astronomy, vol.1 (1970), 116–138, especially at p.120.
  9. ^ أ ب Or "frame" no hypotheses (as traditionally translated at vol.2, p.392, in the 1729 English version).
  10. ^ From Motte's translation of 1729 (at 3rd page of Author's Preface); and see also J. W. Herivel, The background to Newton's "Principia," Oxford University Press, 1965.
  11. ^ The De motu corporum in gyrum article indicates the topics that reappear in the Principia.
  12. ^ Newton, Sir Isaac (1729). "Definitions". The Mathematical Principles of Natural Philosophy, Volume I. p. 1.
  13. ^ Newton, Sir Isaac (1729). "Axioms or Laws of Motion". The Mathematical Principles of Natural Philosophy, Volume I. p. 19.
  14. ^ Newton, Sir Isaac (1729). "Section I". The Mathematical Principles of Natural Philosophy, Volume I. p. 41.
  15. ^ Newton, Sir Isaac (1729). "Section I". The Mathematical Principles of Natural Philosophy, Volume I. p. 41.
  16. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 252.
  17. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 262.
  18. ^ Newton, Sir Isaac (1729). "The Phaenomena". The Mathematical Principles of Natural Philosophy, Volume II. p. 206.
  19. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 213.
  20. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 220.
  21. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 323.
  22. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 332.
  23. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 255.
  24. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 305.
  25. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 306.
  26. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 320.
  27. ^ See online Principia (1729 translation) vol.2, Books 2 & 3, starting at page 387 of volume 2 (1729).
  28. ^ Edelglass et al., Matter and Mind, ISBN 0-940262-45-2, p. 54.
  29. ^ See online Principia (1729 translation) vol.2, Books 2 & 3, at page 392 of volume 2 (1729).
  30. ^ Paraphrase of 1686 report by Halley, in H. W. Turnbull (ed.), 'Correspondence of Isaac Newton', Vol.2, cited above, pp. 431–448.
  31. ^ The fundamental study of Newton's progress in writing the Principia is in I. Bernard Cohen's Introduction to Newton's 'Principia' , (Cambridge, Cambridge University Press, 1971), at part 2: "The writing and first publication of the 'Principia' ", pp.47–142.
  32. ^ أ ب Hooke's 1674 statement in "An Attempt to Prove the Motion of the Earth from Observations", is available in online facsimile here.
  33. ^ See page 239 in Curtis Wilson (1989), "The Newtonian achievement in astronomy", ch.13 (pages 233–274) in "Planetary astronomy from the Renaissance to the rise of astrophysics: 2A: Tycho Brahe to Newton", CUP 1989.
  34. ^ Newton, Isaac. "Philosophiæ naturalis principia mathematica". Cambridge Digital Library. Retrieved 3 July 2013.
  35. ^ http://www.bbc.com/news/science-environment-28329097

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للاستزادة

  • Alexandre Koyré, Newtonian studies (London: Chapman and Hall, 1965).
  • I. Bernard Cohen, Introduction to Newton's Principia (Harvard University Press, 1971).
  • Richard S. Westfall, Force in Newton's physics; the science of dynamics in the seventeenth century (New York: American Elsevier, 1971).
  • S. Chandrasekhar, Newton's Principia for the common reader (New York: Oxford University Press, 1995).
  • Guicciardini, N., 2005, "Philosophia Naturalis..." in Grattan-Guinness, I., ed., Landmark Writings in Western Mathematics. Elsevier: 59–87.
  • Andrew Janiak, Newton as Philosopher (Cambridge University Press, 2008).
  • François De Gandt, Force and geometry in Newton’s Principia trans. Curtis Wilson (Princeton, NJ: Princeton University Press, c1995).
  • Steffen Ducheyne, The main Business of Natural Philosophy: Isaac Newton’s Natural-Philosophical Methodology (Dordrecht e.a.: Springer, 2012).
  • John Herivel, The background to Newton's Principia; a study of Newton's dynamical researches in the years 1664–84 (Oxford, Clarendon Press, 1965).
  • Brian Ellis, "The Origin and Nature of Newton's Laws of Motion" in Beyond the Edge of Certainty, ed. R. G. Colodny. (Pittsburgh: University Pittsburgh Press, 1965), 29–68.
  • E.A. Burtt, Metaphysical Foundations of Modern Science (Garden City, NY: Doubleday and Company, 1954).
  • Colin Pask, Magnificent Principia: Exploring Isaac Newton's Masterpiece (New York: Prometheus Books, 2013).

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Philosophiae Naturalis Principia Mathematica


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