Philosophiæ Naturalis Principia Mathematica (Latin for Mathematical Principles of Natural Philosophy), often referred to as simply the Principia, is a work in three books by Isaac Newton, in Latin, first published 5 July 1687. After annotating and correcting his personal copy of the first edition, Newton also published two further editions, in 1713 and 1726. The PrincipiaPhilosophiæ Naturalis Principia Mathematica (Latin for Mathematical Principles of Natural Philosophy), often referred to as simply the Principia, is a work in three books by Isaac Newton, in Latin, first published 5 July 1687. After annotating and correcting his personal copy of the first edition, Newton also published two further editions, in 1713 and 1726. 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". 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." 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." 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. In a revised conclusion to the Principia (see General Scholium), Newton used his expression that became famous, Hypotheses non fingo ("I contrive no hypotheses")....
Title  :  The Mathematical Principles of Natural Philosophy 
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ISBN  :  30643862 
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The Mathematical Principles of Natural Philosophy Reviews

Of course I have never read the entire text of this monumental work. I did read several parts of it in the period 19721974 when I was studying the History & Philosophy of Science at the University of Melbourne, and still have the two volume paperback set printed by the University of California Press in 1974 (originally published by UC in 1934).There are a lot of mathematical proofs scattered throughout the volumes, which were mostly less interesting to me than parts I could read as simply literature in the history of ideas. The average modern reader can probably gain a lot of insight simply by paging through the Principia and stopping to read anything that looks interesting. There are a few things that are not to be missed however: the Prefaces that Newton wrote to the first three editions; the Preface to the second edition that his disciple, Roger Cotes, wrote; Newton's Definitions and Axioms, or Laws of Motion following the Prefaces; his Rules of Reasoning in Philosophy at the beginning of Book III; and, if your edition includes it, the Historical and Explanatory Appendix contributed by Florian Cajori for the 1934 UC edition. In his lengthy and fascinating preface, Cotes lays out in layman's language, but in great detail, Newton's thinking about the philosophical questions surrounding gravity, his (Newton's) views of some of his predecessors (Boyle, Huygens, Descartes, Galileo), and hints at the proper view of God's relationship to the physical world. (This latter topic, and its relation to Newton's theory of gravity, formed the basis of the famous LeibnizClarke correspondence/controversy. I began to do a Master's thesis on this topic in 1974, but gave it up after returning to the States and my previous job in 1975. One of life's turning points.)The Principia is divided into three Books. Book I: The Motion of Bodies, Book II: The Motion of Bodies (In Resisting Mediums), and Book III: The System of the World. The most accessible part of the Principia for most readers is Book III, in which we find Newton's description of the physical phenomena which his work explains, and the fascinating (indeed, astounding) manner in which he uses the propositions and theorems of the first two books to demonstrate the laws of motion of the heavenly bodies, first observationaly established by Kepler almost 80 years before Newton's work.It is impossible to overstate the importance of the Philosophiae Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy) in the history of science, the history of ideas, and indeed in the history of Western civilization. It is one of the crowning glories of man's ability to observe and explain the natural world, a majestic tourdeforce.

What did i learn from this book?I finally learned why Newton is a genius. Why the planets stay in orbit. Why reason finally and forever took the place of authority. I learned when science was once and for all declared the way to "know". I learned why calculus is necessary and why Newton invented it. I learned why math is the language of the universe. I learned why geometry is so important.I am in awe of Newton. Everything and everyone who followed him was influenced by him. Not just in the science world. In politics and economics and every other field. A mind like his only happens once in a blue moon, oh, and i also learned that the moon is always falling towards the earth! And none of this discounts the presence of Gd.

I tried. But this is Newton using geometry to explain the calculus behind his theory of gravity. Every few pages, between the charts and equations, he writes a one or two sentence introduction to the proposition about to be proved. I understood those. Mostly. And I could see this is where Newton’s Laws of Motions come from. His proofs are beyond me though.Interestingly, one of the few other things I could understand, beyond his Preface, was the General Scholium at the end. After describing the heliocentric solar system, he launches into the modern equivalent of an Intelligent Design argument:All that diversity of natural things which we find suited to different times and places could arise from nothing but the ideas and will of a Being necessarily existing. Pg. 442. Newton’s fascination with Biblical history, alchemy and the occult has been credited with helping him believe in a gravitational force that pervades all matter and affects things unseen at distance. A fascinating mix of science and faith. He was probably as enigmatic as his equations seem to me.I’m sure this book is worth ten stars but, in the interest of intellectual honestly, I’m personally not qualified to rate it.

First, A Clarification: The publication I have is the hardcover revision by Florian Cajori of Andrew Motte's 1729 English translation, copyrighted in 1934 by the Regents of the University of California, and published by UC Berkeley and UCLA Press.I should also note that, although I have read Newton's Principia several times over several years and for various reasons, I doubt I have ever completed the whole book. To do so would be advisable only under limited circumstances.For whatever reason, Newton did not meticulously document his propositions. Hence, the Principia requires its reading audience to do a fairly significant amount of sleuthing to reach a workable grasp of just one proposition. Once completed, congratulate yourself. You have extracted the ten or twenty steps needed to prove a proposition. Now you can confidently advance to the next propositionon page two.To describe Newton's Principia as dense is clichéd, fuzzy, and simplistic, but for 98% of us, dense is most appropriate. If previous generations truly had less trouble with reading Principia, then... WOW... our reading skills have certainly plummeted.Yes, it's true that Newton's Principia changed the world, and is undoubtedly near or at the top of the greatest work ever. Unfortunately, few will directly experience its unvarnished power. Regardless, the endeavor to undertake the challenge is highly recommended and greatly rewarding. Good luck!!

Одма да кажем да немам шта паметно да кажем о овој књизи јер је Њутн ипак можда мало пренапредан за мене. На почетку сам покушавао да пратим и донекле успијевао, али то није дуго потрајало јер су ствари врло брзо постале прекомпликоване. Наравно, овакве научне класике данас је практично немогуће читати без разноразних додатних објашњења и коментара, којих у овом издању нажалост нема, мада морам да напоменем да имам (у папирном облику) једну апсолутну звијер од издања, тешку једно сто кила, са ооооооооооогромним уводом и гомилетином коментара, што такође планирам некад да прочитам, е не бих ли много боље разумио. Ово издање које сам читао је за Киндл и није препоручљиво ако планирате да се удубљујете у материју, зато што су неке формуле тешко читљиве, неким табелама фале комади, а и неке слике се не виде добро. Препоручљиво је ако желите, као ја сад, само да прелетите да бисте видјели о чему се ту отприлике ради.Мало конкретнији ривју слиједи... ахем... за неколико година :)

One of the most intelligent and influential books of all time. Period. This is an older read I remember fondly enough to rate the full 5 stars even though it has been a while.

I learned that there are some problems which simply cannot be solved with a particular framework; that Bezier curves are a fantastic introduction to the philosophical principles of the calculus; that I can, in fact, do math.

The original book is one of the foundational books for modernity, expounding both mechanics and the calculus while explaining astronomy. (The little digression at the end into theology can be ignored.)One can imagine an eedition of this book where, as one reads the description of the ratio of this or that, the relevant lines on the diagram were highlighted. Even better, when areas are described by line segments belonging to the same line, the eedition could add a side diagram with links to the original diagram.That lacking, a print edition could make sure the diagrams are always available without flipping pagesnot true for this one, and make sure the labels are always clear and mutually distinguishable.Any edition would be improved with some supplemental materials. It is perhaps reasonable to expect familiarity with Euclid's rules of triangles, but a glossary entry for items like the 'latus rectum' of a conic section would be most helpful.It would also be nice to explain verbal terms like 'subduplicate ratio' that moderns bury in algebraic notation. The help could be in an introduction, in a footnote upon first use or in a glossary. Their pretty clear from context, so this isn't a necessity.

This book, written by Isaac Newton in 1588, served as the foundation of physics for more than 300 years, or up to the time Einstein developed relativity theory. The fact that it is still in print more than 400 years after being written puts it in nearly the same class as the bible. One does not actually read this book so much as marvel at it. The book is chock full of hundreds of geometric diagrams which essentially deal with systematic measurement and calculation. The thing that strikes one most is the lack of elaborate equations, even though Newton was a major impetus in the development of equationcentric calculus. Contrast this with the typical hardcore science works of today which can be full of elaborate equations of arcane notation and interest. This is a slow contemplative read, and deserves to be on your science book shelf.

 an ingenious and energetic builder who's astonishingly brilliant at composing gorgeous monuments of the most intensely clever design. Sometimes these appear as great books like the Principia itself. Sometimes they appear in experiments. But we would be wrong to look for a single key which unlocks the whole mystery of Isaac Newton.The Mathematical Principles of Natural Philosophy (1729) ... An English translation by Andrew Motte, based on the 1726 3rd edition of Philosophiae Naturalis Principia Mathematica.Download Link: https://archive.org/download/newtonsp...copyright status: NOT_IN_COPYRIGHT

Newton unleashed one of the most startling scientific undertakings in history with his seemingly simple question posed in this hallowed treatise: what would happen if seven people representing various socioeconomic strata of American life were stranded together on a desert island? In the centuries since the publication of this philosophical juggernaut men have agonized over the fundamental question of whether to sleep with Ginger or Mary Ann…but what about the old broad? Why doesn’t anyone go that route? Newton himself was obviously enthralled with the Skipper and his ample buttocks. He liked a big ass, that’s just how they rolled back then.

This book stands as one of the great monuments of science. If you can peer through the ponderous geometric proofs of Newton's physical principles, there is an elegance to his theories that transcends mere science and mathematics and touches the sublime! He actually formulated his theories using his newlyinvented methods of Calculus, but few educated readers of his day understood the Calculus, so he proved his ideas using the methods of geometry (which all educated persons knew). We owe much of modern civilization to this book.

I don't want to create a whole new shelf for this, but I didn't read it  I gave up after reading as far as I could. My giving up has nothing to do of course with this historical book of the highest importance. However, given that the subject is complex and the language arcane I am afraid I would need an interpreter for both concept and language.I'll stick to learning my physics from more modern sources. I love reading original sources, and for the things I could grasp this book was very intriguing. I just wish my autodidactic capabilities could reach this far.I yield.

Hard going since Newton was so shy about using easy calculus when hard analytic geometry could do the job. Still, this is one of the most important books ever written and anyone with an interest in the history of science (or in seeing Newton draw up an epistemology at the start of book three to keep his critics from savaging him like they did with his Optics) should carve out a few months, get a bunch of paper, and go to.

To see how the great man thought...

This book helps me a lot.

Therefore, He was a real genius.Sir Isaac Newton,Chapeau!

I wrote in Chinese, very long, too lazy to translate~总评： 当初想到读这本经典的缘起是什么呢？ 是因为我读广义相对论的时候，意识到爱因斯坦所破的是很多传统观念的冗余，于是我尝试去读类似于《费恩曼物理学讲义》，然而却没有感觉，并且意识到——这种冗余已经很沉重，需要追根溯源，同时我还思考为什么物理学没有进行公理化，很多地方是漫漶不清的。于是开始阅读《自然哲学的数学原理》，追根溯源进行研究，并且我坚持认为运动学的本质应该是变分法，因此计划读完之后去读朗道的力学。同时发现，牛顿当初已经进行了公理化尝试，然而并没有归结到本质性问题（数学工具的不足）。在阅读到一半时，为了追求更本源，去读了亚里士多德的《物理学》，大失所望，才明白牛顿的正经祖宗并不是亚里士多德，而是阿基米德。 牛顿的写书意识逻辑是非常优美清晰的，比伽利略的作品要好很多了。然而其很多观点是建立在伽利略的观点基础上（如惯性的观念等），是伽利略观点的体系化、规范化。虽然都伽利略的书会少趣味，但还是看一看伽利略的力学观点《关于两门新科学的谈话》吧，动力学概念的源头，还是要寻找到伽利略头上啊。牛顿是一个伟大的演绎者，而非概念的原创者~ 在第一和第二编里，牛顿的“力”的概念，均是从作用的效果而非原因来看待的，包括向心力和阻滞力，这是牛顿提出为了解释运动的工具，而并不关注其如何产生以及机理本质是什么。（在第11章最后附注中有很好的说明） 因此，第一编牛顿关于“效果力 ”的概念为“向心力”，就是指指向点中心的吸引力，探讨不同轨迹下向心力的不同形式最终回到主体对圆锥曲线轨道的探讨上来；第二编，则引入新的“效果力”阻滞力，探讨引入不同形式阻滞力之后物体的运动状态。综上所述，提出这两个力的概念无不是为了研究运动的状态。注意：牛顿的“向心力”与我高中教育时候所灌输的“向心力”有很大的区别。牛顿的向心力的概念与“吸引力”是同一个层次，而我们的“向心力”的概念则更冗杂，所有指向中心的力皆源于此。导读： 牛顿认为宇宙的优美来自于上帝。 哥白尼的天体运行论是用神学的语言书写的，伽利略认为自然的语言是数学，并且写了两部名著，伽利略死后十天，牛顿出生。 牛顿出世前面对的最大的宇宙体系是笛卡尔体系，其创造了一些描述性的模型，并且笛卡尔是首次将运动引入几何的人（这很牛逼啊，因为之前的力学实际上就是静力学；当然之后的牛顿把运动的几何学发展到巅峰了），然而其自然哲学多有舛误不合验证（星体旋转的涡旋假说） 牛顿的作品非常注重格式规范，模仿欧几里得。分为“定义”、“运动的公理或定律”、“引理”（数学工具）、“命题”（本书正题）。 牛顿的命题分为“定理”和“问题”，定理是得出的基础性的结论，而问题则是通过基础性的结论来解决实在的问题。或者说，“定理”是建立在自己假说之上的演绎，是纯数学的，而“问题”往往和物理世界联系。 牛顿通过圆周运动的规律，提出平方反比定律，这是牛顿宇宙论最重要的基石。进而提出万有引力定律。（从由天体运行的椭圆轨道，得到平方反比力的规律，并比不上什么（牛顿在第一编做完的事）；然而从平方反比定律推广到万有引力定律，这实际上是非常疯狂的想象力！非常非常宏大、优美的推广！而且最终发现其在数学上的完美符合现实）并能通过万有引力定律预言星体的质量。然而牛顿无法解释万有引力的成因。（实际上这就是他“猜”出来的理论规律，是一个通过不可观察的“力”概念建立的理论模型从而实现对于观察结果的解释。） 全书分为三编： 第一编几乎已经囊括了所有的内容。 第二编是第一编的应用（物体在阻滞介质中的运动、流体） 第三编是牛顿的宇宙论，解释天体运行。 牛顿认为以太是不存在的（颠覆从亚里士多德到笛卡尔，然而直到十九世纪末人们还拿着以太模型，可见革新之困难）定义： 牛顿三定律，以及定义的去歧义的工作，是牛顿自己的思想吗？力的加速度定律应该不是其原创？还是伽利略早就有此观念，牛顿将其标准化以及进行演绎？需要阅读伽利略。真的是做笔记开始思考的时候才能明白自己要做啥呀运动的公理或定律： 以上两部分提纲挈领，等读完第一编再写读后感。需要读完伽利略再来写读后感。这两部分是牛顿自然哲学很重要的核心，也是后来爱因斯坦等人着力修正的地方。第一编 物体的运动 第一章 （全为引理，共11条引理，创造出数学工具：微积分） 第二章 向心力的确定 （命题1~10，引理12） 命题1~4均为“定理”，面积与时间成正比（开普勒第二定律），是与“存在指向点的向心力”等价的（并不依赖于力的形式）。将轨道问题转化为用力描述的问题。 命题5~10为“问题”，根据轨道的不同形态，导出向心力的不同解。在命题10里提出指向椭圆中心对应的力的形式（不是焦点而是中心，结论并非平方反比定律，而是与距离成正比）（此时牛顿仅是根据轨道的不同形式提出力的形式，都是数学，处于假说演绎阶段，没有验证） 最后的附注指出，将椭圆的中心移动到无穷远处，就得到抛物线！ 这一章明确了利用向心力的理论工具入手。 第三章 物体在偏心的椭圆轨道上的运动 （命题11~17，引理13、14） 命题11~13均为“问题”，依旧延续第二章的解决思路，但是指出：轨迹为椭圆、双曲线、抛物线并以焦点为力心时候，力的形式为平方反比定律。（以开普勒第一定律为条件，得出力的形式） 命题14~16为“定理”，得出了环绕中心按照平方反比向心力运行的天体体系之间的关系，进而得出开普勒第三定律的形式。 命题17为“问题”，解决了轨道的预言问题，已知平方反比力和速度，预言其未来轨道。 到第三章为止，牛顿已经可以将开普勒的规律完全按照伽利略的思路来解释，纳入一个优美的体系。 第四、五、六章 （命题18~31，引理15~28） 已知焦点求椭圆、抛物线和双曲线轨道； 焦点未知时怎样求轨道； 焦点未知时怎样求轨道。 这三章所有命题均为“问题”，都是探讨的圆锥曲线的几何问题。 第七章 物体的直线上升或下降 （命题32~39） （很令人惊奇，平方反比吸引力下求给定时间内的下落距离，牛顿是用面积法则来做的！） 命题32是“问题” 命题33~35、38是“定理” 命题36~39是“问题” 这一章里的探讨离开静态的“轨道”的范畴，进而开始研究时间、运动、距离的问题。圆锥曲线上的运动问题。 第八章 受任意向心力作用的物体环绕轨道的确定 （命题40~42） 这一章3个命题，分为一个定理两个问题。内容如题目所示，任意向心力的轨道，可以用计算机模拟，不要太舒服（但是是非分析解）。 第九章 沿运动轨道的物体运动；回归点运动 （命题43~45） 这一章的意义在于，探讨限定轨道的运动，也就是一维的运动。 第十章 物体在给定表面上的运动；物体的摆动运动 （命题46~56） 探讨限定曲面的，也就是二维的运动。同时探讨了物体摆动的规律（伽利略时钟） 这里提到，（命题47）如果中心力的形式是正比于到中心的距离，那么轨道也会是椭圆；如果是直线运动，那么在相同时间里完成各自的周期（这不就是谐振运动吗？）我在这里惊愕了一下，想不应该是平方反比吗？然后意识到这是中心而非焦点。高中物理以圆周运动而非椭圆运动切入是非常不良的，因为中心与焦点重合。而牛顿所探讨的概念，实际是泛函层面的了，按照圆周运动研究，很容易混淆两个函数。 第十一章 受向心力作用物体的相互吸引运动 （命题57~69） 这一章开始，牛顿开始研究二体运动，而非固定吸引中心，这离现实世界的情形更加接近了（在命题66推广到三体）。另外牛顿也指出：他目前的研究都是纯数学的，将物理放到一边。 第十二章 球体的吸引力 （命题70~84，引理29） 如在牛顿第十一章最后附注指出，从这一章开始，牛顿不再以“力的效果”（运动产生的可观察效果）来进行考虑，转而开始考虑“力的成因”（平方反比力所具有的性质）。这里，牛顿将平方反比力的概念替换掉观察到的椭圆运动的概念，用“力”来刻画运动给了其强大的研究武器。这一章，牛顿不再提“向心力”而是“吸引力”，其将力的概念从天体间的吸引推广到每一个无限小质量部分了。 命题70~80为定理，将平方反比力模型应用到球体的每个部分，并分别考察球体内、球体外的作用效果（得出的结论惊人的优美，球壳内不受力球壳外等效于受质点力等等发） 第十三章 非球体的吸引力 （命题85~93） 第十四章 受指向击打物体各部分的向心力推动的极小物体的运动 （命题94~98） 这里通过力的观念的除了类似于光的折射规律。这一章的理念不是很明白，题目的命名也令人费解。第二编 物体（在阻滞介质中）的运动 引入了另一种“效果力”——阻滞力，并研究不同形式阻滞力对运动的影响。 第一章 受与速度成正比的阻力作用的物体运动 第二章 受正比于速度平方的阻力作用的物体运动 第三章 物体受部分正比于速度部分正比于速度平方的阻力的运动 第四章 物体在阻滞介质中的圆运动 第五章 流体密度和压力；流体静力学 （命题19~23，流体定义） 这一章给出了流体的定义，并研究了流体静力的观念（没有阻滞力的），给之后进一步的讨论奠定理论基础。（这一章内容是站在哪位巨人的肩膀上呢？静力学的基础是阿基米德，流体静力学也是吗？） 第六章 摆体的运动与阻力 在阻滞空力作用下单摆的运动规律。 牛顿对于摆体的研究似乎非常在意，疑惑：这是很重要的模型吗？ 第七章 流体的运动，及其对抛体的阻力 这一章开始研究流体内的阻力作用，并有实验验证 第八章 通过流体传播的运动 牛顿将流体看作粒子组成。看来牛顿已经有默认的“微粒组成万物”的观念，或者说原子的观念了。 这一章的主体，是研究流体上的波。 第九章 流体的圆运动 主要是研究涡旋，同时给笛卡尔学说知名的打击第三编 宇宙体系（使用数学的论述） 按照这一编的前言，其数学基础是：定义、公理部分加上第一编的前三章。牛顿开始用其创造出的理论工具，按照最简单的原则，有序地解释这个宇宙了！ 哲学中的推理规则 （牛顿四规则）： 这是牛顿的科学哲学： 规则一，简单性（自然倾向简单，这就是奥卡姆剃刀！） 规则二，普适规律（寻找能普遍解决的规律） 规律三，实验规律视作普适规律（默认实验的可重复性） 规律四，对经验规律可靠性的坚持（我想，其实牛顿对于其平方反比的万有引力定律也是不自信的，因为他并不明白其机制是什么） 现象： 牛顿以开普勒定律为底本，加上木星土星卫星以及月球的运行规律，描述观察到的天文现象 命题 （共33条命题） 感觉牛顿虽然是按照标准的体例写的，但其实有点乱。定理、问题分得不太清，层次递进的关系也不明确。而其万有引力定律也是在一个定理中（命题7、8）提出，这实际上是极其重大的推广。而牛顿当初却似乎把这重要的原理，隐藏在了定理与实际问题之中，从这个程度而言，牛顿的作品很伟大，但没有达到“艺术品”高度，当然，这是指他写的书（和欧几里得相比）。但其思想经过归纳整理，是当之无愧的艺术平。 月球交会点的运动 这是处理具体的问题了，实际上上一部分已经处理了好多了总释 总释真的非常精彩！ 总释里牛顿先是打击了用涡旋解释行星运动的模型。 然后提出了波义耳的真空实验，验证其阻滞观念（波义耳也是牛顿站立其上的一个“巨人”，有必要去读一读这位化学家，我发现，无论物理、生物、化学，都是自然哲学的不同剖面！）。 然后牛顿赞美了伟大的上帝，牛顿相信全知全能的上帝！并且牛顿表示，要想认识上帝，没有比自然哲学更好的手段了！（是的，我们学习物理，实际上才是一群真正的朝圣者） 在倒数第二段，牛顿很明确理解自己学说的局限性：引力理论是一个对运动的解释，而牛顿对于其原理一无所知。（牛顿说的“我不构造假说”，意思是我不会提出假设的东西来探讨引力的原因是什么，我以前的理解都断章取义了！可见读原典可以消除断章取义！）在这里牛顿不得不化为实用主义者，他表示“对于我们来说，能知道引力确实存在着，并按我们所揭示的规律起作用，并能有效地说明天体和海洋的一切运动，即已足够了”。 因此，从这个层面而言，牛顿的“引力理论”，他自己也意识到不过是“经验定律”而算不上是引力理论。爱因斯坦的广义相对论的引力场方程 ，并不是颠覆牛顿的学说，实际上是补上了一块拼图。爱因斯坦用时空弯曲的概念，通过对运动更加深入的探讨，将引力的本质解释提出来。爱因斯坦不是牛顿的颠覆，而是牛顿的补完。由于是本质解释的优越性，其精度定然是会超过牛顿定律这是毋庸置疑的（牛顿四规则里实际上已经预言到了），并且即便是广义相对论没有实现任何对牛顿定律的修正，它也是伟大的，因为它实现了更本质的统一，将这个“力”的概念消除了，划归为了自然运动。 在最后一段里，牛顿意识到自己虽然解释了天空和大海，但自己依旧面对着真理的海洋。要解释世界，还是很远的路途。牛顿是人类历史的一个里程碑，功在万代千秋。

The Principia (1687) was Isaac Newton's grand synthesis of (1) Copernicus' heliocentric theory, (2) Kepler's three planetary laws, (3) Galilei's study's of motion and forces and (4) Netwon's own mathematical analysis. It was more than this though; it was the first philosophical system of the world since Aristotle's philosophy (which had been used by christian theologians since the 12th century as the system of the world).Newton writes this book in the style of Euclidean geometry: starting with axioms and then deducing, step by step, new truths. This, in combination with the complexity and Newton's notation of the mathematics used, makes the Principia almost impossible to read for modern day readers. Not that it was easier for contemporaries  it was only in the 18th century that this raw material was digested enough for third parties to write more accessible accounts of the new mechanics.In essence, Newtons explains the motion of all the matter in the universe; he does this with three laws of motion and the (infamous) universal law of gravitation.Netwon's three laws of motion:1. All bodies remain at rest or move in uniform, rectilinear motion, unless acted upon by a net force.2. The net force acting upon a body is proportional to the product of its mass and acceleration.3. When a body is acted upon by another body, the net force of the one body on the second body is reciprocal to the net force of the second body on the one body (i.e. action = reaction).Newton's law of universal gravitation:1. The gravitational force between two bodies is proportionate to the product of both masses and inversely proportional to the square of the distance between the centres of both bodies.With these four propositions in his hands, Newton is able to explain why apples fall from trees, why planets move in their orbits, why the oceans on Earth have tides and why comets have the strange orbits they have (and why they return after some amount of time). The universality, consistency and totality of this system was amazing; I think we moderns cannot truly understand the shift in thinking this has brought about.I think it is good to mention that Newton clearly describes the assumptions (or axioms) that underlie his system. These axioms have become the cornerstones of modern day science:1. No more causes of natural things should be admitted than are both true and sufficient to explain their phenomena.2. Therefore, the causes assigned to natural effects of the same kind must be, so far as possible, the same.3. Those qualities of bodies that cannot be intended and remitted [that is, qualities that cannot be increased or diminished] and that belong to all bodies on which experiments can be made should be taken as qualities of all bodies universally.4. In experimental philosophy, propositions gathered from phenomena by induction should be considered exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions.In other words, we should give up Aristotle's vain attempt to discover truth by applying axiomaticdeductive systems  gone is the philosopher who can get to know Nature from his armchair. What we should do, according to Newton (and he bases this on his ancestors Bacon and Galilei) is make observations, use the method of induction to discover explanations and by synthesizing these explanations into complete theories, assume that all similar effects have similar causes, throughout the whole universe and all of time. This is (almost exactly) the modern method of doing science. There are three important remarks to make on Newton's mechanics, as outlined in his principia. The first is that with Newton, the notions of absolute, infinite time and space become necessary. This is because, if everything attracts everything else in a circumscribed universe, the universe would collapse in on itself. Infinite space leaves open the possiblity that every piece of matter is counterbalanced by (infinite) other pieces; therefore no 'Big Crunch'. Infinite time, also means no possiblity of a definite event of Creation; it is not strange that many theologians weren't happy with Newton's system  their conception of the Universe would demand a beginning of time when God created the world, as mentioned in Genesis.The second remark is that Newton says in his Principia "hypotheses non fingo"  I don't feign hypotheses. He posits gravity as a force to explain the planetary orbits and the movements of matter on Earth. He doesn't know the mechanism by which gravity works or 'what gravity is', but that's not necessary for his theory. (This, by the way, is one of the reasons why later physicists would postulate ethers, because if gravity works instantaneously between two bodies, what is the medium through which it works?). This not using 'occult qualities' to explain natural phenomena, in effect, cuts religion from science  this would become as ground breaking as Newton's mechanics itself.The third remark is that Newton's switch from deduction to induction would bring back the problem of induction into science, as already mentioned by Sextus Empiricus in the second/third century AD. If you use particular events (e.g. planetary orbits) to discover, by means of induction, universal truths (e.g. law of gravity), you will encounter a problem: there's no way to garantuee that the next observation will not falsify your theory. To prove your theory, you need to have access to all observations  past, present and future  and this is simply not possible. So absolutely proving inductive reasoning is impossible; this leaves room for doubt  therefore skepticism about scientific theories. It is a problem that has never been solved satisfactorily (Popper got close, but failed in the end; while Bayesian probability theory is just a logical rule  trash in leads to trash out).Safe to say, this is a book that has been influential for centuries; in science, philosophy, religion, culture, literature, and what else. Newton's mechanics are still used by astronomers who work in the range of everyday motions and masses (anything approaching the enormous needs general relativity and anything approaching the subatomic world needs quantum mechanics). But this book is unreadable for contemporary people, it is too complex and too obscure for that. One can read the first part of the work to get a good insight, but additional information (i.e. interpretation) on the Principia is necessary.

What can top this?!? Laws of motion. F=ma rules! (Though quantum mechanics have proven it to be fundamentally false.) And calculus?!? Pure genius. The thought of one human mind creating such an elegant tool to calculate everything from force to economics to anything requiring calculations of rate of change 'almost' makes being human worthwhile. Poetry at its most finest. Almost makes one believe there must be a god.

It is a rare pleasure to sit down and read a book upon which your entire culture owes its existence. This would be a five star book, but I threw the other star ninjastyle at the editor who gave primacy to Hawking's name on the binding.

I have a feeling that I've learnt nothing abt math the past 15 years....

An open door into the mind of the man who revolutionized the way to think about mathematics and physical science. It is technical.

Who am I kidding? I never read more than 10 pages of this masterpiece of arcane physics. Still, a book for the millenia.

هنا ولد كل شيء.قبله العدم .. وبعده هو لكن بشكل آخر.

This book is epic. I once spilled glucosamine on it and my soul was ripped from my body by a jealous god.

Newton interjects philosophy and debate into math, making theory easier to accept than when handed down for rote memorization in textbooks hundreds of years later.

One of the densest books that I've ever read, but also the most elegant and structured.

Чтобы познать мир, нет необходимости измышлять новое, фантазировать и предполагать нечто, не опираясь на конкретные примеры. Чем озадачены философы, того избегают в суждениях физики. Собственно, натуральная философия — это и есть физика. Так она ранее называлась. Возникает вопрос: что предложил Ньютон современникам, чего до него не знали? Ответ прост — ничего не предложил. В построении предположений им использовались научные изыскания предыдущих поколений учёных и философов. Ньютон постарался математически доказать верность одних теорий и указать на вздорность других. Прежде, чем перейти к непосредственному доказательству, потребовалось ввести в общий курс определений, не вызывающих сомнений. Этому посвящены первые страницы «Математических начал».(c) Trounin

The notes go a long way toward helping the science enthusiast to enjoy this perhaps greatest of all physics texts. So clear and concise that I learned heaps more than I have with other editions, even as I realized much more stuff was slipping through my grasp. A real adventure of the mind I'll be sure to revisit again and again.