Philosophiæ Naturalis Principia Mathematica

Philosophiæ Naturalis Principia MathematicaNewton 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 socio economic strata of American life were stranded together on a desert island following a mishap during a three island tour 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 Newton posed a question most poeple had never stopped to consider 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 That s what British public school does to a tender lad like Newton.Of course, I didn t read this Do I look like a guy who s read The Principia No, I look like a guy who grew up watching Gilligan s Island Definitely Mary Ann, but why not a threesome with Ginger. , Table Of Contents Are Active Completed Annotated About The Author, About This Ebook, Historical Context And Postscript English This Book Is The Original Latin Language Illustrated The Original And Some IllustrationsPhilosophi Naturalis Principia Mathematica, Latin For Mathematical Principles Of Natural Philosophy , Often Referred To As Simply The Principia, Is A Work In Three Books By Sir Isaac Newton, First Published July After Annotating And Correcting His Personal Copy Of The First Edition, Newton Also Published Two Further Editions, In And 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 ScienceThe French Mathematical Physicist Alexis Clairaut Assessed It In 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 Recent Assessment Has Been That While Acceptance Of Newton S Theories Was Not Immediate, By The End Of A Century After Publication In , 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 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 proposition on page two.To describe Newton s Principia as dense is clich d, 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 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. 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. This book, written by Isaac Newton in 1588, served as the foundation of physics for than 300 years, or up to the time Einstein developed relativity theory The fact that it is still in print 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 equation centric calculus Contrast this with the typical hard core 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. 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 e edition 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 e edition 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 pages not 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 sub duplicate 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. To listen to this review as a podcast, click below It is shown in the Scholium of Prop 22, Book II, that at the height of 200 miles above the earth the air is rare than it is at the surface of the earth in the ratio of 30 to 0.0000000000003998, or as 75,000,000,000,000 to 1, nearly. Marking this book as read is as much an act of surrender as an accomplishment Newton s reputation for difficulty is well deserved this is not a reader friendly book Even those with a strong background in science and mathematics will, I suspect, need some aid The historian of mathematics Colin Pask relied on several secondary sources to work his way through the Principia in order to write his excellent popular guide Texts by S Chandrasekhar, J Bruce Brackenridge, and Dana Dens are among the notable vade mecums for Newton s proofs Gary Rubenstein, a math teacher, takes over an hour to explain a single one of Newton s proofs in a series of videos and he had to rely on Brackenridge to do so.It is not that Newton s ideas are inherently obscure though mastering them is not easy but that Newton s presentation of his work is terse, dense, incomplete from omitting steps , and at times cryptic Part of this was a consequence of his personality he was a reclusive man and was anxious to avoid public controversies He says so much himself In the introduction to Book III, Newton mentions that he had composed a popular version, but discarded it in order to prevent the disputes that would arise from a wide readership Unsurprisingly, when you take material that is intrinsically complex and then render it opaque to the public, the result is not a book that anyone can casually pick up and understand.The good news is that you do not have to Newton himself did not advise readers, even mathematically skilled readers, to work their way through every problem This would be enormously time consuming Indeed, Newton recommended his readers to peruse only the first few sections of Book I before moving on directly to Book III, leaving most of the book completely untouched And this is not bad advice As Ted said in his review, the average reader could gain much from this book by simply skipping the proofs and calculations, and stopping to read anything that looked interesting And guides to the Principia are certainly not wanting Besides the three mentioned above, there is the guide written by Newton scholar I Bernard Cohen, published as a part of his translation I initially tried to rely on this guide but I found that, despite its interest, it is mainly geared towards historians of science so I switched to Colin Pask s Magnificent Principia, which does an excellent job in revealing the importance of Newton s work to modern science.So much for the book s difficulty on to the book itself.Isaac Newton s Philosophi Naturalis Principia Matematica is one of the most influential scientific works in history, rivaled only by Darwin s On the Origin of Species Quite simply, it set the groundwork for physics as we know it The publication of the Principia, in 1687, completed the revolution in science that began with Copernicus s publication of De Revolutionibus Orbium Coelestium over one hundred years earlier Copernicus deliberately modeled his work on Ptolemy s Almagest, mirroring the structure and style of the Alexandrian Greek s text Yet it is Newton s book that can most properly be compared to Ptolemy s For both the Englishman and the Greek used mathematical ingenuity to draw together the work of generations of illustrious predecessors into a single, grand, unified theory of the heavens.The progression from Copernicus to Newton is a case study in the history of science Copernicus realized that setting the earth in motion around the sun, rather than the reverse, would solve several puzzling features of the heavens most conspicuously, why the orbits of the planets seem related to the sun s movement Yet Copernicus lacked the physics to explain how a movable earth was possible in the Aristotelian physics that held sway, there was nothing to explain why people would not fly off of a rotating earth Further, Copernicus was held back by the mathematical prejudices of the day namely, the belief in perfect circles.Johannes Kepler made a great stride forward by replacing circles with ellipses this led to the discovery of his three laws, whose strength finally made the Copernican system efficient than its predecessor which Copernicus s own version was not Yet Kepler was able to provide no account of the force that would lead to his elliptical orbits He hypothesized a sort of magnetic force that would sweep the planets along from a rotating sun, but he could not show why such a force would cause such orbits Galileo, meanwhile, set to work on the new physics He showed that objects accelerate downward with a velocity proportional to the square of the distance and he argued that different objects fall at different speeds due to air resistance, and that acceleration due to gravity would be the same for all objects in a vacuum But Galileo had no thought of extending his new physics to the heavenly bodies.By Newton s day, the evidence against the old Ptolemaic system was overwhelming Much of this was observational Galileo observed craters and mountains on the moon dark spots on the sun the moons of Jupiter and the phases of Venus All of these data, in one way or another, contradicted the old Aristotelian cosmology and Ptolemaic astronomy Tycho Brahe observed a new star in the sky caused by a supernova in 1572, which confuted the idea that the heavens were unchanging and observations of Haley s comet in 1682 confirmed that the comet was not somewhere in earth s atmosphere, but in the supposedly unchanging heavens.In short, the old system was becoming unsustainable and yet, nobody could explain the mechanism of the new Copernican picture The notion that the planets orbits were caused by an inverse square law was suspected by many, including Edmond Haley, Christopher Wren, and Robert Hooke But it took a mathematician of Newton s caliber to prove it.But before Newton published his Principia, another towering intellect put forward a new system of the world Ren Descartes Some thirty years before Newton s masterpiece saw the light of day, Descartes published his Principia PhilosophiHere, Descartes summarized and systemized his skeptical philosophy He also put forward a new mechanistic system of physics, in which the planets are borne along by cosmic vortexes that swirl around each other Importantly, however, Descartes s system was entirely qualitative he provided no equations of motion.Though Descartes s hypothesis has no validity, it had a profound effect on Newton, as it provided him with a rival The very title of Newton s book seems to allude to Descartes s while the French philosopher provides principles, Newton provides mathematical principles a crucial difference Almost all of Newton s Book II on air resistance can be seen as a detailed refutation of Descartes s work and Newton begins his famous General Scholium with the sentence The hypothesis of vortices is pressed with many difficulties In order to secure his everlasting reputation, Newton had to do several things First, to show that elliptical orbits, obeying Kepler s law of equal areas in equal times, result from an inverse square force Next, to show that this force is proportional to the mass Finally, to show that it is this very same force that causes terrestrial objects to fall to earth, obeying Galileo s theorems The result is Universal Gravity, a force that pervades the universe, causing the planets to rotate and apples to drop with the same mathematical certainty This universal causation effectively completes the puzzle left by Copernicus how the earth could rotate around the sun without everything flying off into space.The Principia is in a league of its own because Newton does not simply do that, but so much The book is stuffed with brilliance and it is exhausting even to list Newton s accomplishments Most obviously, there are Newton s laws of motion, which are still taught to students all over the world Newton provides the conceptual basis for the calculus and though he does not explicitly use calculus in the book, a mathematically sophisticated reader could have surmised that Newton was using a new technique Crucially, Newton derives Kepler s three laws from his inverse square law and he proves that Kepler s equation has no algebraic solution, and provides computational tools Considering the mass of the sun in comparison with the planets, Newton could have left his system as a series of two body problems, with the sun determining the orbital motions of all the planets, and the planets determining the motions of their moons This would have been reasonably accurate But Newton realized that, if gravity is truly universal, all the planets must exert a force on one another and this leads him to the invention of perturbation theory, which allows him, for example, to calculate the disturbance in Saturn s orbit caused by proximity to Jupiter While he is at it, Newton calculates the relative sizes and densities of the planets, as well as calculates where the center of gravity between the gas giants and the sun must lie Newton also realized that gravitational effects of the sun and moon are what cause terrestrial tides, and calculated their relative effects though, as Pask notes, Newton fudges some numbers.Leaving little to posterity, Newton realized that the spinning of a planet would cause a distortion in its sphericity, making it marginally wider than it is tall Newton then realized that this slight distortion would cause tidal locking in the case of the moon, which is why the same side of the moon always faces the earth The slight deformity of the earth is also what causes the procession of the equinoxes the very slow shift in the location of the equinoctial sunrises in relation to the zodiac This shift was known at least since Ptolemy, who gave an estimate too slow of the rate of change, but was unable to provide any explanation for this phenomenon.The evidence mustered against Descartes s theory is formidable Newton describes experiments in which he dropped pendulums in troughs of water, to test the effects of drag He also performed experiments by dropping objects from the top of St Paul s Cathedral What is , Newton used mathematical arguments to show that objects rotating in a vortex obey a periodicity law that is proportional to the square of the distance, and not, as in Kepler s Third Law, to the 3 2 power Most convincing of all, Newton analyzes the motion of comets, showing that they would have to travel straight through several different vortices, in the direction contrary to the spinning fluid, in order to describe the orbits that we observe a manifest absurdity While he is on the subject of comets, Newton hypothesizes correctly that the tail of comets is caused by gas released in proximity to the sun and he also hypothesizes intriguingly that this gas is what brings water to earth.This is only the roughest of lists Omitted, for example, are some of the mathematical advances Newton makes in the course of his argument Even so, I think that the reader can appreciate the scope and depth of Newton s accomplishment As Pask notes, between the covers of a single book Newton presents work that, nowadays, would be spread out over hundreds of papers by thousands of authors The result is a triumph of science Newton not only solves the longstanding puzzle of the orbits of the planets, but shows how his theory unexpectedly accounts for a range of hitherto separate and inexplicable phenomena the tides, the procession of the equinoxes, the orbit of the moon, the behavior of pendulums, the appearance of comets In this Newton demonstrated what was to become the hallmark of modern science to unify as many different phenomena as possible under a single explanatory scheme.Besides setting the groundwork for dynamics, which would be developed and refined by Euler, d Alembert, Lagrange, Laplace, and Hamilton in the coming generations, Newton also provides a model of science that remains inspiring to practitioners in any field Newton himself attempts to enunciate his principles, in his famous Rules of Reasoning Yet his emphasis on inductivism generalizing from the data does not do justice to the extraordinary amount of imagination required to frame suitable hypotheses In any case, it is clear that Newton s success was owed to the application of sophisticated mathematical models, carefully tested against collections of physical measurements, in order to unify the greatest possible number of phenomena And this was to become a model for other intellectual disciples to aspire to, for good and for ill.A striking consequence of this model is that its ultimate causal mechanism is a mathematical rule rather than a philosophical principle The planets orbit the sun because of gravity, whose equations accurately predict their motions but what gravity is, why it exists, and how it can affect distant objects, is left completely mysterious This is the origin of Newton s famous I frame no hypothesis comment, in which he explicitly restricts himself to the prediction of observable events rather than speculation on hidden causes though he was not averse to speculation when the mood struck him Depending on your point of view, this shift in emphasis either made science rational or superficial but there is little doubt that it made science effective.Though this book is too often impenetrable, I still recommend that you give it a try Few books are so exalting and so humbling Here is on display the furthest reaches of the power of the human intellect to probe the universe we live in, and to find hidden regularities in the apparent chaos of experience. 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.

Sir Isaac Newton, FRS , was an English physicist, mathematician, astronomer, natural philosopher, and alchemist His Philosophi Naturalis Principia Mathematica, published in 1687, is considered to be the most influential book in the history of science In this work, Newton described universal gravitation and the three laws of motion, laying the groundwork for classical mechanics, which dominated

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