Talk:Philosophiæ Naturalis Principia Mathematica

message: I think I added most of the original information in this section, but I have come across a possible confusion concerning Newton's own copy of Principia.
Having added the photograph of the Principia on the Wren Library, Cambridge, I came across a news item saying that Newton's Principia was currently in a touring exhibition at the New York City Library between October 8, 2004 through February 5, 2005 . Indeed, the good online version of the exhibition includes a photo of a better page  with copious notes for the second edition (it looks like the page shown is on gravity and orbits). 
Initially I worried about how the book could be in two places at once, but this can easily be satisfied since the book is actually three volumes. However, the book in NYC is identified as coming from the Portsmouth Collection in Cambridge University Library. And this reminded me that indeed most of Newton's best scientific papers were found in the Portsmouth library and are now securely kept at the University Library . The edges of the bindings of the books in the two photos look quite different and they both seem to have very different catalogue numbers, which would imply that the one in the Wren Library isn't on loan from the Portsmouth collection.
Does anyone know if there is more than one set of Newton's 'own' copy of Principia around? -- Solipsist 07:49, 13 Nov 2004 (UTC)
thread_title: Location of Copies

message: Various Web sites claim that Cambridge was closed in 1665 consequent to a plague (eg. google "cambridge university 1665 plague"). Further that during that time Newton retired to the family home where he was exceptionally creative and productive. What substantiates the claims? Likely there are records about Cambridge being closed. Is there any tangible evidence that he spent the time at home? Does anyone else consider the topic worthy of mention? Regards, ... PeterEasthope (talk) 23:18, 16 March 2020 (UTC)
thread_title: Circumstances Surrounding Writing

message: I'm confused about the following two sentences:
:A second point that has been made is that Newton had to reject Descartes' views on inertia in order to understand and generalise Galileo's new ideas. 
Who made the point?  How is Galileo's ideas new to the 17thc, when Galileo was writing a generation or two before?  What is it about Descartes' views on inertia that Newton had to reject?
:He simultaneously rejected Descartes' new language of geometry: since he recognised that it was equivalent to Euclid's, and it lay within Newton's powers to recast the calculus in these terms.
"He" is now back to Newton.  What evidence did he have to say it was "equivalent" to Euclid's?  That's a bold statement I think.  "Equivalent" isn't defined in this article.  Equivalent how?  In terms of its proof power?
Thanks!  --M a s 20:15, 9 May 2006 (UTC)
replies: text: THE NEWTONIAN CREED: We are all pretending that Newton used geometric proofs to show that an inverse-square force law must result in an elliptical orbit. Several books contain deep, sometimes long, explanations of this proof. However, no one can simply, briefly, and clearly give this proof. Most authors bypass it. Richard Feynman, John Locke, and Thomas Edison were baffled by it. It is one of mankind's hidden, sacrosact mysteries. Only the high priests, they say, really understand it, and we take them at their word. The mass of humans, including Robert Hooke, were not meant to know how that inverse-square force law necessarily results in an elliptical orbit. Humanity must believe it. We affirm our faith.Lestrade 23:32, 12 May 2006 (UTC)
replies: text: In Prop. 11, Prob. 6, Newton supposedly proved that elliptical orbits occur with inverse-square attractions. Read it yourself and see if it convinces you. In subsequent propositions, he then supposedly proved that circular, parabolic,and hyperbolic orbits also occur with inverse-square attractions. But, he never proved that inverse-square attractions necessarily result in elliptical orbits. So, he never really solved Halley's problem. Why can't minds like Feynman and Chandrasekhar show how Newton gave this assumed proof? I consider this to be an important question. The situation almost seems to resemble the famous "Emperor's New Clothes" fable in that it is generally agreed that Newton proved that an inverse-square force necessarily results in an elliptical orbit.Lestrade 15:36, 14 May 2006 (UTC)
replies: text: Halley asked Newton, "If there is an inverse-square attractive force, what shape is the orbit?" Newton replied, "An ellipse, and I have proved it." He looked for his proof but unfortunately couldn't find it. Instead of simply providing the proof of the solution to this problem, he wrote On the Motion of Bodies, in which he tried to show that elliptical orbits could be related to such a force. Then he wrote the Principia in which he included this demonstration and added many more topics. But, he never really provided the proof that he mentioned to Halley. Most people attribute the obscurity of Newton's so-called proof to the brilliance of his eccentric and peculiar mathematics, which are supposed to be beyond the comprehension of ordinary minds. Dana Densmore wrote a 525 page book in order to explain Newton's claim. It is titled Newton's Principia: The Central Argument, Green Lion Press, . It took that many pages for a very intelligent author to try to clarify Proposition 11, Problem 6, in Newton's Principia. In spite of this, many books seem to consider it an easy, settled matter and quickly move on to other issues.Lestrade 12:27, 15 May 2006 (UTC)

text: IF bodies obey an inverse square law of attraction (and also standard assumptions about one body of negligible mass to the other, etc.) THEN one body will move as an ellipse relative to the other, 
and you are arguing that Newton provided a questionable proof of this, or in a sense failed to prove it succinctly.  But it's not true- inverse square implies any conic.  Perhaps Newton meant "a conic, and I have proved it."
Regardless, you then seem to imply Newton, for want of priority? or for other motives? fudged his answer and response to Halley... and because of this, Newton's current reputation should be tarnished?  should be reduced?  And I think I would argue that Newton was a nut-job egomaniac who had a strong sense of Schadenfreude, and in addition studying the historiography of Principia is an interesting exercise in 17thC British academic culture, but we can't take the leap from being a despicable man to being a despicable scientist.  Thanks!  --M a s 16:12, 15 May 2006 (UTC)
thread_title:  More on Euclid, Descartes, and Newton 

message: The terse paraphrase, "I do not assert that any hypotheses are true", does not seem supported by the block quote following the statement.  If I understand Newton's remark, it is not that he is offering hypotheses but refusing to defend them, as I think the paraphrase suggests, but that he does not pretend that what he exposits is a hypothesis, an explanation, for what he observes.  To whatever exactly the quote refers is offered as description of phenomena. IHendry 19:16, 16 November 2005 (UTC)
thread_title:  On "I feign no hypotheses" 

message: In excerpts from book, one paragraph begins with "hi, i am karthik". Replace it please
:Just some vandalism introduced by User:203.174.79.131 an hour ago — now reverted. -- Solipsist 09:02, 13 December 2005 (UTC)
thread_title: What is it

message: Robert Hooke, Christopher Wren, Edmund Halley, and Christiaan Huygens believed that there was a relationship between the inverse-square force law and elliptical orbits. Newton told Halley that he had proved that the inverse-square force resulted in an elliptical orbit. In his subsequent publications, however, Newton tried to prove the converse. That is, Newton tried to prove that if an orbit is an ellipse (or any other conic section), then the force is inverse-square. I find that I can't fit this fact into the article as it now exists.Lestrade 02:02, 18 February 2006 (UTC)
thread_title: The Converse Theorem

message: Newton did not use Euclidean geometry. He used his own geometry. This was a geometry that investigated triangles that have curved, instead of straight, sides.Lestrade 02:07, 18 February 2006 (UTC)
replies: text: Very few diagrams in the Principia show rectilinear figures. Most figures are curvilinear and many show a triangle that has one side as a curve. This is because Newton was investigating curved orbits. In so doing, he was concerned with curved conics such as circles, ellipses, parabolas, hyperbolas, and spirals. Euclid's rectilinear plane geometry was inadequate for this task.  Newton tried to use traditional geometry, but had to invent his own version. Dana Densmore, in her Newton's Principia: The Central Argument () stated that "Newton chose to express his proofs in an idiosyncratic modification of the classic geometry of the ancient Greeks" (p. xlvi). In his study of orbits, Newton's own geometry was used to study triangles that had one side as a curve or arc. In order to accomplish this, he used his mysterious concept of "ultimate limits." At the ultimate limit, a curve starts to become a straight line and can be considered as such. The lines retain their curved existence but can be considered as straight lines for purposes of calculation. Lemma 3, Corollary 4 shows how "these ultimate figures … are not rectilinear, but curvilinear limits of rectilinear figures." By reducing curved orbital lines to very small straight lines, Newton tried to use a kind of Euclidean geometry to solve his problems. This procedure is very awkward and difficult. Many intelligent people confess to being unable to follow Newton's mathematical proofs and, instead, merely accept the results of his propositions on his authority. During his investigations, Newton stopped using his idiosyncratic version of geometry and invented calculus. With calculus, a curve can be calculated as though it is a sum of very small straight tangential lines. That is the very essence and purpose of differential calculus and is the main reason why Newton developed his fluxions or calculus. When he wrote the Principia, however, he did not express his proofs by using his new calculus, Instead, he used his idiosyncratic version of traditional geometry, with its curved triangles and its ultimate limits.Lestrade (talk) 15:02, 25 March 2009 (UTC)
replies: text: "Idiosyncratic" means "peculiar to one individual." As Dana Densmore asserted, this is true of Newton's geometry. Regarding ultimate limits, Berkeley described their mystery. They are fictions that Newton used as a device for his purpose. I am not convinced that mathematicians of his day or of our day can follow his proofs with "no trouble." Regarding physicists, two Nobelists, Feynman and Chandrasekhar, struggled with Newton's proofs. Feynman admitted that he could not follow them, and Chandrasekhar tried to convert them to calculus in order to explain them because he couldn't clearly render them lucid. Of course, the old defense can be used that Newton was just smarter, so if people cannot follow his proofs, it is because they are just not intelligent enough to understand. That ruse never fails, but it also never leads to clear explanations. Feynman and Chandrasekhar were intelligent men, but they were not able to follow the proofs. In the end, we just accept or reject everything and simply move on to other topics. The problem is resolved by its disappearance, but no clarity is ever attained.Lestrade (talk) 13:47, 27 March 2009 (UTC)
thread_title: Newton's Geometry

message: "In the plague year of 1665, Newton had already experienced the famous revelation under an apple tree in Woolesthorpe, which led him to conclude that the strength of gravity falls off as the inverse square of the distance..."
This seems to refer to the apocryphal story of the apple falling from a tree. Although Newton told this in his old age (and by that time he has undergone a transformation - moving to London, becoming the master of the mint, MP and president of the RS which was an extraordinary change considering his earlier life).
He spent time lying in the apple orchard in Woolesthorpe but I sincerely doubt that there was any falling apple that created a revelation in his mind. I don't believe he ever wrote anything in his notes to this effect (and they are copious) although many minor details are in those notes.
To my mind, to say that an apple falling from a tree created the revelation of gravitational attraction holding the moon in orbit would be as amusingly laughable as claiming that had Newton seen a banana he would have been prompted to use the calculus to prove planetery orbits were eliptical!
I think that Newton probably told this story to help others to understand some of the basic concepts of his works - remember that very few scientists could understand the Principia at all and so some assistance from the mundane would have been useful. By trivialising the actual thought behind his work he could assist others in making the leave to understand that there was no physical mechanism to hold the planets in orbit.
I think that perhaps there should be a page devoted to the story in both fact and fiction as it is of considerable interest. In this text the reference to the apple tree revelation needs to be struck. I also think that revelation may also need to be removed. Any comments?
Candy 03:23, 9 September 2006 (UTC)
thread_title:  Newton's Apple 

message: I'm putting this is a seperate section becasue I am trying to draw attention to the language used in "The reason for Newton's use of Euclidean geometry as the mathematical language of choice in Principia is puzzling in two respects. The first is the trouble that today's physicists, trained in modern analytical methods, face in following the arguments." 
Does that sound very odd to anyone else. The reason for Newton's use ..... is puzzling to me implies that we do not understand why Newton did  what he did clearly. However, then to mention that the trouble is how modern physicists find it difficult to follow the arguments is non sequitur.
If one said, "Two puzzles are created from Newton's use of Euclidean geometry as the mathematical langauge of choice in Principia. The first is that today's .... I would be happier .. or am I missing a point here?
If I can also be so bold as to suggest why Newton used Euclidean geometry I would suspect that it is because like many "new fangled" developments sometimes we all have the potential to be intellectual luddites (just look at the number of scholars using pre-Rechtschreibung reform German regardless of the new rules) but more importantly  Newton's work with Alchemy involved his belief that the Greek myths held coded secrets of the fundamental truths behind the structure of matter. With this in mind I can see why he used Euclidean geometry as it was closer to the "truth".
Candy 03:44, 9 September 2006 (UTC)
thread_title:  The Mathematical Language 

message: Principia directs here?  I was hoping for at least a disambiguation page, if it didn't go straight to the Principia Discordia.  Mathiastck 13:21, 14 September 2006 (UTC)
thread_title:  Principia Discordia 

message: This article indicates General Scholium was attached to the second edition of Principia.  However, the article on Hypotheses non fingo, which is linked to from the section on Hypotheses non fingo in this article, indicates it was the third edition.  I have no information as to which is correct, I only noticed the disagreement.  Djkeng65 21:49, 5 July 2007 (UTC)
replies: text: This page is right: second edition. But why does it say the General Scholium attacks the Trinity? It certainly does not do so explicitly. I'm not a theologian but I can't see that any of the comments there would count as such an attack. And I would have thought that even a fairly subtle attack would have been very risky for a public official like Newton (this was published when he was Master of the Mint.) PaddyLeahy 02:17, 9 August 2007 (UTC)

text: Every soul that has perception is, though in different times and in different organs of sense and motion, still the same indivisible person. There are given successive parts in duration, co-existent parts in space, but neither the one nor the other in the person of a man, or his thinking principle; and much less can they be found in the thinking substance of God.
he is denying that the "substance of God" can be divided in "co-existent parts in space", which is tantamount to denying the possibility of God incarnate. dab (𒁳) 20:53, 17 August 2007 (UTC)

text: The natural reading of this quote is that Newton is defending himself from those who would claim that Newton's very literal interpretation of omnipresence implicity allows God to be separated into physical parts. A great deal of the Scholium (also Cotes' preface to the 2nd edition) appears to be targeted at Leibniz, and this question of the presence of God at each point in space was certainly an issue in the Leibniz-Clarke correspondence. Of course you may be right that this is a very subtle dig at the Trinity as well (your blog reference doesn't explicitly highlight this passage). But I'm sure this was not perceived as an attack on the Trinity at the time, except possibly by Newton's very close friends. Newton had enough enemies on both sides of the channel to cause a huge fuss if they had even a suspicion of this. So I think including the comment on the article page without qualification is very misleading. PaddyLeahy 21:30, 18 August 2007 (UTC)
thread_title:  General Scholium 

message: On the first page of the book it says MDCLXXXVII (1687) but the article states the book is from 1686.
Which on is it? Is the date in the book something else or is the article wrong? --131.174.17.112 (talk) 10:13, 3 March 2008 (UTC)
replies: text: I. Bernard Cohen wrote that Principia was first published in 1687, but he gave no month or day.Lestrade (talk) 19:51, 3 March 2008 (UTC)
thread_title:  1686 or 1687 

message: This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 10:01, 10 November 2007 (UTC)
thread_title:  WikiProject class rating

message: Wouldn't specific fact checks be more appropriate here? 74.78.162.229 (talk) 00:24, 5 July 2008 (UTC)
thread_title:  Basis for the refimprove? 

message: As of July 5 2008 there's an incomprehensible sentence in the section "Newton's Role"; looks like a cut-and-paste problem.  Can't fix it, because I don't know what it's supposed to mean.  Any ideas?  The sentence is:  "At this time, the central not the resulting theory of colours, to overwhelmingly favourable response, and a few inevitable scientific disputes with Robert Hooke and others, which forced him to sharpen his ideas to the point where he composed sections of his later book Opticks already by the 1670s."  —Preceding unsigned comment added by 89.176.31.200 (talk) 06:27, 5 July 2008 (UTC)
replies: text: I cleaned it based on commonly known facts. 74.78.162.229 (talk) 11:57, 5 July 2008 (UTC)
thread_title:  Screwed up sentence 

message: This might (or might not) seem a bit odd, but according to some sources The Chronology of Ancient Kingdoms was "... originally intended to be the last book of the Principia, The System of the World" according to these guys .  Shouldn't this info be included somewhere in this article?  The two works to me seem entirely disconnected, but perhaps not to Newton. --Trippz (talk) 08:50, 4 August 2008 (UTC)
replies: text: [From Terry0051]Forgive me (and this response looks pretty late, but better late than never), but if you look at the semicolons and commas in your cited source, I think you'll see that what it means is that the originally-intended last book of (what became) the 'Principia' is the next, not the last, item in their list, i.e. they mean the book eventually published as 'System of the World'.  This is now dealt with in the main article here, under the subsection "A preliminary version". Terry0051 (talk) 19:24, 1 October 2009 (UTC)
replies: text: Ah, now makes more sense.  I believe you are correct. Thanks for checking that out. --Trippz (talk) 20:09, 1 October 2009 (UTC)
thread_title:  "Chronology of Ancient Kingdoms" as part of Principia 

message: There were 3 books, but the article's intro says there were 2 volumes. Were the three books published as 2 volumes, or is it wrong? Have all three books also been subsequently published in a single volume?
Jackd88 (talk) 23:14, 25 September 2009 (UTC)
replies: text: [From Terry0051] There were lots of different editions in different numbers of 'n' physical volumes -- where 'n' ranges from 1 to 4, I think! (I've made an edit that looks to me consistent with the facts, E & OE.) Terry0051 (talk) 19:15, 1 October 2009 (UTC)
thread_title:  Intro/Volumes 

message: You can find the Latin version here: http://www.gutenberg.org/etext/28233   The English version is available via Bittorrent.--Noghiri (talk) 18:03, 16 April 2010 (UTC)
thread_title:  Copies 

message: I assume the book was written in Latin. The article does not explicitly say this. BigJim707 (talk) 13:33, 14 September 2011 (UTC)
thread_title: Latin, right?

message: Hoe about a reference to "On the Shoulders of Giants", Ed. Stephen Hawking, Running Press,  - Writings of Copernicus, Galileo, Kepler, Newton, Einstein.  I've lost ready access myself, but it should be reasonably accessible and is in English. 94.30.84.71 (talk) 22:48, 12 December 2011 (UTC)
thread_title:  Reference 

message: I love that this article links to the specific propositions and sections while describing the layout of the book. WikiSource has an excellent 1846 translation of the Principia, including scans of the diagrams. I think it'd be a great idea to replace the links to Google Books with links to this editions: as internal links they'd look cleaner on the page, and would provide support to WikiSource as well! -- Gaurav (talk) 09:04, 12 January 2012 (UTC)
replies: text: Nobody has moved on this reasonable suggestion, presumably considering it too much work or not having enough knowledge of WikiSource citation. Instead, I added a book citation of the Google book English translation version of 1729 using Wikipedia citation tool for Google Books. The many plain links to this Google book in the article could be converted to page range references using this citation, for the first volume and equivalent ones for the later volumes, to be consistent with Wikipedia style and avoid linkrot. I tried User:Dispenser/Reflinks and this got rid of the bare links but I was unable to change the plain links possibly due to my lack of knowledge of this tool. I only wanted the basic book citation for my editing elsewhere and don't know how to do the page range references, but others are welcome to jump in. Puzl bustr (talk) 18:43, 16 March 2012 (UTC)
replies: text:  You manually edit the ‘page=X-Y’ field of the cite book citation to indicate page numbers. Or a shorter way is to just use (N (2010), pp X-Y  to briefly indicate the page range referring to the main citation. Puzl bustr (talk) 19:12, 16 March 2012 (UTC)
thread_title:  Linking to WikiSource instead of Google Books? 

message: In July 2011 Yworo added the link warning banner  with this edit summary: "There should not be text-linked external links in text, they should be moved to footnotes". 
This might be persuasive if we were linking to external reference works, but here we are just trying to bring up the text section from Principia Mathematica that this article is commenting on at the time. If we require people to go through the reference section every time, then they need to make two clicks to bring up the text for review rather than one. In case a part of the objection is seeing the external link syntax scattered through the text, please see my proposed remedy in the section called Book 2. I edited that section to make the external links display differently. I used ... to make the external links display in the same style as internal ones. 
I agree with User:Gaurav above that linking to WikiSource would be better, just because WikiSource provides the same translation with modern spelling, while keeping Newton's original diagrams. If anyone has another proposal for fixing the complaint about the external links, you can go ahead and revert my changes to the 'Book 2' section. Here is a link to WikiSource for Book 2 Section 1. Here is a link to the same section using Google Books. To appreciate the improved presentation in WikiSource, locate the sentence 'If a body is resisted in the ratio of its velocity..' in both editions.
If nobody disagrees with this, I'll eventually complete my change to the link syntax, switch to WikiSource, and then remove the  banner. EdJohnston (talk) 02:27, 22 May 2012 (UTC)
thread_title:  External links banner 

message: As part of Wikipedia:WikiProject Royal Society a special photo session in the Royal Society Library in London has resulted in Commons:Category:Royal Society Library, with over 50 photos of their treasures, mostly 17th century manuscripts, including several of one of the early minute books, Boyle's notebooks etc, the manuscript fair copy of Newton's Principia etc. Please add these as appropriate. Thanks! Wiki at Royal Society John (talk) 22:05, 25 June 2014 (UTC)
thread_title:  New photos on Commons from the Royal Society Library 

message: I can't hide that a proof of the second law of Kepler is not possible from Newtons laws.
Conservation of angular momentum is typical for a central force field. Newtons laws don't demand a central force field. They are only about linear momentum.
The beautiful animated "proof" you give is not from Newton. Only the ideas of this proof are found in its works.
The proof is false. The linear movement in the animation is not perpendicular to the attraction of the sun. An acceleration in direction of the sun will take place. The secant of the second segment will not have the same length as the first one.  — Preceding unsigned comment added by ThvAq (talk • contribs) 08:31, 18 August 2015 (UTC)
thread_title:  The proof of the second law of Kepler is wrong 

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thread_title:  External links modified 

message: Is this WP:original research (currently "citation" [81])
I can't find any commentators that use the term "blunder", let alone "several"? --𝕁𝕄𝔽 (talk) 20:56, 12 January 2024 (UTC)
thread_title:  Blunder?