• Also known as Mathematical Principles of Natural Philosophy
  
• The sacred book of the Cult of the Vis
  
• Newton’s Principia: The greatest science book never read by Newton’s disciples the physicists.
  

This is copied from Densmore, p.3

1. The ancients, as Pappus wrote, made mechanics of the highest value in the investigation of natural matters, and more recent writers, having dismissed substantial forms and occult qualities, have made an approach to referring the phenomena of nature back to mathematical laws.
   
2. It has accordingly seemed fitting in this treatise to develop mathematics insofar as it looks to philosophy.
   
3. Now the ancients established two branches of mechanics: rational, which proceeds accurately by demonstrations; and practical.
   
4. To practical mechanics all the manual arts look, and from here its name “mechanica” is borrowed.
   
5. But since artisans are accustomed to work with little accuracy, it happens that mechanics is a whole is so distinguished from geometry, that whatever is accurate is referred to geometry, and whatever is less accurate, to mechanics.
   
6. The errors, however, belong to the artisan, not the art.
   
7. One who works less accurately is a more imperfect mechanic, and if any could work with perfect accuracy, this would be the most perfect mechanic of all.
   
8. For the drawing of both straight lines and circles, upon which geometry is founded, belongs to mechanics.
   
9. Geometry does not teach how to draw these lines, but requires [/postulat/] that they be drawn.
   
10. For requires that the beginner learn to draw them accurately before crossing the threshold of geometry, and then teaches how problems are solved by these operations.
    
11. To draw straight lines and circles are problems, but not geometrical problems.
    
12. The solution of these is required of mechanics, and once the solutions are found, their use is taught in geometry.
    
13. And it is the glory of geometry that so much is accomplished with so few principles that are obtained elsewhere.
    
14. Thus geometry is founded upon mechanical procedure, and is nothing else but that part of universal mechanics that accurately sets forth and demonstrates the art of measuring.
    
15. Further, since the manual arts are chiefly concerned with making bodies move, it happens that geometry is commonly related to magnitude, and mechanics to motion.
    
16. In this sense, rational mechanics will be the science of the motions that result from any forces whatever, and of the forces that are required for any motions whatever, accurately bet forth and demonstrated.
    
17. This part of mechanics was developed into five powers by the ancients, looking to the manual arts, since they considered gravity (which is not a manual power) not otherwise than in the weights that were to be moved by those powers.
    
18. We, however, are interested, not in the arts, but in philosophy, and write of powers that are not manual but natural, treating mainly those matters pertaining to gravity, levity, elastic force, the resistance of fluids, and forces of this kind, whether attractive or impulsive.
    
19. And on that account we present these [writings] of ours as the mathematical principles of philosophy.
    
20. For the whole difficulty of philosophy appears to turn upon this: that from the phenomena of motion we may investigate the forces of nature, and then from these forces we may demonstrate the rest of the phenomena.
    
21. And to this end are aimed the general propositions to which we have given careful study in the first and second books.
    
22. In the third book, on the other hand, we present an example of this procedure, in the unfolding of the system of the world.
    
23. For there, from the celestial phenomena, using the propositions demonstrated mathematically in the preceding books, we derive the forces of gravity by which bodies tend to the sun and the individual planets.
    
24. Then from the forces, using propositions that are also mathematical, we deduce the motions of the planets, of comets, of the moon, and of the sea.
    
25. In just the same way it would be possible to derive the rest of the phenomena of nature from mechanical principles by the same manner of argument.
    
26. For I’m lead by many reasons to strongly suspect that all of them can depend upon certain forces by which the particles of bodies, by causes not yet known, either are impelled towards each other mutually and cohere in regular shapes, or flee from one another and recede.
    
27. These forces being unknown, philosophers have hitherto probed nature in vain.
    
28. It is my hope, however, that the principles set forth here will shed some light upon this manner of philosophizing or upon some truer one.
    
29. [the rest is omitted]
    

1. This is what physicists claim
   
2. They never read the Principia. They learned the Newtonian mechanics from textbooks.
   
3. “ Principia is of importance only to historians of science.”
   
4. Well, this is not true. Principia is still relevant.
   
5. We see clearly how Newton’s incoherent ramblings presented as laws, stolen mostly from Descartes, has been polished, fixed an presented and finally presented as “Newtonian mechanics.”
   

1. Usually, books associated with a scholastic cult acquire a Latin title. Principia is one of those books.
   
2. The Principia is the official master book of the Cult of the Vis. Vis or Vi of course is Latin for “force.”
   
3. And what is force in Newtonian Wonderland called Newtonian Mechanics? Who knows. Everything is force in Newtonian Wonderland called euphemistically the “System of the World.”
   
4. But calling Newton names will only strengthen the Newtonian myth.
   
5. But in this case, Newton’s deceptions in his Principia has fundamental importance.
   
6. Why is it that when we read the Principia seriously we quickly get disillusioned and disappointed? Is this the “greatest scientific book ever written”?
   
7. We are disappointed with Newton’s slapdash presentation, intentionally vague definitions and outrageous generalizations. Newton offers only vague sketches of his proofs that must be filled in, Newton’s errors corrected or rationalized.
   
8. Newton knew that he was writing the Principia to be the master book of a cult. Newton knew that he was replacing Aristotle as the scholastic master of the European scholasticism. Newton knew that generations of his disciples would be filling in the gaps in the coming centuries just like Aristotle’s disciples have done. This is the reason we say that Newton is the last of the Aristotelians and first of the Newtonians.
   

1. Is there such a thing as “Newton’s Theory of Universal Gravitation”?
   
2. First of all this phrase is an abuse of the word “universal”.
   
3. It’s also an abuse of the word “gravitation”. What is gravitation?
   
4. When I read Newton’s Principia I don’t see any “universal”, “theory” of “gravitation”. In Principia all Newton does is to compute some orbital properties of planets by using Kepler’s Rule.
   
5. So “gravitation” in this context means “mutual attraction between masses”.
   
6. What attraction? Newton’s force is a supernatural cause and it does not exist in this world.
   
7. “Gravitation”, “force of gravity”, “mutual attraction”, “centripetal force” are all names or euphemism Newton made up to hide the fact that Newton is using a supernatural cause to explain natural phenomena like orbital motions.
   
8. So what is the source of the myth that Newton discovered some universal theory of universal mutual attraction between matter
   
9. The universality refers simply to Newton’s expansion of terrestrial gravity to the moon and planets. And by Newtonian propaganda by Newton’s disciples Newton’s three or four computations in the solar system is considered universality of the mutual attraction.
   

1. No. Newton’s force does not exist in any of the geometrical figures as a quantity, that is, as a line.
   
2. Force in the Principia enters only as verbal propaganda Newton attaches to his geometric drawings.
   
3. Newton’s apologists, Newton’s disciples, take Newton’s word and accept his supernatural cause by Newton’s authority.
   
4. I ignore Newton’s words and Newton’s authority and I only look at mathematics.
   

1. Principia was written to establish British, Newtonian worldview of nature as the only true nature.
   

1. Principia is a hodgepodge of mathematical looking propositions, sophistry, equivocation and deception.
   

[chatgpt]

In Phenomena 4 in the Principia Newton writes, “the periodic times are necessarily the same, as well as the dimensions of the orbits, whether the sun revolve around the earth or the earth around the sun.” So, in this geometry, do the planets revolve around the sun as the sun revolves around the earth?

In Phenomena 4 of Principia Mathematica, Isaac Newton is emphasizing the geometric equivalence of certain orbital parameters. He argues that the periodic times and the dimensions of the orbits remain consistent, regardless of whether we adopt a geocentric or heliocentric frame of reference. This reflects Newton’s focus on relative motion and his recognition that the physical laws governing celestial bodies are invariant across different reference frames.

To address your specific question:

• Do the planets revolve around the sun as the sun revolves around the earth?
  From Newton’s framework, the answer is “yes,” but only in a relative sense. In his description, Newton acknowledges that the motions of celestial bodies can be described from either a heliocentric (sun-centered) or geocentric (earth-centered) perspective, provided the mathematical relationships governing those motions are preserved. However, he strongly favored the heliocentric model, as it provided a simpler and more accurate explanation of gravitational dynamics.
  

1. One can spend years and make a career out of studying propositions in Books 1 and 2 in Newton’s Principia. And there are some interesting things in there.
   
2. Newton makes astronomical calculations in Book 3 (and in these propositions in Book 2) but he is not using all those laws he stated and propositions he proved in Books 1 and 2. Newton simply uses Kepler’s Rule to make astronomical computations.
   

1. Why does Newton conflate axiom and law?
   
   1. The statement Newton calls “Law 1” is neither an axiom nor a law. With a charitable interpretation it can be said to a kind of an axiom. But it is definitely not a law.
      

[chatgpt]

Newton titles the section about his laws of motion, “Axioms or Laws of Motion.” What is the difference between an “axiom” and a “law” in this context? Does “or” make sense here?

The phrasing “Axioms or Laws of Motion” in Newton’s Principia reflects the interplay between the terms “axiom” and “law” in scientific and philosophical contexts of Newton’s time. Here’s how the two terms differ and how the use of “or” makes sense in this context:

1. No. If by “law” we mean a law of nature Newton’s first law is not a law that can legislate nature in this world because Newton’s first so-called law is based on several supernatural and absurd notion that unless we suspend our disbelief we cannot take them seriously.
   
2. The first law is the law of inertia, right?
   
3. First of all a law must make a single statement. Newton’s first so-called law makes several dubious statements.
   
4. Every body…
   
   1. We define something as a “body” if it moves as a unit. So, we define bodies by their motion.
      
5. perseveres
   
6. in its state of rest…
   
   1. There’s no state called rest.
      
   2. Rest can only mean absence of motion. But all is motion and change of motion so by definition there is no rest.
      
   3. A “law” that assumes that rest exists cannot be a law of nature because rest does not exist in this world.
      
7. or of uniform motion…
   
   1. Uniform motion is forced motion, it is not inertial motion.
      
   2. You need to propel a body to sustain uniform motion. This is how our world works. Yes in a Newtonian fairy tale bodies can move uniformly without a propeller.
      
8. in a right line…
   
   1. This is a joke nothing moves in a right line unless kept on a right line
      
9. unless it is compelled to change that state by forces impressed thereon.
   
   1. You cannot impress a force.
      
   2. Motion can only be transferred.
      
   3. Motion can only be transferred from one motion to another.
      
   4. In order to change the motion of a body you need to hit it.
      
   5. There is no transfer of motion without contact.
      
   6. Only motion can impart motion. Newton violates this universal rule.
      
10. What Newton states as his Law 1 cannot be a law valid in this world because it is only a silly collection of Newton’s hallucinations.
    
11. I admit that Newton’s Law 1 can be a valid law in a fairy tale.
    

• Principia Mott translation American edition
  

p.v

1. The Principia, above all, glows with the immortality of a transcendant mind.
   
2. Marble and brass dissolve and pass away; but the true creations of genius endure, in time and beyond time, forever: high upon the adamant of the indestructible, they send forth and near, over the troublous waters of life, a pure, unwavering, quenchless light whereby the myriad myriads of barques, richly laden with reason, intelligence and various faculty, are guided through the night and the storm, by the beetling shore and the hidden rock, the breaker and the shoal, safely into havens calm and secure.
   
3. Further quotes from the book:
   
4. p.33 The principle of Universal Gravitation, namely, that every particle of matter is attracted by, or gravitates to, every other particle of matter, with a force inversely proportional to the squares of their distances — is the discovery which characterizes The Principia. This principle the author deduced from the motion of the moon, and the three laws of Kepler—laws, which Newton, in turn, by his greater law, demonstrated to be true.
   

From the first law of Kepler, namely, the proportionality of the areas to the times of their description, our author inferred that the force retained the planet in its orbit was always directed to the sun; and from the second, namely, that every planet moves in an ellipse with the sun in one of its foci, he drew the more general inference that the force by which the planet moves round that focus varies inversely as the square of its distance therefrom: and he demonstrated that a planet acted upon by such a force could not move in any other curve than a conic section; showing when the moving body would describe a circular, an elliptical, a parabolic, or hyperbolic orbit. He demonstrated, too, that this force, or attracting, gravitating power resided in every, the least particle; but that, in spherical masses, it operated as if confined to their centers; so that, one sphere or body will act upon another sphere or body, with a force directly proportional to the quantity of matter, and inversely as the square of the distance between their centers; and that their velocities of mutual approach will be in the inverse ratio of their quantities of matter. Thus he grandly outlined the Universal Law. Verifying its truth by the motions of terrestrial bodies, then by those of the moon and other secondary orbs, he finally embraced, in one mighty generalization, the entire Solar System — all the movements of all its bodies — planets, satellites and comets — explaining and harmonizing the many diverse and theretofore inexplicable phenomena.

Guided by the genius of Newton, we see sphere bound to sphere, body to body, particle to particle, atom to mass, the minutest part to the stupendous whole — each to each, each to all, and all to each — in the mysterious bonds of a ceaseless, reciprocal influence. An influence whose working are shown to be alike present in the globular dew-drop, or oblate-spheroidal earth; in the falling shower, or vast leaving ocean tides; in the flying thistle-down, or fixed, ponderous rock; in the swinging pendulum, or time-measuring usn; in the varying and unequal moon, or earth’s slowly retrograding poles; in the uncertain meteor, or blazing comet wheeling swiftly away on its remote, yet determined round. An influence, in fine, that may link system to system through all the star-glowing firmament; then firmament to firmament; aye, firmament to firmament, again and again, till, converging home, it may be, to some ineffable center, where more presently dwells He who inhabiteth immensity, and where infinitudes meet and eternities have their confluş, and where around move, in softest, swiftest measure, all the countless hosts that crowd heaven’s fathomless deeps.

p.36
God suffers nothing from the motion of bodies; bodies find no resistance from the omnipresence of God.
p.38
The introduction of the pure and lofty doctrines of the Principia was perseveringly resisted.

Descartes, with his system of vortices, had sown plausibly to the imagination, and error had struck down deeply, and shot up luxuriantly, not only in the poyular, but in the scientific mind.

Besides the idea – in itself so simple and so grand – that the great masses of the planets were suspended in empty space, and retained in their orbits by an invisible influence residing in the sun– was to the ignorant a thing inconceivable, and to the learned a revival of the occult qualities of the ancient physics. This remark applies particularly to the continent. Leibniz misapprehended, Huygens in part rejected; John Bernoulli opposed; and Fontenelle never received the doctrines of the Principia. So that, the saying of Voltaire is probably true, that though Newton survived the publication of his great work more than forty years, yet at the time of his death, he had not above twenty followers out of England.

[The quote continues with Newton’s views on God.]

1. According to Newton spheres attract as if all of their masses at their center.
   
2. This force is supernatural and no spherical body can be said to use this force