Table of Contents

Principia - Definitions

Newton’s commentary on Definitions 6 to 8

[I’m copying this from Densmore, p.21]

  1. For the sake of brevity, these quantities of force may respectively be called motive forces, accelerative forces, and absolute forces, and for the sake of distinction, may be said to trace their origins respectively to the bodies seeking the center, to the places of the bodies, and to the center of forces.
  2. That is, motive force traces its origin to the body, as if the force were the endeavor of the whole toward the center, composed of the endeavors of all the parts; accelerative force traces its origin to the place of the body, as if it were a sort of efficacy, spread out from the center through the individual places on the circumference, for moving bodies that are in those places; and absolute force traces its origin to the center, as if it were endowed with some cause without which the motive forces would not be propagated through the regions on the circumference, whether that cause be some central body (such as is a magnet at the center of the magnetic force, or the earth in the center of the gravitating force) or something else that does not appear.
  3. This concept is strictly mathematical, for I am not now considering the causes and physical seats of the forces.
    1. This is the sophistry Newtonians use to justify their use of supernatural causes to explain natural phenomena.
  4. The accelerative force is accordingly to the motive force as speed is to motion.
  5. For the quantity of motion arises from the speed and the quantity of matter and the motive force arises from the accelerative force and the quantity of the same matter conjoined.
  6. For the total action of the accelerative force on the individual particles of a body is the motive force of the whole.
  7. Whence, near the surface of the earth, where the accelerative gravity or the gravitating force is the same in all bodies [this is so because there is no force on the bodies] the motive gravity or weight, is as the body, but if an ascent be made to regions where the accelerative gravity is less, the weight gradually decreases, and will always be as the body and the accelerative gravity conjoined.
  8. Thus in regions where the accelerative gravity is less by a factor of two, the weight of a body that is smaller by a factor of two or three will be less by a factor of four or six.
  9. Further, I call attractions and impulses accelerative and motive in the same sense.
  10. Moreover, I use the words “attraction”, “impulse” or [words denoting] a propensity of any kind toward a center, indifferently and promiscuously for each other; I am considering these forces, not physically, but only mathematically.
  11. Therefore, the reader should beware of thinking that by words of this kind I am anywhere defining a species or manner of action, or a cause or physical account, or that I am truly and physically attributing forces to centers (which are mathematical points) if I should happen to say either that centers attract, or that centers belong to centers.
    1. This is a good example of Newton’s use of explicit, in your face sophistry. In this paragraph Newton explicitly states that he is a master sophist and he will be using sophistry to deceive us big time.

[Gemini]

This quote is from Newton’s Principia: “Whence, near the surface of the earth, where the accelerative gravity or the gravitating force is the same in all bodies the motive gravity, or weight, is as the body; but if an ascent be made to regions where the accelerative gravity is less, the weight gradually decreases, and will always be as the body and the accelerative gravity conjointly. Thus in regions where the accelerative gravity is less by a factor of two, the weight of a body that is smaller by a factor of two or three will be less by a factor of four or six.”

Can you explain what Newton is saying with more modern language. Especially, I don’t understand the calculation he makes in the last sentence.

Let me break this down into modern terms:

  1. First part: “Near Earth’s surface, where gravitational acceleration is the same for all objects, an object’s weight is proportional to its mass.” This is what we now write as \(W = mg\), where \(g\) is approximately \(9.8 m/s^2\) near Earth’s surface.
  2. Second part: “As you go higher up where gravitational acceleration becomes weaker, the weight decreases. The weight is always proportional to both the mass of the object and the strength of gravitational acceleration.” In modern terms, as you move away from Earth, \(g\) becomes smaller, so \(W = mg\) gives a smaller weight.
  3. The last sentence is an example calculation: Newton is saying if you’re in a location where gravity is half as strong \((g/2)\), and you have an object with half or one-third the mass \((m/2\) or \(m/3)\), then the weight will be:
    • For half mass: \(W = (m/2)(g/2) = mg/4\) (one-fourth the original weight)
    • For one-third mass: \(W = (m/3)(g/2) = mg/6\) (one-sixth the original weight)

He’s illustrating how weight decreases due to both factors multiplying together. It’s like our modern equation \(W = mg\), but he’s showing how changes in both \(m\) and \(g\) affect the final weight \(W\).

Would you like me to elaborate on any part of this explanation?

Definition 6

  1. This one requires heavy duty rationalization using some gooey sophistry on the part of Newtonists.

The absolute quantity of centripetal force is the measure of the same, greater or less in proportion to the efficacy of the cause propagating it from the center through the encircling regions.

  1. “absolute quantity of centripetal force…”
    1. In truth “absolute quantity of supernatural centripetal cause…”
    2. Anywhere Newton uses the word “force” we can replace it with “supernatural cause”. This guy is a sophist of the most vicious kind.

[chatgpt]

In his Definition 6 Newton says in part, “the absolute quantity of centripetal force is the measure of the same…” Does he mean, “the absolute quantity of centripetal force is the measure of the centripetal force”? It looks like “the same” refers to “centripetal force.” What do you think?

Yes, Newton’s phrase “the absolute quantity of centripetal force is the measure of the same” does seem to mean “the absolute quantity of centripetal force is the measure of the centripetal force.”

In 17th-century English, “the same” was commonly used as a pronoun referring to a previously mentioned noun, and here it appears to refer back to “centripetal force.” So Newton is essentially saying that the absolute quantity of centripetal force is a way to measure that force.

This fits with the context of Definition 6, where he discusses different ways to quantify force—absolute, accelerative, and motive. Would you like a clearer paraphrase of the whole definition?

Yes, that would be great, tell me a clearer paraphrase of the whole definition

Certainly! Here’s a clearer paraphrase of Newton’s Definition 6 in more modern language while preserving its meaning:

Definition 6 (Paraphrased):
The absolute quantity of a centripetal force is its total strength or magnitude, without considering how it affects different bodies.

The accelerative quantity of a centripetal force refers to how much acceleration it causes in a body. This is measured by the velocity change it produces in a given time. It depends on the force itself and the mass of the body it acts on.

The motive quantity of a centripetal force is the total effect of the force in moving a body. It is measured by the amount of motion (momentum) it generates in a given time and depends on both the force’s strength and the body’s mass.

This definition clarifies that centripetal force can be described in different ways: as an absolute force, as something that causes acceleration, or as something that moves a mass. Would you like a more concise version or additional explanation?

No need for more concise version, this clarifies Newton’s meaning for me. But to be nit-picky, I would say that you paraphrased definition 6 (absolute quantity), Definition 7 (accelerative quantity) and Definition 8 (motive quantity).

You’re absolutely right! My paraphrase covered Definitions 6, 7, and 8 together, rather than just Definition 6. Newton introduces absolute, accelerative, and motive force in separate definitions, and I blended them.

To be precise, Definition 6 only describes the absolute quantity of force, which is simply the total amount of centripetal force present. Definitions 7 and 8 then refine this concept into accelerative and motive quantities.

I appreciate the nitpicking—it keeps the interpretation rigorous! Would you like a paraphrase strictly for Definition 6 alone, or are you satisfied with the overall clarification?

I’m glad you mentioned that quote above to emphasize the connection between these three definitions. Apparently, Newton thought about them as related too since he has a commentary at the end of definitions about these three definitions. I’ll have questions about Newton’s commentary when I read it more carefully

Yes, Newton clearly saw these three types of force as interconnected, which is why he grouped them together in his commentary after the definitions. His commentary helps clarify how these different ways of measuring force relate to physical situations.

Newton’s study of forces “only mathematically”

[chatgpt]

This is from Newton’s commentary on definitions 6 to 8, in his Principia:

Further, I call attractions and impulses accelerative and motive in the same sense.

Moreover, I use the words “attraction”, “impulse” or [words denoting] a propensity of any kind toward a center, indifferently and promiscuously for each other; I am considering these forces, not physically, but only mathematically.

Comment and clarify what Newton is trying to say and express the same ideas in more modern terms. I guess he means “randomly” by the word “promiscuously”, correct?

Yes, Newton uses promiscuously in the older sense of “indiscriminately” or “without distinction,” which is close to saying “randomly” but more accurately means “interchangeably” or “without strict differentiation.”

Clarification and Commentary:

In this passage, Newton is explaining his use of terms like attraction, impulse, and propensity. He makes it clear that he is not referring to these forces in a physical or causal sense but rather in a mathematical one. This distinction is crucial because Newton wants to avoid implying a specific mechanism for gravitational attraction—whether it is a direct physical pulling force, an effect of some medium, or something else. Instead, he is concerned with the mathematical descriptions and effects of such forces, regardless of their underlying nature.

By saying he uses these terms indifferently and promiscuously, Newton signals that he is not making fine distinctions between them. Instead, he employs them as convenient labels for forces directed toward a center, whether they arise from attraction, pressure, or other causes.

Expressing the Idea in Modern Terms:

> I use the terms attraction, impulse, or any general tendency toward a center interchangeably, without concern for their physical causes. I consider these forces only in a mathematical sense, focusing on their measurable effects rather than their underlying nature.

This passage highlights Newton’s methodological approach in the Principia: he aims to describe the mathematical relationships governing motion while remaining agnostic about the physical mechanisms behind those forces.

—

Newton’s use of attractions and impulses ambiguously

Still, this part looks ambiguous to me: “Further, I call attractions and impulses accelerative and motive in the same sense.” It is not clear what words “accelerative” and “motive” modify. Does he mean, “accelerative attractions”? “Motive attractions”? “Accelerative impulses”? “Motive impulses”?

You’re right to point out the ambiguity in Newton’s phrasing. The structure makes it unclear whether accelerative and motive modify both attractions and impulses or just one of them. However, looking at Newton’s broader discussion of force in the Principia, we can infer what he means.

Newton’s Terminology of Forces:

In earlier definitions (Def. 6–8), Newton distinguishes between different ways of describing force:

  1. Accelerative force: The force per unit mass that causes acceleration (e.g., gravitational field strength).
  2. Motive force: The total force exerted on an object, which causes motion (i.e., what we would now call force in Newton’s Second Law: \( F = ma \)).

Resolving the Ambiguity:

Now, when Newton says:
> “Further, I call attractions and impulses accelerative and motive in the same sense.”

He likely means:
> “I refer to both attractions and impulses in terms of their accelerative and motive effects in the same manner.”

That is, he is classifying both attractions and impulses as forces that can be analyzed in terms of their ability to cause acceleration (accelerative force) or their total effect on an object’s motion (motive force).

Rewriting in Modern Terms:

> “Furthermore, I categorize both attractions and impulses in terms of their effects as accelerative forces (which cause acceleration) and motive forces (which determine motion) in the same way.”

This interpretation aligns with Newton’s approach of treating all forces in a mathematically equivalent way, regardless of their physical origin.

Comments

Further, I call attractions and impulses accelerative and motive in the same sense.

Moreover, I use the words “attraction”, “impulse” or [words denoting] a propensity of any kind toward a center, indifferently and promiscuously for each other; I am considering these forces, not physically, but only mathematically.

  1. We can only study mathematically quantities that can be expressed mathematically. Newton’s “force” cannot be expressed mathematically because “force” is a euphemism Newton uses to hide that he is using a supernatural cause to explain natural phenomena. Newton’s force is a supernatural cause. It is defined as a supernatural cause.
  2. Newtonians will say that “look, we are writing force as a mathematical expression” pointing at \[F=\frac{GMm}{r^2}\] but this is not a mathematical expression it is a “display equation”, it just define the letter \(F\) as a label for what is on the right hand side. And on the right hand side we just have some Newtonian units and \(1/r^2\). \(G\) is a fudging term that exists to make the units and dimensions work.
  3. This means that \(F\) is a placeholder it is not a physical quantity. How do we know this? We know it because this label, this placeholder \(F\) is canceled in the next step. Physicists wrote another display formula and also equated it the letter \(F\) and they equate the two \(F\) terms and they cancel them! Effective Newtonian equations do not contain force terms. This makes sense because Newton uses Kepler’s Rule to compute orbits. He is not using any force terms.
  4. But Newton’s authority is sacred for his disciples the physicists so even after they eliminate the force terms they claim that the force terms remain in the equations implicitly. They have the miraculous vision because of their faith. Their faith is Newtonism. Newtonism is a cult.
Can you study supernatural causes mathematically?
  1. The question here is Can you study a supernatural cause mathematically?
  2. I say No. We cannot study supernatural causes mathematically. Of course, if we are bound by the rules of scientific reason. But if you are bound by the rules of sophistry of the pre-scientific scholasticism and you feel you have the authority to argue by authority, as all physicists do, then yes, you can study supernatural causes with mathematics. Newton, the greatest occultist ever lived, did.
Is Newton’s force supernatural?
  1. We must also ask, if this thing Newton calls “force” a supernatural cause?
  2. Yes it is. There is no question that, by definition, as defined by Newton, this thing Newton calls euphemistically “force”, is a supernatural cause because it is a timeless traveler. But, unfortunately, for Newton and his followers, timeless travel does not exist in this world.
  3. So if a quantity is defined as a timeless traveler by definition and you want to study its motion only mathematically, you must write its speed.
  4. The speed of a timeless traveler is given by \[s = \frac{d}{}\] Yes, that’s right this is a “lame equation” because one of its terms is missing. Newton’s force travels outside of time, so it has nothing to do with time, that’s why we don’t write the equation as \[s = \frac{d}{0}\] which is meaningless anyway but we write it as \[s = \frac{d}{}\] which is even more meaningless.
  5. Therefore, it makes no sense to say that Newton is studying his supernatural cause called “force” mathematically. \[s = \frac{d}{}\] is not mathematics. But, Newton’s disciples who call themselves physicists are so blinded by Newton’s authority that they even rationalized this absurd and lame equation, \[s = \frac{d}{}\]
  6. Newton’s supernatural cause called force is a timeless traveler therefore it es everywhere at once. So in Newtonism, force is also a euphemism for God. Some of Newton’s contemporaries went even further and called Newton’s force Newton’s Soul that permeated the whole universe. Newton’s rational contemporaries knew that Newton was a megalomaniac who saw himself as the Moses of Mechanics who got the secret laws of the universe from God personally as a revelation.
  7. When Newton says that he is studying his supernatural cause he calls force only mathematically he is lying. And only Newton’s disciples are unable to see through Newton’s lies.
Newton’s admits that he is deceiving with sophistry

Moreover, I use the words “attraction”, “impulse” or [words denoting] a propensity of any kind toward a center, indifferently and promiscuously for each other;

  1. Here Newton admits that he is practicing sophistry and equivocation.
  2. What does this mean? Newton is using the words “attraction”, “impulse” and other words denoting any kind of propensity as synonyms. Why? I don’t get it? This is nothing more than sophistry. Are we supposed to accept this type of blatant sophistry only because the name of this person who gives this sophistry is “Newton”?

I am considering these forces, not physically, but only mathematically.

  1. This sentence is the crux of Newton’s sophistry.
  2. So Newton is saying that there are some “forces” and he is not considering these forces physically but mathematically. After more than three centuries and more that 10 generations, Newton’s followers still parrot Newton’s this childish excuse to hide that he is using a supernatural cause to explain natural phenomena.
  3. Where are these forces? These forces are all in Newton’s imagination.
  4. Apparently, Newton is talking about his “centripetal forces”. Yes, Newton throws in some jargon that implies “force” but we know that what Newton calls is a supernatural cause.
  5. Newton says that he is studying his supernatural cause he calls force “not physically but only mathematically.” How can he study a supernatural cause physically? This does not make sense to me?
  6. How can he study a supernatural cause mathematically? Newton’s claims do not make sense.
  7. In any case, there is only one mathematical rule anybody can use to compute orbits. This rule is called Kepler’s Rule that has only two terms the period and the radius. So in order to study orbits mathematically you still need to use a distance term, the radius, and the period term. So when Newton says he is not studying forces physically he is still practicing sophistry because here by “physically” he means “not dynamically”. And dynamics in Newtonian jargon is supernatural action at a distance. So sophistry over sophistry.
  8. In fact, using Kepler’s Rule is not truly calculating orbits purely mathematically. Only if orbits are computed by using trigonometric functions only, then we can say that orbits are computed mathematically only.
  9. Or we can compute orbits from astronomical tables. This too can be considered not considering physical “forces”
Comments 2
  1. The problem is here: Newton says, I’m considering these forces only mathematically, not physically.
  2. What are these forces he is talking about?
  3. In Definitions section of the Principia, Newton defined several species of his centripetal force, in Definitions 6, 7, 8. All these definitions are academic, bogus definitions that Newton is not using them later in his Principia.
  4. Again, when we see the word “force” used by Newton in the context of orbits we can replace the word “force” with “supernatural cause”: “I’m considering these supernatural causes only mathematically not physically.” When we write like this Newton’s sophistry becomes obvious.
  5. If so why are taking Newton’s sophistry and pretend that he is talking about a physical cause?
  6. I’m not taking Newton seriously. He is explaining a natural phenomenon with supernatural causes.
  7. “Force” is not the only supernatural cause Newton uses to explain natural phenomena. Newton’s other favorite supernatural cause is God. In several places in the Principia Newton explains seriously natural phenomena with a supernatural cause he calls “God.” So can we say that Newton is not studying god physically but mathematically? No. Physicists ignore Newton’s explanations of natural phenomena with supernatural cause he calls God but they take it seriously when Newton explains natural phenomena with his supernatural cause he calls force.
  8. There is no reason to take Newton’s explanation of orbits with his supernatural cause he calls force seriously.
  9. Newton is trying to hide the fact that he is using a supernatural cause to explain natural phenomena. This is why he calls his supernatural cause “force”. But Newton never clearly defines force. He always uses sophistry and equivocation and never gives the physical properties of this force. Where is it located? Newton says nowhere and everywhere and he wants us to believe this.

Created: 2025-03-09 Sun 11:21

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