Now we get to the laws, and what in the world does the term law mean? It looks like for Descartes, what it means, is a claim the holds universally all off all matter in the universe at all times. And that added feature. It has no further basis than the fact that this is the way God chose to create the world.
Okay? So these fundamental three laws he's going to issue are supposed to apply to everything at all times number one. And number two there's no further explanation for why they do. Then that's the way God created the world. And the obvious question is why didn't this notion show up in Kepler and Galileo?
Galileo occasionally uses the word lex, law, or the equivalent in Italian. But where Stillman Drake translated him as laws, if you go back and look at my correction, where I put in the Italian word, it's governing. So they talk about governed by principles, but that's not necessarily the same as what Descartes means by a law.
But the real reason Kepler and Galileo did things this way, is they were not trying to lay foundations in their work. They weren't asking, what are the ultimate answers to why questions? Descartes was proposing that. And he was proposing it in direct contrast to Aristotle's four kinds of answers.
To why question the so called four causes. You will see that a little later from a passage in Le Mond. So the Principle, the idea behind laws in the sense he wants, of course he is importing a term from renaissance naturalism. But these things are so fundamental that they are not local whatsoever.
They instead characterized all of nature. And the quote I give you, the rules, reguli, or laws of nature, which are the secondary and particular causes of the diverse movements which we notice in individual bodies, those are the things that God put there for them to work mechanically. Everything works according to them, okay.
So it's just not a notion we've seen in any of the reading we've done so far. Because nobody is trying to give that kind of a universal foundation for all of mechanics. First law of nature, as it is in the Principia. Each thing provided it is simple, and undivided, always remains in the same state as far as in it's power and never changes except by external causes.
The phrase quantum inseas translated here as far as in it's power, however much it is in itself I think the literal Latin. Is that right? Quantum is how much? That's from Lucretius, and it's something Lucretius uses constantly in the connection of things being able to change themselves versus change is external.
So, Newton adopts it from Lucretius, maybe from Descartes as well, but other do. The version in Le Monde is much simpler. Each individual part of matter always continues to remain in the same state unless collision with others forces it to change that state. So the two are fairly different.
Then the explanation in the Principia. If it is at rest, we do not believe that it will ever begin to move. Unless driven to do so by some external cause. So, this is a principle about external causes. And the word external is crucial here. Nor if it is moving is there any significant reason to think that it will ever cease to move of it's own accord and without some other thing which impedes it.
For there is no other reason why things which have been thrown should continue to move for some time after they have left the hand which threw them, except that having once begun to move, they continue to do so until they are slowed down. By encounter with other bodies.
Now, again, that's a very, very radical proposal. What did we see at Galileo? We accumulate impetus and spend impetus then as we go back up. There's nothing like that here. Just, if a body's in motion, it's in motion and bodies can't do anything about that themselves. It requires external cause, so far, so good?
Second, glob nature. Each part of matter considered individually, tends to continue its movement only along straight lines, and never along curved ones. In Le Monde. When a body is moving, even if its motion most often takes place along a curved line, it can never take place along any linen that is not in some way circular.
Nevertheless, each of its individual parts tends to always continue its motion along a straight line. And thus there action, i.e., the inclination they have to move. I think inclination is propentiatum, is different from their motion. Actually it can't be propentiatum, it's in French.
This rule, like the preceding one, results from the immutability and simplicity of the operation by which God maintains movement and matter. For he only maintains it precisely as it is at the very moment at which he is maintaining it and not as it may perhaps have been at some earlier time.
Of course no movement is accomplished in an instant, yet it is obvious that every moving body at any given moment in the course of its movement is inclined to continue that movement in some direction in a straight line. And never in a curved one. Now I've always found that question making.
Why can't God have things just naturally going in curved lines? What is it about a straight line that favors it over a curved line? And maybe Descartes himself felt a little uncomfortable with that argument because now he gives the sling argument and the sling argument is of course, what became very, very important.
When the stone A is rotated in the sling EA, and describes the circle ABF, at the instant at which it is at point A, it is inclined. Notice the actual word, determined, to move along the tangent of the circle toward C. We cannot conceive that it is confined to any circular movement, because although it will have previously come to L to A along a curved line, none of this circular movement can be understood to remain in it when it is at point A.
Moreover this is confirmed by experience because if the stone leaves the sling it will continue to move not toward B but towards C. From this it follows that anybody which is moving in a circle constantly tends to move away, that's recede, receder, from the center of the circle which it is describing.
Indeed our hand can even feel this while we are turning the stone in the sling added in the French for it pulls and stretch the rope in an attempt to move away from our hand in a straight line. The word stretch is by the way that's. No. It's I'm sorry.
And that's usually translated as attraction in translations of Newton's Principia. Newton actually distinguishes two words. And. Here, means to draw something, pull something. And that's the word being used here. This consideration is of such importance and will be so frequently used in what follows that it must be very carefully noticed here.
I shall explain it more fully later. All right, we're gonna look next week, spend a substantial portion of next week on the four pages where he considers it further. The very fact that he says this here is screaming at you he's saying something really important here. The important thing is, curvilinear motion is not self sustaining.