We have one further document. This is from Rupners paper of year 2000. Which is what I put under supplementary material. This is a Newton page. It's a set of propositions on comets at the top, you'll notice the number. You'll notice something else, at the bottom of the page is writing but it's upside down.

This is fairly typical of Newton. If he wants to write something down, he'll grab almost any paper and just start writing it down and doesn't date it. We don't know when this dates from. And when you see what he says in it, you'll see why I wish we knew how to date it.

Ruffner dated it before Halley visited him in 1684 but after, of course, the Flamsteed for residual C right now. This is Ruffner's translation of the Latin. And it's actually 15 points with numbers ten and 11 skipped, but an insert where they are. Comets are higher than the moon.

The matter of the Heavens is fluid. The matter of the heavens revolves around the center of the cosmic system in the direction of the courses of the planet's vortices. According to the most ancient philosophy of Aristarchus of Samos restored by Copernicus the sun is the center of the cosmic system and the Earth is a planet.

Pause there a moment. Ruffner's view. I don't know whether I agree with him or not. We know at this time Newton started developing a view that others were developing during the period. Namely that the wisdom of the ancients had been lost. Lost in the intervening period and we had to recover it.

That included recovering true Christianity from what the medievalist had done to butcher it. And Catholics have done to butcher. But he's also suggesting that the ancient Greeks had far more knowledge than the past, I'll come right back. And his view, Newton's view, is the whole problem is people started taking, as literal claims that were metaphoric.

So you had to reinterpret the classic claims. Now this is the only sign here of that appeal to ancients. The appeal to Aristarkis. It's because it's there that I bring this up. This is Ruffner's view of what changed Newton's mind. His reading about ancient text and hearing this idea that ancient wisdom had been lost.

Caused him to take seriously some claims about comet returning in ancient writing. There's gravitation towards the center of the sun in each of the planets, and that towards the center of the sun is far greater. That gravitation in things diminishes in duplicate ratio to the distance from the center of the sun or planet, as they receive from the surface of the sun or a planet.

The motion of a comet is accelerated until it is in parahelium and retorted afterwards. A comet does not travel in a straight line but in some curve, the maximum curvature of which is at the minimum distance from the sun. The concave part faces the sun, then the plain passes through the sun and the sun is in its near focus.

The angular motion of a comet around the sun is very nearly reciprocal to the distance from the sun, whence the motion would be uniform only if preformed in a straight line. Again, we don't know whether he's saying nearly one over r because the area rule holds. Or because he said 1 over r disturbed by the vortex, we don't know.

All we have are these. The curve is an oval if the comet returns in an orbit. If not, the curve is nearly hyperbola. Twelve, the tail of the, the rest of this is less interesting, though it's a big deal. What I'm skipping over here is all the discussion of the tail and what it tells us about comets.

Okay. And, by the way that comet of 1680, 81 stretched over 40 degrees in the sky. That's 80 moon widths, it was spectacular at one point. So they're often spectacular. This one was apparently just remarkable. And by the way, the very best observations of it were done in early December by Halley but Newton didn't learn of those at this time.

We don't know when Newton finally came to learn of him but somewhere along the way. This last one the comet descended below the sphere of Mercury. This is proved from the longitude of the tail. The same point is proved from the quantity of light by reason of the distance.

All right enough of this, somewhere in here he has changed his mind about comets. The presumption is this is before Halley visited him in August 1684, but we don't actually know that. And we don't know why he changed his mind. We also don't know how he decided inverse square oval motion for planets.

And is denying it for comets unless he's following the Hooke idea that different matter responds differently to gravity. In which case, of course, universal gravity is very, very far from his mind. I've used this for years to say universal gravity had just not even occurred to him at this juncture.

Not this, I didn't know this existed. I should have known it was in my copy that was found. But 3965, the manuscripts pertaining to the Principia that got put together by Stokes and John Adams in the 1880s. It's around 750 or 800 pages all hand-written. You don't sit, and most of it in Latin.

You don't sit and read it. And if it's a page, it's all scribbled. You look at it and it's not what you're looking for and you just skip it. Obviously, Ruffner was lucky for just this sort of thing and he found it. So this wasn't known when I started this course, that document I just gave you.