That's great if Mars is going around the sun. What about Ptolemy? Every 687 days on Ptolemy's account, Mars is not in the same place. It's the attachment point of the epicycle that's in the same place. Meanwhile, Mars is swinging in conjunction with the sun. So, what does Kepler do?

He runs the same argument, now, with four observations of the Earth from A, which is the attachment point of the epicycle, to see if the epicycle of Mars has to have bisected eccentricity. And it's the argument just transfers because of course, the Mars' epicycle is just the Earth's sun orbit in image.

So the whole reasoning can be carried over. It just runs the page showing the same numbers work out. He again has the four observations and he then concludes that indeed, using triangulation in a Ptolemaic system, we can conclude with some finality that the epicycle does not have uniform circular motion.

It has an equin off the center. The center of the circle is not the attachment point. The attachment point is on the opposite side of the center from the equin. Okay? I trust you should be impressed by that, because he's now got an argument both ways. But not in the Ptolemaic for the Earth-Sun orbit, an Ptolemaic only for the epicycle.

And here's what he concludes. That these characteristics belong to the Ptolemaic epicycle is properly demonstrated. That's just what preceded before and I announced it. But that they are carried over from the epicycle to the theory of the Sun is shown by a probable argument only pieced together from Ptolemaic opinions.

And I'm not gonna bother to give you the argument, it's in effect saying Ptolemy himself, says that the epicycle is an image of the actual orbit of the Sun around the Earth, etcetera. He then goes on. So by this reasoning, even Ptolemy will be persuaded that sigma tau, the eccentricity of the Sun's motion found by Tico, should be bisected at epsilon, no, excuse me, that's psi, and the center of uniformity of motion at tau.

Bisected eccentricity. Now this argument in the Ptolemaic form, as I have just now began to say, is no firmer than the Ptolemaic world system itself. For anyone who believes Ptolemy, thinking that for the three superior planets, there are three theories of epicycles, exactly equal to the theory of the Sun in quantity and quality, in lines, as well as in motions, in absolutely all respects.

This same person will not admit this one inconsistency but will gladly derive the bisection tool from the epicycle, transferring it to the solar theory as if from an image in a mirror to the face itself. And finally, when the comparison of hypotheses has been made and it has appeared that four theories of the sun, or rather six as will be shown elsewhere, can be generated from a single theory of the Earth like many images from one substantial face.

The sun itself, the clearest of truth, will melt all this Ptolemaic apparatus like butter and will disperse the followers of Ptolemy. Some to Copernicus' camp, some to Tico's. Okay? And at this point, understand now, he has made a point here, and it's gonna continue through the book. We're almost at the break point.

Anything he does with the Earth's sun orbit, or with the Mars' orbit in a Copernican or Ticonic system, can always be transferred to a Ptolemaic. Okay? Always. Now he says, let it be enough for now to present this form of demonstration and the three hypotheses. He's been running all the hypotheses all the way through to this point.

In what follows whenever there is need of the same demonstration, I shall use Copernicus' form alone, it being the simplest, so as not to be long winded. Here in contrast, the industrious reader has seen how any of these diagrams can be transformed into either the Ptolemaic or the Copernican form using parallel lines.

Okay? So for the rest of the book, we run a Copernican only argument with full acknowledgement that can be transferred to be either of the system. Okay? Last points on this. Well first of all what's happened with the bisection of the eccentricity of Mars's ellipse? Remember that earlier curve, with the very low four degrees of inaccuracy happened?

It's gone. We don't need an ellipse. We don't need the area rule. We're home free the moment we adjust to the actual Sun, and recognize that the Earth's sun orbit and therefore all those epicycles have to be bisected the eccentricity as well. So the two curves here are, the best Ptolemy you can do.

With bisected eccentricity and the other is the original Ptolemaic. And Voelkel and Gingerich explain here the 15-year pattern. What's happening is an inaccuracy in Mars and an inaccuracy in the Earth's Sun, every 15 years align to produce the very large error. It is actually even worse, it's even more clear repetitive in 32 years.

Now notice what's happened here. Kepler's famous for the area of rule in the ellipse, but we start out with four to five degree discrepancies. We now have discrepancies around 20 minutes of arc maximum. Maybe 30, it's hard to read that, but it's down to very small amount and we haven't touched either the aerial or the ellipse yet.

Okay? So the things he's not famous for are the things that eliminated almost all the error. Now don't underestimate how hard it was to get the ellipse, because as I told you several times, the minor axis of Mars is only four-tenths of 1%, shorter than the major axis.

These are much more gross revisions. But he's got those in place. Part Three then ends with a long discussion of the Physics. I'm going to read this and then we will stop for a break. It was demonstrated in the previous chapter, this is Chapter 33, that the elapsed times of a planet on equal parts of the eccentric circle, are in equal distance in the ethereal air, are in the same ratio as the distances of those spaces, from the point whence the eccentricity is reckoned.

Or more simply, to the extent that a planet is farther from the point which is taken as the center of the world. To the extent that a planet is farther from the point, which is taken as the center of the world, it is less strongly urged to move about that point.

It is therefore necessary that the cause of this weakening is either in the very body of the planet, in a motive force placed therein or right at the supposed center of the work. Three possibilities. Now it is an axiom in natural philosophy of the most common in general application that of those things which can occur at the same time in the same manner, and which are always subject to light measurements.

Either one is the cause of the other or both are effects of the same cause. Isn't that an interesting thing to hear about correlations? Just so, in this instance, the intention and remission of motion is always in the same ratio as the approach and recession from the center of the world.

Thus, either that weakening will be the cause of the star's motion away from the center of the world. Or the motion away will be the cause of the weakening. Or both will have some common cause. But it would be impossible for anyone to think up some third concurrent thing which would be the clause of these two.

And in the following chapters, it will become clear that we have no need of feigning any such course since the two are sufficient in themselves. Of course, the third course, I guess everyone can anticipate as Newtonian gravity. But that's okay, nobody can quite imagine. Further, it is not in accord with nature that strength or weakness and longitudinal motion should be the cause of distance from the center.

For a distance from the center is prior both in thought and in nature to motion over an interval. Therefore, distance will be the cause of intensity of motion. And a greater or lesser distance will result in a greater or lesser amount of time. And with that we start getting a story for several chapters of a rotating sun, magnetism driving, etc.

And that almost ends part three. The last part of part three, I will discuss after break. And we're at 3 after, can we resume at 13 after? And I'll field questions at that point as well. I got to where I wanted to only three minutes late.