All right, so the next slide is from Tom Coon of course. Showing how the illusion of retrograde motion occurs, because the sun is moving in this case, faster than Mars. So it goes by Mars, it approaches Mars, goes past it, and as you look at these different angles, you get the allusion of retrograde motion.
Okay? It's a nice figure, but it's not what I want to dwell on. I want to turn to De Rev, itself. Coon makes the remark, everybody makes some version of this remark, Coon makes the remark anybody who thinks De Rev is simpler than the Almagast has never read book three.
That's a paraphrase. That's not quite an exact quote. Owen Gingrich has a whole book out entitled The Book Nobody Ever Read. Namely De Rev, because after the first few pages it's actually harder to read and I'll illustrate that. Fairly significantly harder to read than the Almagest, though the Almagest is not easy at all.
So what we're gonna do first is look through the table of contents. The opening Book I is the counterpart to Ptolemy's Book I, where he gives you what I've called his working hypothesis. His background assumptions off of which he's gonna do evidential reasoning. In Copernicus' case, he's giving you his defense of heliocentrism.
So most of the argument for heliocentrism is contained in those opening pages, first almost 40 pages. Then he does a little trigonometry after that but all that's going on here is he's mimicking Ptolemy. I am putting book one the the Copernicus under the supplementary material so you can read it.
You already have Ptolemy there, you can see them side by side. Book two is you can start seeing the circles in their names. It's introduction to the main part of astronomy. I don't wanna dwell on that. Book three is the earth's sun orbit. And notice he calls it.
He talks about the motion of the sun because from his point of view it's the earth's sun orbit. Sure enough it's the earth going around the sun. But we on the earth see it. It's the sun going around us so it's just a relative motion to go from one to the other.
This is very messy. Book three. I'll come back. Well I'll start saying now what's involved here. He concluded two things. He concluded the trepidation is a real phenomenon. And therefore there had to be some sort of cyclic character with the procession of the equinox. He also concluded from observations from prior centuries.
Not his own, he did very few observations himself. He did some, but very few. He concluded that the eccentricity of the earth is not constant. That in fact it varies over a 3434 year period. 3434 year period. So as a consequence, all of book three is probably the most complicated book in the whole of the thing.
He's got to set up procession of the equinoxes. You can see that's what he's doing. He's got to set up this variation in the eccentricity of the earth's orbit. So it's the most complicated of all the orbits, suddenly. The solar orbit becomes the most complicated. For what it is worth.
So, what he actually does, is he's got an eccentric on a circle to vary the eccentricity. Has various consequences, I'm not gonna dwell on it. I do wanna say something though about the third motion in the procession of the equinox cuz it will drive a deep point home to you.
He represented, well I have to do this in two steps. We know the first motion, rotation of the earth. Second motion, earth around the sun. The third motion, he pictures the planet at a 23-degree angle, with its poles, sitting on a sphere. Now, if it's sitting rigidly on a sphere, when it turns around, what happens?
The part that's nearest the sun is always nearest the sun. Ha, no summer and winter anymore. So he concludes that each year, the axis has to do a 360 degree rotation to give us winter and summer. Notice how I did it. I did it the correct way. That is, the axis always has the same orientation.
If it's fixed to the sphere it doesn't, it goes differently and you have to do this. And then precession of the equinox is an inequality in the annual motion wobble of the poles so it ends up being a very complicated story for the procession of the equinox, and of course it's mistaken.
On the other hand, other reforms he did on the solar orbit are really important. He went to sidereal time. But having said that, he references everything to the mean sun just like Ptolemy did. Okay, so the center of everything is not the sun, it's the mean sun, is start to being what it is.
Anyway, book four is on the moon and it's essentially the same as the Ibn al-Shatir account with multiple circles. In, well I'll get to it, in the planets where originally in Commentariolus he eliminated eccentricity with a circle. In De Rev he decides to restore the eccentricity getting him down to only one epicycle per orbit.
An epicycle to handle the equin. It looks like he decided he really didn't want epicycles on top of epicycles, which of course is a famed, just as an aside, that's a famous quotation of what was wrong with Ptolemy, epicycles on top of epicycles. Ptolemaic astronomy never did that, except for Mercury.
Ibn al-Shatir did that, but nobody knew that. The person who seems to have said epicycles on top of epicycles was actually King Alfonse. And complaining about the Mercury orbit, but that's an aside. Finally, book six is on the planets, and all the planets are done in unison. They're not three separate books the way they are in the Almagest.
You'll notice Mercury gets some special attention as it is needed, but it turns out, that the Mercury orbit once again is just taken out of it and Ibn al-Shatir dropping one of the largest epicycle, and restoring eccentricity versus Ibn al-Shatir. Solution to Mercury is lifted, and it's not new.
And then the most dramatic thing, well two dramatic things. In the Almagest, we have a whole section of stars, and a catalogue of stars with over 1,000 stars. There's nothing like that here. That is, he did not make any effort to replace Ptolemy's catalog of the stars. It's just, the stars he simply skipped over.
Think of him all alone, working as a church canon, lawyer, and doing medicine, I'm reluctant to call it being a doctor given the state of medicine at the time. But he never took clergical whatever it is. But he remained one step below that and had a full day's work day after day in the church, and then worked on astronomy for twenty years on the side.
How much can one person do by themselves? The answer is it's limited. And he did not have anybody else to reticus comp. But that's the striking thing about the latitudes. What does he do about altitudes? Well remember Ptolemy has tilting things. He can't do tilting things the same way and it violates Aristotelian principles anyway.
So, he introduces a system of latitudes, but all he tries to do is to match calculated values from Ptolemy, which we know are far off. That is, there's no effort whatsoever to improve on the theory of latitudes other than to get rid of violations of uniform circular motion.
But, it's a gigantic book. It's a book that takes enormous effort. Fortunately, Noel Swerdlow working with Neugebauer have a two volume work on the mathematical astronomy of Copernicus that go through the mathematics page after page systematically. And I did bring that book tonight, but if you start wanting to know more about Copernican mathematical astronomy, that's where you turn.