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Anonymous at Tue, 5 Nov 2024 21:02:12 UTC No. 16464075
I have been reading Kepler. Does anyone want to tell me what the FUCK he is talking about with this relation? I cannot figure this shit out.
Astronomia Nova, Johannes Kepler, p.362 (Green Lion Press ed.)
'...And we would then say that as the length of the semicircle is to the sum of all the distances on the semicircle, so is this distance of the arc DG to the length of FD, which is the apparent size of CD seen from B.'
Now, if this strikes you as off, it should because that is a STATIC ratio to a dynamic one, something that necessarily changes.
Now, confusing things even more is what he means by this. Forget the fact that the first ratio is astronomically small (no pun intended), the second ratio is pretty clearly a very large one, as the distance of the overall arc from the Sun, which is what they are referring to, is compared to the overall length of the arc itself, which being 1 degree in the example given, is very small.
If he literally means the lengths of GD compared to FD, this doesn't make sense either, as this is clearly a large ratio, not a small.
Does anyone have any idea what the hell Kepler is referrring to in Chapter 48 of Book 4 of Astronomia Nova?
Anonymous at Tue, 5 Nov 2024 21:29:56 UTC No. 16464104
So, I believe Kepler has made a mistake. The fixed relation in the beginning has a relation, not on another functional, variable relation, but another circular, fixed relation.
The outer edge of the sector to the distance of the arc, has the same ratio that the entire perimeter of the circle taken together does to the sum of the 360 different distances of the different degrees of anomaly.
It's simply just a mistake on Kepler's part. It actually came about because he introduced some elliptical notion earlier in the chapter that did not follow. This was a relation that was somewhat obscure but I understood it to follow from that earlier, introduced relation obscurely.
If anyone wants I can explain further, but I have solved this on my own. It's almost immaterial as I can't imagine that Kepler would have actually used this to compute areas correctly, he must have actually used the comparative relation instead of the inverse relation that he stated here in the chapter.