Tracing the history of medieval astronomy
Now that we’ve done a bit of preliminary theory, we’re ready to jump into an example problem. As with before, Ptolemy selects Rhodes at a latitude of 36º. Since we’ve been seeing several of the same diagrams here, I’m going to forego the buildup and give a mostly completed diagram:
Continue reading “Almagest Book II: Calculation of Rising Times at Sphaera Obliqua”
When construction initially began on my quadrant, I had little to go on except the etching of the instrument and my own knowledge of how such an instrument should work. I knew the image came from a work of Tycho Brahe’s, Astronomiae Instaurate Mechanica (Instruments for the Restoration of Astronomy), but at the time was unable to find a translation to see if there was anything I was missing.
Fortunately, a few months ago, I finally located a translation of the vast majority of the book. However, the website seemed to lack the beautiful etchings that should accompany the text. However, scans of the original work were available through the NASA ADS. Unfortunately, being scans of a book over 400 years old, not all of the images were in good condition.
Still, I have worked to piece the text back together with the images, working over the past few months to digitally clean the images, removing smudges and stains, and reproducing the text as a digital copy best matching the original format as possible.
I now provide it as a .pdf for those interested.
In the last post, we proved that two arcs of the ecliptic that are equidistant from the same equinox rise in the same amount of time. In this post, we’ll prove something similar for what happens with arcs of the ecliptic equidistant from the same solstice.
It’s been awhile since I’ve been able to update the blog with anything from the Almagest. As noted in the last post from the book, this section is not one of the better written ones. Indeed, it’s taken me the better part of a month to really work out how the diagram is put together.
Ultimately the trouble stemmed from the fact that it’s not a single diagram; it’s actually two pasted together1, so instead of throwing it all at you at once like Ptolemy did, let’s work through each piece in turn before pasting it together.
To begin, let’s start with a simple celestial sphere:
This weekend was Crucible at the Crossroads here in my home Barony of Three Rivers. I taught two classes, one on a general overview of medieval astronomy, and one introducing practical observational astronomy. In addition, it was the autumnal equinox on Saturday, so some minor adjustments were made to the quadrant to allow for solar angle observations. Lastly, I was called up in court for a few awards related to the project.
More on all of that beneath the fold. Continue reading “Data: Stellar Quadrant Observations – 9/22/18 (Crucible at the Crossroads)”
In this next chapter, Ptolemy’s goal is to
show how to calculate, for each latitude, the arcs of the equator… which rise together with [given] arcs of the ecliptic.
To do this, we’ll do a bit of convenient math, breaking the full ecliptic into its traditional 12 parts. However, since these signs are not of equal size, Ptolemy takes an even 30º for each sign, beginning with Aries, then Taurus, etc…
The first goal will be to prove that
arcs of the ecliptic which are equidistant from the same equinox always rise with equal arcs of the equator.
So you’re interested in coming to help do some observations with the quadrant, but not sure if you can really help since you’re not a science person. This post should get you started! Continue reading “Quadrant Crash Course”
I’ve known this chapter was coming for awhile, and have struggled to decide how to deal with it. The reason is that, Ptolemy goes through various climate zones as defined by Hipparchus. In particular, they are defined by their latitudes, beginning with the equator, all the way up to the north pole. For that 90º, it is broken into 39 zones.
As such, this chapter has much in common with the tables we’ve seen previously. But those were straightforward to reproduce. But since the information in this chapter is not particularly tabular, it would be a hefty post to cover each one. But on the other hand, the footnotes in the translation make specific note that the information in this chapter is not referenced again.
Continue reading “Almagest Book II: Exposition of Special Characteristics, Parallel by Parallel”
First off, what’s a gnomon?
Apparently it’s the part of a sundial that casts shadows. Now you know.
To start this next chapter, Ptolemy dives straight into a new figure, but I want to take a moment to justify it first. To begin, let’s start with a simple diagram. Just a side view of the meridian, the horizon, and the north celestial pole. The zenith is also marked (A).
Continue reading “Almagest Book II: Ratio of Gnomon Equinoctial and Solsticial Shadows”
The fourth chapter in book two is a very short one. In fact, it’s a single paragraph so I almost didn’t dedicate an entire post to it but ultimately decided to as it didn’t really fit with either the previous or next chapter.
In this, Ptolemy says,
it is a straighforward computation to determine for what regions, when, and how often the sun reaches the zenith. For it is immediately obvious that for those beneath a parallel which is farther away from the equator than the 23;51,20º (approximately), which represents the distance of the summer solstice, the sun never reaches the zenith at all, while for those beneath the parallel which is exactly that distance, it reaches the zenith once a year, precisely at the summer solstice.
For the past few Almagest posts, we’ve been working on the following diagram:
As a refresher, AEG is the celestial equator and BED is the horizon of an observer. Z is south. H is the point of the winter solstice as it crosses the horizon (or rises).
In the first post we determined $arc \; EH$. In the second post, we used that to determine $arc \; BZ$. In the third, we’ve determined $arc \; E \Theta$ and then came full circle and showed another way to get $arc \; EH$.
Now, Ptolemy wants to generalize. Continue reading “Almagest Book II: Symmetries of Arcs and Day/Night Lengths”
