Having laid out his order of the spheres, Ptolemy still has more to say as an introduction to planetary theory before moving on to a specific one. Continue reading “Almagest Book IX: Purpose of the Planetary Theory”
Almagest Book IX: On the Order of the Spheres
Having laid out “the sum total of the chief topics one may mention as having to do with the fixed stars, in so far as the phenomena [observed] up to now provide the means of progress in our understanding” Ptolemy now moves on to “the treatment of the five planets” each one getting a book to itself.
But before diving in, Ptolemy first proposes that we “avoid repetition” by “explain[ing] the theory of the [planets] by means of an exposition common [to all five], treating each of the methods [for all planets] together.”
Beginning this discussion, Ptolemy introduces us to the order of the spheres for these planets, the sun, and moon. Continue reading “Almagest Book IX: On the Order of the Spheres”
Almagest Book VIII: On the First and Last Visibilities of the Fixed Stars
In the final chapter of Book VIII, Ptolemy discusses the first and last visibilities of stars. Before diving into the text, let’s first take a moment to think about what this means.
The description is, in some ways, self evident – we’re considering when, based on the movement of the sun, are stars first and last visible.
Recall that, when viewed from inside the celestial sphere (i.e., on earth), the sun appears to move west to east along the ecliptic. Thus, as time passes, stars that were washed out by the sun will, at some point, become visible because they have risen while the sun has moved far enough along the ecliptic that it will be sufficiently far below the horizon as to not wash the star out in the morning glow before the sun actually crosses the horizon. This point in time is known as their helical rising and describes when they are first visible in the sky throughout the year.
These stars will, of course, initially be only briefly visible as the daily rotation of the sun will quickly cause them to be lost in the morning glow, but as the sun continues to progress eastward along the ecliptic1, the star will be visible for longer.
Similarly, we can ask at what point the sun has moved sufficiently close to a star that, even after the sun has set, the star will be lost in the evening glow and thus, it is effectively invisible for the season until its next helical rising.
In case you haven’t been checking the dates on these posts, you may well notice that it’s been nearly a month and a half since my last post. It’s because this section has been quite challenging as I find Ptolemy’s descriptions here are an absolute mess. This is probably among the least sensical sections I’ve yet encountered. I think you’ll see why as we go through Ptolemy’s commentary. Continue reading “Almagest Book VIII: On the First and Last Visibilities of the Fixed Stars”
Almagest Book VIII: On Simultaneous Risings & Settings of the Fixed Stars
In the last post, we looked at how Menelaus’ theorem could be used to tell us which point on the ecliptic would culminate with a star. In this post, we’ll do something similar, but instead look at
the points on the equator and ecliptic which rise or set simultaneously with a fixed star. Continue reading “Almagest Book VIII: On Simultaneous Risings & Settings of the Fixed Stars”
Almagest Book VIII: On Simultaneous Culminations of the Fixed Stars
Having laid out, in the last chapter, several “configurations” that Ptolemy finds of interest, he now goes about laying out a methodology by which they can be calculated “by purely geometrical methods.”
For the points on the ecliptic with which each fixed star simultaneously culminates, rises, or sets can be derived geometrically by means of the theorems [already] established.
In this post, we’ll explore specifically the culminations and leave the risings and settings for the next post.
Continue reading “Almagest Book VIII: On Simultaneous Culminations of the Fixed Stars”
Almagest Book VIII: Configurations of the Fixed Stars
In the next chapter, Ptolemy gives some configurations of stars that he considers important. These are in addition to stars being on straight lines with one another which we encountered previously. He outlines three general categories. Continue reading “Almagest Book VIII: Configurations of the Fixed Stars”
The Ptolemaic Zodiac Project
This past year, while working on researching the history of Ptolemy’s star catalog, I came across the following quote from Toomer:
Ideally one should provide a reconstruction of the outline of each constellation as it appears on Ptolemy’s star-globe. Unfortunately no one has done the necessary work of assembling and comparing all the literary and iconographic evidence from antiquity and from the derivative Arabic tradition (notably as-Sufi). This would be an interesting and valuable enterprise.
Essentially what Toomer is noting here is that, while historians of astronomy have spent considerable time trying to reconstruct what stars the catalog described, less attention has been paid to how the constellations looked.
Thus, I’m launching a spin-off from my main project to look at this topic. Continue reading “The Ptolemaic Zodiac Project”
All Done with Gulf Wars XXXI
The past month has been rather quiet here in the blog, but there was quite a bit going on for me behind the scenes due to Gulf Wars. This was largely due to the number of classes I taught. Continue reading “All Done with Gulf Wars XXXI”
Data: Stellar Quadrant Observations – 2/17/2023
It’s getting to that time of year where the weather becomes extremely unpredictable. Warm enough to have the windows open one day and an ice storm the next.
Despite it being cold this past Friday night, the sky was at least clear with no wind so Yseult and I went out to do some observing. Continue reading “Data: Stellar Quadrant Observations – 2/17/2023”
Gulf Wars 2023 Class Schedule
I’ll be teaching six classes at Gulf Wars this year. Information is below the fold! Continue reading “Gulf Wars 2023 Class Schedule”