Tracing the history of medieval astronomy
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”
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”
Having laid out the general structure of the milky way, Ptolemy next describes the process of “the construction of the solid globe and the delineation of the constellations”. Continue reading “Almagest Book VIII: On the Construction of a Solid Globe”
Having laid out the star catalog, Ptolemy next faces a somewhat more abstract challenge: attempting to describe the nebulous structure of the Milky Way. He first describes the general shape and color:
Now the Milky Way is not strictly speaking a circle, but rather a belt of a sort of milky colour overall (whence it got its name); moreover this belt is neither uniform nor regular, but varies in width, colour, density and situation, and in one section is bifurcated. [All] that is very apparent even to the casual eye, but the details, which can only be determined by a more careful examination, we find to be as follows.
There’s not really much to discuss here, so instead, I’ll combine Ptolemy’s descriptions with some screenshots from Stellarium to help highlight what he’s talking about.
Continue reading “Almagest Book VIII: On the Location of the Milky Way”
In a previous post, we discussed a bit about Aratus’ poem, the Phaenomena, to which the Aratus Commentary was a response.
What I haven’t mentioned yet is that this original poem is still around. In fact, we have numerous copies of it thanks to it exploding in popularity in the $8^{th}$ century. However, sometime before then the poem itself had evidently been padded with other astronomical works. Among them were some descriptions of constellations. And these descriptions would provide new insight to our conversation. Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: The Aratus Latinus & Codex Climaci Rescriptus”
Another argument over the authorship of the star catalog examines the stars near the southern horizon. Since Hipparchus observed from Rhodes with a latitude of $\approx 37º$ and Ptolemy from Alexandria which is $\approx 31º$ N, this means that Ptolemy could have observed starts $5º$ further south that were never above the horizon of Hipparchus.
However, Delambre notes that there’s not a single star in the catalog that could not have been observed by Hipparchus at his latitude. So if Ptolemy was the originator of the catalog then, for some unknown reason, he declined to observe stars near the horizon1.
Thus, the inclusion or exclusion of stars cannot settle the matter. But astronomers have turned to other questions regarding stars near the southern horizon to approach it. So in this post, we’ll explore three papers on this subject. Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Stars at the Southern Limit”
Finally, in the discussion of Ptolemy’s star catalog, we’ll be moving beyond Grasshoff2.
In this post, we’ll explore a new technique, first considered in the late $1980$’s to use high proper-motion stars to attempt to determine the epoch of the star catalog. Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Proper Motion Analysis”
Previously, we discussed Vogt’s attempt to reconstruct the Hipparchan catalog by reverse calculating its coordinates from Hipparchus’ Commentary on Aratus. This Commentary was Hipparchus’ response to a poem by Aratus entitled the Phaenomena. Grasshoff ultimately took issue with Vogt’s methods, finding them insufficiently explained given the number of assumptions required to perform the transformation, to put too much stock in. Although not overtly stated, the fact that no one else has attempted to reproduce Vogt’s methods with better explanations, including Grasshoff himself, implies that the uncertainty surrounding such assumptions are considered sufficiently prohibitive that it is not worth attempting to refine Vogt’s methods.
However, Grasshoff isn’t finished with the Aratus Commentary just yet. While the issues with the dates and longitudes may make the Aratus Commentary too messy to use to reverse calculate Hipparchus’ catalog from, Grasshoff instead proposes going the other way around – using Ptolemy’s catalog to calculate same rising/culminating/setting descriptions given in the Aratus Commentary. These can then be compared to those in the Aratus Commentary without needing to worry about recovering Hipparchus’ catalog. Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Ptolemy’s Phaenomena”
In the last post, we explored a few potential explanations for the distributions of the increment for latitude. In this post, we’ll explore the various explanations for the distribution in longitude.
What Grasshoff is really doing in this section is exploring various scenarios and asking which one best gives the reason for the distribution of increments in longitude. So let’s take a look at the different scenarios. Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Fractions of a Degree in Longitude”
The next manuscript I’ve reviewed is the Paris graecus $2391$, a copy of which can be found here. Continue reading “The Almagest Manuscripts – Paris 2391”