Scholarly History of Commentary on Ptolemy’s Star Catalog: The Aratus Latinus & Codex Climaci Rescriptus

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”

Scholarly History of Commentary on Ptolemy’s Star Catalog: Stars at the Southern Limit

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”

Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Ptolemy’s Phaenomena

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”

Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Fractions of a Degree in Longitude

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”

Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Fractions of a Degree in Latitude

So far, all of the tests that Grasshoff has reviewed to try to determine whether or not Ptolemy used a Hipparchan star catalog have proven inconclusive. In the last post, we showed that the solar theory was quite obviously in use in constructing the star catalog. This provides a reasonable explanation for the mean error being $\approx 1º$ as well as why the distribution of errors could have matched Hipparchus’ even without Ptolemy having used his data3. But just because it provides a reasonable explanation of how Ptolemy could have gotten similar incorrect results doesn’t mean that he did. Thus, Grasshoff needs another way to try to distinguish between these two historical interpretations.

Grasshoff now turns to the frequency of the fractions of degrees which he describes as a “powerful criterion to decided between suggested historical interpretations.” Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Fractions of a Degree in Latitude”

Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Errors in the Solar Theory

So far in Grasshoff’s analysis, he’s come to the conclusion that the distribution of errors (as well as some of the specific ones) point to Ptolemy having used Hipparchus’ data. The only possibility to rescue Ptolemy as an observer is if there is some sort of underlying bias in both of their observations that led to a similar set of errors.

The primary suspect for this would be errors in the solar theory because Ptolemy’s model was essentially the same as that of Hipparchus’4. So, at long last, Grasshoff is ready to explore the errors in the solar theory. Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Errors in the Solar Theory”

Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Structures in the Catalog

In the last post, we followed along as Grasshoff explored the distribution of errors within Ptolemy catalog as compared to those of the reconstructed Hipparchan one. He demonstrated that the errors are highly correlated indicating that Ptolemy likely did use Hipparchan data, unless there was a systematic error common to both.

To build on that concept, Grasshoff begins exploring structures in the catalog by mapping the position of the stars in Ptolemy’s catalog as compared to the true positions as calculated by modern astronomy for the year $137$ CE5. Mapping things in this manner allows for several patterns to become apparent.

Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Structures in the Catalog”

Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Reviewing Gundel

Having reviewed Vogt’s work, Grasshoff now turns to dissecting Gundel’s. As a reminder, Gundel discovered a $15^{th}$ century set of hermetic writings that contained a list of stars that was dated to the time of Hipparchus, potentially making it the first direct evidence of a Hipparchan star catalog.

But what Gundel’s analysis lacked is any exploration of how this related to  whether or not Ptolemy stole Hipparchus’ data. In this post, we’ll explore Grasshoff’s analysis of that topic. However, before doing so, Grasshoff works to ensure that we have the best possible understanding of the hermetic catalog before comparing the hermetic catalog to Ptolemy’s. Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Reviewing Gundel”