Category: Almagest

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The Almagest Manuscripts – Paris 2389

In an effort to make sure the various manuscripts of the star catalog that I have copied into my spreadsheet are accurate, I have attempted to located images of the original copies when possible to review each value even when transcriptions are available. Each manuscript has its own unique eccentricities so, as I go through them, I’d like to dedicate a post to discussing the various things I notice.

To start with, I’ll discuss the Paris $2389$ manuscript, beginning with an overview of how to read the Greek. As a note, I’m not getting into translating the descriptions which is far beyond my skill level. Rather I’ll just discuss the coordinates and magnitudes since the catalogs generally keep the same order1.

Continue reading “The Almagest Manuscripts – Paris 2389”

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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 data2. 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”

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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’3. 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”

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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 $137$ CE4. 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”

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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”

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

Over the past several posts, I’ve used the excellent history of the scholarly discussion surrounding the star catalog in the Almagest as given in Gerd Grasshoff’s History of Ptolemy’s Star Catalogue. At this point, we’ve caught up to the time the book itself was published. However, we’re not even half way through the book. The remainder of the text is Grasshoff reviewing the previous authors and offering a more comprehensive and in-depth analysis than done previously.

But before getting into that, Grasshoff attempts to ensure that we really understand the Ptolemaic catalog in its own right. For Grasshoff, this requires “a meticulous edition of the text and a correct identification of the ancient positional description with the stars known by their modern names,” as well as “the accurate position of the star at the historical epoch.” Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Refining the Catalog”