Author: VoijaRisa

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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”

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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”