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”
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 data1. 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’1. 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 $137$ CE1. Mapping things in this manner allows for several patterns to become apparent.
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”
Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Reviewing Vogt
Having discussed the authoritative version of the text and the stellar identifications, Grasshoff now turns towards reviewing and checking the work of previous authors, starting with Vogt. Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Reviewing Vogt”
Scholarly History of Commentary on Ptolemy’s Star Catalog: Newton (1977)
In the past few posts, we’ve demonstrated a rapidly forming consensus that Ptolemy’s star catalog was largely an original work. However, there were some holdouts. In $1977$ R. R. Newton published the book The Crime of Claudius Ptolemy1. In this work, Newton generally agrees with Lalande and Delambre – That Ptolemy’s “observations” are not true observations, but merely the result of theoretical calculations, extending this argument well beyond the star catalog, which Newton frequently describes as “fabricated”.
As a forewarning, this book raised a great deal of popular media attention as the alleged scheming of scientists is always a popular topic, but scientists reviewing the book have generally panned it as using flawed methodology, as we’ll see. Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Newton (1977)”
Scholarly History of Commentary on Ptolemy’s Star Catalog: 137 CE – 1918 CE
I’m going to take a bit of a break from direct progress on the Almagest as we get to the star catalog. This is because there is, what I feel to be a fascinating and important discussion surrounding its legitimacy and I want to explore the history of this discussion, even though almost all of it is outside the range of the SCA period1. Namely, the discussion is whether or not Ptolemy’s star catalog is legitimate, one which he took the measurements himself, or if Ptolemy stole the data from an astronomer that came before him and tried to update it, but failed due to an incorrect value for the rate of precession.
Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: 137 CE – 1918 CE”
Almagest Book VII: On the Method Used to Record [the Positions of] the Fixed Stars
Having established that the sphere of fixed stars has a rearwards motion, Ptolemy turns now to
making our observations and records of each of the above fixed stars, and of the others too, to give their positions, as observed in our time, in terms of longitude and latitude, not with respect to the equator, but with respect to the ecliptic, [i.e.,] as determined by the great circle drawn through the poles of the ecliptic and each individual star. In this way, in accordance with the hypothesis of their motion established above, their positions in latitude with respect to the ecliptic must necessarily remain the same, while their positions in longitude must always traverse equal arcs towards the rear in equal times.
Almagest Book VII: On the Rate of Precession from Other Greek Astronomer’s Observations
In the last post, we showed how we can determine the rate of precession if we know how much a star has changed its declination over a long period. In it, we used a baseline of $265$ years, corresponding to the time between Hipparchus and Ptolemy.
Next, Ptolemy wants to increase that baseline further and turns to the observations of three other Greek Astronomers: Timocharis, Agrippa1, and Menelaus. However, these astronomers did not give the position of the stars in equatorial coordinates. Rather, they described occultations of various stars by the moon. Thus, Ptolemy turns to the lunar model to determine the positions of these stars and instead of finding a change in declination, is able to directly compare the ecliptic longitude of them over time. Continue reading “Almagest Book VII: On the Rate of Precession from Other Greek Astronomer’s Observations”