Before diving into the star catalog itself, there’s quite a bit I want to say about it. But if you don’t want to wait, here’s a link to the Google Sheet where I’ve transcribed it. More information is below the fold.
First off, if you’ve clicked the link, you’ll immediately see that this isn’t one version of the star catalog. It’s several and I’m consistently working to add more as I find online copies and have time to review them. And you’ll also quickly find they don’t always agree on values for any given star.
This is because the star catalog, being just meaningless numbers, is especially hard for scribes to transcribe correctly. Thus, corruption occurs frequently and it becomes hard to say what the original intended value was. Modern scholars have attempted to determine what this was by comparing the available values to the coordinates of the presumed stars, but Toomer notes that there are still some stars that just aren’t a good fit. This could indicate that the values were corrupted prior to the earliest manuscripts extant today or the values were incorrect from the start.
This comparison is meant as an updating of Peters’ & Knobel’s $1915$ Ptolemy’s Catalogue of Stars. This work was important because, not only did it give what they believed to be the correct values from amongst the variants, but it also offered a comparison between manuscripts. My version is formatted differently since I can have an essentially infinitely wide table to display the data since it’s digital, but the principal is the same.
For these comparisons, I have tried to include a color coding system. If a value in one of the manuscripts is different than Toomer1, I will mark it with colors based on how rare that variant is by looking at the variants listed in Peters & Knobel.
Yellow is a common variant, orange is rare ($3$ or less manuscripts), and red is unique. You may also occasionally find values in blue. These ones indicate that the values are correct, but were entered on incorrect lines and, by comparison with other manuscripts, we can infer the error and correct it. This generally results in a line that is blank for the one that was skipped.
Lastly, italics are used to indicate that the reading is unclear. When there are two possible readings, I tend to favor the one that is more consistent with other star catalogs. Similarly, if there are corrections written in the same hand, I consider the value emended, but do not if it is written in a later hand.
With all that out of the way, let’s get into the fields that are included!
Catalog Number
To make the catalog easier to use, prior historians have simply numbered the stars, beginning at $1$ and going through $1,028$. This makes referring to them quite easy, but it was not something that Ptolemy included, and indeed, not included in the manuscripts from period. I have done so here ensuring that my numbers align with Grasshoff.
Number in Constellation
Similar to the above, Toomer numbered the star in each constellation. I don’t believe this was original to Ptolemy either but I find it quite handy and have included it as well.
Description
Ptolemy didn’t have catalog numbers for the stars as we do today. Instead, he described the position of the star based on the imagined portrait of the constellation, or relative to other stars. Here, I am generally following Toomer’s translations. However, Toomer’s translations often included a row that described the group of the next several stars which I don’t believe was original to Ptolemy and as such, have chosen to omit. For example, in Cetus, he had a line for stars $2-4$ which were the “three stars in the snout” after which he listed each of the three stars. I have chosen to omit this descriptive grouping line and instead, include the grouping description in brackets as part of each star in that grouping.
Ecliptic Longitude (Sign)
In this column, I give the ecliptic longitude preceded by the sign of the zodiac so that the maximum value for the latitude in each sign is $29;59º$. This follows the Ptolemaic format but is less useful for graphing. This column is omitted for sources that never presented the longitude in this fashion.
In previous posts, we’ve explored the rate of precession. But to calculate that, we’d need to know what year to apply precession from.
Ptolemy tells us that the catalog’s epoch is “the beginning of the reign of Antoninus” which was July 20, 137 CE.
Ecliptic Longitude (Sexagesimal & Decimal)
To help produce a computer readable version of this table, I have also converted the ecliptic longitude to basic sexagesimal ($0-360º$) as well as decimal. However, I generally hide these columns so they’re not in the default view as it makes the table exceptionally wide.
Ecliptic Latitude
This column presents the ecliptic latitude in sexagesimal. Positive signs indicate the object is north of the ecliptic. Negatives are south.
Magnitude
This column gives the recorded magnitude of the star, recalling that higher numbers are fainter. There is a bit of variation here in that some authors have slightly ambiguous values here. Specifically, Peters-Knobel and Toomer both denote stars that are not a specific magnitude, but somewhere between two. Peters-Knobel denote this by giving two magnitudes (ex: $4-3$ for a magnitude somewhere between those two values). Toomer gives a greater than or less than sign (ex: $>4$). However, with Toomer, it’s not immediately clear what the sign means. In the example of $>4$, this would imply a magnitude somewhere between $4-5$, but comparison with Peters-Knobel indicates this is backwards. So the sign is indicating the brightness is greater than $4$, with would mean a lower magnitude. Very confusing.
Two other values occur in this table infrequently. The first “f” which is an abbreviation for faint. The word “obscura” is used in the Latin text I’ve reviewed. The other is “neb” which is short for “nebulous” which is generally used for clusters which may not be easily resolved by the unaided eye.
Modern Designation
For the modern editions I also give the modern designation for the star as provided by each of the authors. Where possible, I use the Bayer designation. But when not available, I have followed Toomer.
When giving the identification for other authors, I have tried to ensure that the identifications are given the same as Toomer if the stars match to make comparison easier. At some point, I intend to make a supplementary table giving the various designations for the same star as this can be confusing.
As a quick note, the modern designation column will only apply in the cases of the modern critical editions in which the authors gave their opinion on the identification of stars. Since the period manuscripts do not, this field is excluded.
A few abbreviations used here
BSC: This stands for Bright Star Catalogue and the number following this is also the Harvard Revised (HR) number.
Notes
For many of the catalogs, I have also included a column for notes. For the historical ones, this is my notes. In general, these are meant to provide further information if the reading was unclear (indicated by a value being in italics).
For the modern editions, these are mostly notes provided by that author (if they have any), but may include notes I have added as well2. There are some of Toomer’s notes that I have chosen to exclude – primarily ones on the translation of the description.
Toomer’s notes frequently contain references to other manuscripts and sources and I have made a separate post about the abbreviations used here. Over time, I will probably remove many of the notes Toomer made regarding other sources as I locate those sources and make them available. This will allow users to see the values in those sources directly instead of relying on Toomer’s notes.
Again, this column I generally hide.
Sources
As described previously, I have provided the values from as many sources as I have been able to find and had time to review. For the historical sources, I have an index of them here which provides more information on each of the sources, giving links to view the sources yourself, as well as a dissection of the hands and notations used.
Although there is some variation in the way various values may be presented, I have tried to be consistent with Toomer. As an example, when considering the magnitude, some are listed as “Obscura” which I have replaced with an “f” to be consistent with Toomer’s notation. Similarly, “neb” is short for “nebula” and I have consistently used this to be consistent with Toomer.
Modern Critical Editions
Francis Baily
Baily published his critical edition of the star catalog in $1843$3. A copy is available to view for free here as it is in the public domain. This text is important because it introduced the numbering system in which all entries are given a number ($1-1,028$) in order of their appearance in the catalog. Many other writers thereafter have maintained this4. Thus, I maintain this order as well.
This edition is also of importance because the Peters-Knobel version (below) also includes the values for $26$ period manuscripts, but, instead of giving every value from every source, Peters & Knobel only note where they differ from Baily5. Thus, a complete comprehension of those editions can be only had in comparison to this edition unless one is to check each of them independently.
Manitius
The $1912$ copy of Karl Manitius’ text can be found here6.
Peters-Knobel
This data comes from an $1915$ critical edition of the star catalog from Peters and Knobel. It can be viewed in its entirety for free (as it is in the public domain) here. References to this work in notes will be abbreviated P-K.
Toomer
These values (as well as the other portions I have indicated above) are from G.J. Toomer’s translation of the Almagest. I am using the $1998$ second edition.
Grasshoff
The values here come from Gerd Grasshoff’s History of Ptolemy’s Star Catalogue ($1990$). There is a very odd recurring error I have noticed in Grasshoff’s latitudes. Frequently, when a latitude is a whole number, Grasshoff’s values are consistently $-2$ from all others if the values are positive, or $+2$ if the latitudes were negative. I believe there is some sort of error in the printing.
Other
A few other things deserve mentioning.
Reading of the Texts
One of the challenges in reading period manuscripts is deciphering the numbers. Of the manuscripts available, there are three distinct languages: Greek, Arabic, and Latin. I haven’t directly engaged with the Arabic yet, but with the Greek and Latin, fractions are a bit of a problem.
In my version of the catalog, I have listed the coordinates in sexagesimal because spreadsheets do not handle fractions well. However, all of the original manuscripts used fractions. And on top of that, they often broke the fractions up. For example, $\frac{5}{6}$ would have been expressed as $\frac{1}{2} + \frac{1}{3}$. This extra step meant that it was quite easy for a transcriptionist to forget one or the other.
On top of that is how fractions were written. In the Latin manuscript I’ve reviewed7, a half is written as a script “d” for “dimidi”, a third is written as a short “t” with a line over it for “tertie”, and a quarter is written as a squashed “q” with the tail going horizontally so it looks more like an “a”, standing for “quartie”. These are all fairly recognizable.
However for $\frac{1}{6}$, the author would write the Roman numeral for $6$ (vi) and then indicate it should be a fraction by putting a wavy line as if it were an exponent. I have read that other authors used even less obvious marks such as what we would consider an apostrophe. Thus, the fraction $\frac{1}{6}$ would read as $vi’$. You can quite easily see how this mark being lost would change the meaning. For example $x \; vi’$ ($10 \frac{1}{6}$ would could easily be read $x \; vi$ ($16;00$) if the mark denoting the fraction was forgotten, smudged, misinterpreted or otherwise.
This exact same error occurs in the Greek texts. For example, there a $6$ is expressed as ϛ whereas $\frac{1}{6}$ is ϛ‘8.
This is a common sort of error that plagued transcriptionists in period as well as modern ones.
In the example above, it may be somewhat more obvious that this should have been a fraction as I have placed a space between the $x$ and $vi$. However, different conventions on how numbers should be spaced existed throughout period, so it was not always so obvious.
As such, when considering differences between interpretations, this sort of de-fractionification is something to watch out for. My suspicion is that it happened in both directions and things could also become fractions due to a stray mark of the quill.
Additions to Ptolemy
First, the flow of the table is frequently interrupted with totals of the previously given constellation. Toomer indicates these were certainly not done by Ptolemy and were later additions. He has decided to keep them, and I have as well.
Furthermore, I have added two rows at top to account for the numerous sources as well as the category of said sources.
Unfortunately, this interrupts the flow of data and makes it hard to import into data analysis programs. As such, if you’re interested in using the data from this table in a machine readable format, I’ve included a column, entitled Include Row? which has the value “yes” if it’s a row containing actual data. This excludes all of the header rows for each constellation, the counts of stars, and the grouped columns at top. There’s also a hidden row (row $4$) which has modified column header names with the source so you won’t get numerous rows called the same things. So pull in the data and filter based on the Include Row? column to quickly remove the unwanted rows.
My intent is to eventually create a Power BI file which pulls in all of the data and allows for data analysis on it. When I’ve completed that, I will make it publicly available.
Originality of the Star Catalog
Lastly, if you’re interested in the discussion about the star catalog and whether or not it is an original work by Ptolemy or stolen from Hipparchus, you can find an index of those posts here.
As I add more manuscripts and editions, I will continue to update this post.
Update Log
- 1/30/2023 – The Paris $2391$ manuscript is complete (reviewed against original manuscript).
- 1/26/2023 – The Paris $2390$ manuscript is complete (reviewed against original manuscript).
- 1/20/2023 – The Paris $2389$ manuscript is complete (reviewed against original manuscript).
- 1/13/2023 – Added Baily ($1843$).
- 1/12/2023 – Added Peters-Knobel ($1915$).
- 6/26/2023 – Added Paris $2394$ based on Peters-Knobel’s reporting and began checking against original manuscript)
- 8/26/2023 – Added Cambridge MS $32$ (reviewed against original manuscript)
- 11/10/2023 – Began work on Vatican $1594$ manuscript. Created separate index of manuscripts.
- Specifically, the value found in the second edition of Toomer’s translation.
- In particular, I was quite interested in identifying the stars given with an accuracy of $\frac{1}{4}º$ since, as Grasshoff indicated, most stars are given with an accuracy of $\frac{1}{6}º$, especially in longitude.
- As a bonus, this text also contains copies of the star catalogs of Ulugh Beg, Tycho Brahe, Halley’s catalog of southern stars, and Hevelius catalog!
- Toomer, oddly, is an exception.
- I am suspicious as to the accuracy of this as there are many misreadings from those manuscripts that have since been corrected. As such, I’ll take Peters and Knobel’s word for their values for now, but only until such time as I am able to give my own reading of them.
- If you’re interested in Volume I (Books I – VI), it can be found here.
- Vatican 2056.
- For more on how to read the Greek texts, see the post here.