History Online - Ptolemy

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Almagest

Ptolemy

The Almagest Star Catalogue was published in Alexandria around 150 AD, as part of the famous Almagest, the book in which the great Greek astronomer Claudius Ptolomaeus presented his geocentric theory of the planets. There are reasons to believe that most of the stars of the catalogue were observed by Hipparchus, between the years 160 BC to 130 BC. In the later Middle Ages and in the Renaissance the Almagest had a tremendous impact on European astronomy. Copernicus, Tycho Brahe and Kepler made an extensive use of this book. Almost an exact copy of the Star Catalogue was included by Copernicus in his De Revolutionibus.

The catalogue itself is made up of 1028 star entries. The stars are listed by constellations, which in turn are grouped in Northern, Zodiacal and Southern. For each star the following information is given.
Description of its position within the figure of the constellation. Ecliptic longitude, given in degrees and minutes of arc within one of the twelve zodiacal signs. Ecliptic latitude, given in degrees and minutes of arc, plus the indication of North or South of the Ecliptic.
Brightness expressed in magnitudes from 1 to 6. In some cases these are qualified as bright ('major') or dim ('minor'). For some stars brightness is expressed as obscure ('obscura') or nebulous ('nebulosa').
Positions are generally given in sixths of a degree (10' of arc), except for a few latitudes which are given in fourths (15' of arc). The sky is covered from the North Pole to about 52 of Southern Declination (for 150 BC), which was the practical limit of observation from the latitude of Alexandria (31 N) .

An important point is to establish the epoch for which the positions are given. Though Ptolomaeus implies that the catalog should be dated near 138 AD, the best fit when compared to modern observations gives an epoch of 43 AD. The explanation is that Ptolomaeus seems to have used Hipparchus' positions and precessed them to his own times, by adding 240' to each longitude. But as he followed Hipparchus in using a wrong value for the precession, 1/century, instead of the real value, 1.4/century, his longitudes are too small. If we restore Hipparchus' original catalogue by subtracting 240' to all Ptolomaeus' longitudes, the resulting values correspond to an epoch around 140 BC, quite compatible with the known dates when Hipparchus performed his observations.

One of the tasks of the modern historian of astronomy is to link the catalogue entries with existing stars. For that purpose he uses the tabulated positions, the magnitudes and the descriptions of the place of the stars within the figure of their constellations. These must be compared with the data of a modern star catalogue, expressed in the same coordinate system, for the same epoch and including corrections for proper motion. This may result in a very tiresome process when done without an adequate graphical tool as that provided by this Almagest Catalogue for Guide users. When comparing the identifications done in the past, one is amazed to see the discrepancies between the different efforts, showing that there is still an opportunity for improvement in this process.

For most of the catalogue entries, the identifications are pretty straight forward. Only one star of a similar magnitude is found near the place tabulated in the Almagest. In these cases the average difference between the Almagest position and modern values is about 30' of arc in each coordinate. But in about 10% of the situations, identification is not that easy. Either the position does not agree with the catalogue description, or there is a great difference in magnitude, or there are no stars or too many near the tabulated values. Additionally the positions themselves may have become corrupted during the many centuries of manuscript transcription. There is nothing as boresome as copying long strings of numeric data. As a consequence for many stars different values are found in the various sources. Some may be easily spotted and corrected, as when the longitude is expressed with a wrong Zodiacal sign, or when North and South are interchanged. Others are less obvious, and the investigator must look into the Greek figures to understand the ways these transcription errors are made. For instance, in many cases a latitude is found as 33 in a source and as 30 20' in another one. This is easier to understand when you know that the first number is written in Greek as lg (30 + 3) and the second as lg' (30 + 1/3).

But in some cases the blame cannot be put on the copyists. Hipparchus and specially Ptolomaeus did made mistakes. Some of them are systematic and can be accounted for. An example is offered by the stars of the Southern Cross, which are shifted almost 4 to the South of the real positions. In other cases we presume an error when all the sources agree in a position distant several degrees from the star corresponding to the description. There are some extreme cases where no identification is possible with any degree of probability: there are no actual stars matching either the descriptions nor the tabulated positions.


Greek Astronomy

The Revival of an Ancient Science

One of the most powerful creations of Greek science was the mathematical astronomy created by Hipparchus in the second century B.C. and given final form by Ptolemy in the second century A.D. Ptolemy's work was known in the Middle Ages through imperfect Latin versions. In fifteenth-century Italy, however, it was brought back to life. George Trebizond, a Cretan emigre in the curia, produced a new translation and commentary. These proved imperfect and aroused much heated criticism. But a German astronomer, Johannes Regiomontanus, a protege of the brilliant Greek churchman Cardinal Bessarion, came to Italy with his patron, learned Greek, and produced a full-scale "Epitome" of Ptolemy's work from which most astronomers learned their art for the next century and more. Copernicus was only one of the celebrities of the Scientific Revolution whose work rested in large part on the study of ancient science carried out in fifteenth-century Italy.

Byzantine Astronomical Collection

In the thirteenth and fourteenth centuries, a number of recent Arabic and Persian astronomical works were translated into Greek by scholars who traveled to Persia under the Ilkhanid Empire. One short and confused treatise, translated by Gregory Chioniades, describes Tusi's lunar theory, illustrated, not altogether correctly, in this figure along with Tusi's device for producing rectilinear from circular motions. A part of the planetary and lunar theory of the astronomers of Maragha was later utilized by Copernicus, though scholars do not know how he gained access to this material.

Ptolemy, Almagest

George Trebizond, one of the notable Greek scholars who came to Italy in the early fifteenth century, made a new translation of the "Almagest" from the Greek for Pope Nicholas V between March and December of 1451. Due to a dispute about the quality of Trebizond's commentary on the text, the translation was never dedicated to Nicholas. This very elaborate manuscript of the translation, with the figures drawn in several colors, was dedicated to Pope Sixtus IV by George's son Andreas. These pages show Book VI Chapter 7, on the computation of the duration of solar and lunar eclipses.

George Trebizond, Commentary on the Almagest

During the same nine months that George Trebizond made his translation of the "Almagest," he also wrote a commentary as long as the original text. The commentary was severely criticized, however, which resulted in a falling out with Pope Nicholas V. This opulent manuscript was dedicated to Pope Sixtus IV by George's son Andreas along with Vat. lat. 2055 of the translation. These pages contain a large figure of the model for the planet Mercury, shown at its least distance from the earth, with a list of Mercury's parameters and distances, and then the beginning of the treatment of Venus in Book X.

Nasir ad-Din at-Tusi, Tadhkira

Nasir ad-Din at-Tusi was among the first of several Arabic astronomers of the late thirteenth century at the observatory of Maragha in Persia who modified Ptolemy's models based on mechanical principles, in order to preserve the uniform rotation of spheres. This early Arabic manuscript contains his principal work on the subject, the "Tadhkira fi ilm al-Haya" (Memoir on Astronomy).

Georg Peurbach and Johannes Regiomontanus,
Epitome of the Almagest

The "Epitome of the Almagest" was written between 1460 and 1463 by Georg Peurbach and Johannes Regiomontanus at the suggestion of Cardinal Bessarion. It gave Europeans the first sophisticated understanding of Ptolemy's astronomy, and was studied by every competent astronomer of the sixteenth century. The illustration here shows the distance of the sun from the earth as 1210 terrestrial radii (about 4,800,000 miles), which is too small by a factor of twenty, but gives a solar parallax (the maximum displacement due to observing the sun from the surface rather than from the center of the earth) of less than 3 minutes, still well below the limit of observational accuracy.

Ptolemy, Geography

Ptolemy's "Geography" contains instructions for drawing maps of the entire "oikoumene" (inhabited world) and particular regions, along with the longitudes and latitudes of about eight thousand locations in Europe, Africa, and Asia. The maps in manuscripts of the "Geography," however, date only from about 1300, after the text was rediscovered by Maximus Planudes. There are two versions, the A recension with twenty-six large regional maps, and the B recension, displayed here, with sixty-four smaller regional maps and four large additional maps. Shown here is the additional map of Europe which reveals Ptolemy's systematic exaggeration of west to east distances, particularly in the eastward extension of Scotland and the west to east slope of Italy.

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