Almagest
The Almagest
Ptolemy set up a public inscription at Canopus, Egypt, in 147 or 148. N. T. Hamilton found that the version of Ptolemy's models set out in the Canopic Inscription was earlier than the version in the Almagest. Hence the Almagest could not have been completed before about 150, a quarter-century after Ptolemy began observing.[2][3]
Names
The name comes from Arabic اَلْمَجِسْطِيّ al-majisṭī, with اَل al meaning
]The work was originally titled "Μαθηματικὴ Σύνταξις" (Mathēmatikē Syntaxis) in
Contents
The Syntaxis Mathematica books
The Syntaxis Mathematica consists of thirteen sections, called books. As with many medieval manuscripts that were handcopied or, particularly, printed in the early years of printing, there were considerable differences between various editions of the same text, as the process of transcription was highly personal. An example illustrating how the Syntaxis was organized is given below; it is a Latin edition printed in 1515 at Venice by Petrus Lichtenstein.[4]
- Book I contains an outline of planets revolving around the Earth. Then follows an explanation of chords with table of chords; observations of the obliquity of the ecliptic (the apparent path of the Sun through the stars); and an introduction to spherical trigonometry.
- Book II covers problems associated with the daily motion attributed to the heavens, namely risings and settings of celestial objects, the length of daylight, the determination of latitude, the points at which the Sun is vertical, the shadows of the gnomon at the equinoxes and solstices, and other observations that change with the observer's position. There is also a study of the angles made by the ecliptic with the vertical, with tables.
- Book III covers the length of the year, and the motion of the epicycles.
- Books IV and V cover the motion of the apogee, and the sizes and distances of the Sun and Moon relative to the Earth.
- Book VI covers solar and lunar eclipses.
- Books VII and VIII cover the motions of the fixed stars, including precession of the equinoxes. They also contain a ecliptic longitude and latitude.[note 1]
- Book IX addresses general issues associated with creating models for the five naked eye planets, and the motion of Mercury.
- Book X covers the motions of Venus and Mars.
- Book XI covers the motions of Jupiter and Saturn.
- Book XII covers stations and retrograde motion, which occurs when planets appear to pause, then briefly reverse their motion against the background of the zodiac. Ptolemy understood these terms to apply to Mercury and Venus as well as the outer planets.
- Book XIII covers motion in latitude, that is, the deviation of planets from the ecliptic.
Ptolemy's cosmos
The cosmology of the Syntaxis includes five main points, each of which is the subject of a chapter in Book I. What follows is a close paraphrase of Ptolemy's own words from Toomer's translation.[7]
- The celestial realm is spherical, and moves as a sphere.
- The Earth is a sphere.
- The Earth is at the center of the cosmos.
- The Earth, in relation to the distance of the fixed stars, has no appreciable size and must be treated as a mathematical point.[8]
- The Earth does not move.
The star catalogue
The layout of the catalogue has always been tabular.[9] Ptolemy writes explicitly that the coordinates are given as (ecliptical) "longitudes" and "latitudes", which are given in columns, so this has probably always been the case. It is significant that Ptolemy chooses the ecliptical coordinate system because of his knowledge of precession, which distinguishes him from all his predecessors. Hipparchus' celestial globe had an ecliptic drawn in, but the coordinates were equatorial.[10] Since Hipparchus' star catalogue has not survived in its original form, but was absorbed into the Almagest star catalogue (and heavily revised in the 265 years in between),[11][10] the Almagest star catalogue is the oldest one in which complete tables of coordinates and magnitudes have come down to us.
As mentioned, Ptolemy includes a star catalog containing 1022 stars. He says that he "observed as many stars as it was possible to perceive, even to the sixth magnitude". The
Since Tycho Brahe found this offset, astronomers and historians investigated this problem and suggested several causes:
- that all coordinates were calculated from Hipparchus' observations, whereby the precession constant, which was known too inaccurately at the time, led to a summation error (Delambre 1817);[12][13]
- that the data had in fact been observed a century earlier by Menelaus of Alexandria (Björnbo 1901);[12]
- that the difference is a sum of individual errors of various kinds, including calibration with outdated solar data;[14][12]
- that Ptolemy's instrument was wrongly calibrated and had a systematic offset.[15]
Subtracting the systematic error leaves other errors that cannot be explained by precession. Of these errors, about 18 to 20 are also found in Hipparchus' star catalogue (which can only be reconstructed incompletely).[15][10] From this it can be concluded that a subset of star coordinates in the Almagest can indeed be traced back to Hipparchus,[12] but not that the complete star catalogue was simply "copied". Rather, Hipparchus' major errors are no longer present in the Almagest[10] and, on the other hand, Hipparchus' star catalogue had some stars that are entirely absent from the Almagest.[10] It can be concluded that Hipparchus' star catalogue, while forming the basis, has been reobserved and revised.[10][11]
Errors in the coordinates
The figure he used is based on Hipparchus' own estimate for precession, which was 1° in 100 years, instead of the correct 1° in 72 years. Dating attempts through proper motion of the stars also appear to date the actual observation to Hipparchus' time instead of Ptolemy.[16]
Many of the longitudes and latitudes have been corrupted in the various manuscripts. Most of these errors can be explained by similarities in the symbols used for different numbers. For example, the Greek letters Α and Δ were used to mean 1 and 4 respectively, but because these look similar copyists sometimes wrote the wrong one. In Arabic manuscripts, there was confusion between for example 3 and 8 (ج and ح). (At least one translator also introduced errors. Gerard of Cremona, who translated an Arabic manuscript into Latin around 1175, put 300° for the latitude of several stars. He had apparently learned from Moors, who used the letter س (sin) for 300 (like the Hebrew ש (shin)), but the manuscript he was translating came from the East, where س was used for 60, like the Hebrew ס (samekh).)[17]
Even without the errors introduced by copyists, and even accounting for the fact that the longitudes are more appropriate for 58 AD than for 137 AD, the latitudes and longitudes are not fully accurate, with errors as great as large fractions of a degree. Some errors may be due to atmospheric refraction causing stars that are low in the sky to appear higher than where they really are.[18] A series of stars in Centaurus are off by a couple of degrees, including the star we call Alpha Centauri. These were probably measured by a different person or persons from the others, and in an inaccurate way.[19]
Constellations in the star catalogue
The star catalogue contains 48 constellations, which have different surface areas and numbers of stars. In Book VIII, Chapter 3, Ptolemy writes that the constellations should be outlined on a globe, but it is unclear exactly how he means this: should surrounding polygons be drawn or should the figures be sketched or even line figures be drawn? This is not stated.
Although no line figures have survived from antiquity, the figures can be reconstructed on the basis of the descriptions in the star catalogue: The exact celestial coordinates of the figures' heads, feet, arms, wings and other body parts are recorded.[10] It is therefore possible to draw the stick figures in the modern sense so that they fit the description in the Almagest.[note 3]
These constellations form the basis for the modern constellations that were formally adopted by the International Astronomical Union in 1922, with official boundaries that were agreed in 1928.
Of the stars in the catalogue, 108 (just over 10%) were classified by Ptolemy as 'unformed', by which he meant lying outside the recognized constellation figures. These were later absorbed into their surrounding constellations or in some cases used to form new constellations.[20]
Ptolemy's planetary model
Ptolemy assigned the following order to the
- Moon
- Mercury
- Venus
- Sun
- Mars
- Jupiter
- Saturn
- Sphere of fixed stars
Other classical writers suggested different sequences.
Ptolemy inherited from his Greek predecessors a geometrical toolbox and a partial set of models for predicting where the planets would appear in the sky.
The Syntaxis adopted Hipparchus' solar model, which consisted of a simple eccentric deferent. For the Moon, Ptolemy began with Hipparchus' epicycle-on-deferent, then added a device that historians of astronomy refer to as a "crank mechanism":[21] he succeeded in creating models for the other planets, where Hipparchus had failed, by introducing a third device called the equant.
Ptolemy wrote the Syntaxis as a textbook of mathematical astronomy. It explained geometrical models of the planets based on combinations of circles, which could be used to predict the motions of celestial objects. In a later book, the Planetary Hypotheses, Ptolemy explained how to transform his geometrical models into three-dimensional spheres or partial spheres. In contrast to the mathematical Syntaxis, the Planetary Hypotheses is sometimes described as a book of cosmology.
Influence
Ptolemy's comprehensive treatise of mathematical astronomy superseded most older texts of Greek astronomy. Some were more specialized and thus of less interest; others simply became outdated by the newer models. As a result, the older texts ceased to be copied and were gradually lost. Much of what we know about the work of astronomers like Hipparchus comes from references in the Syntaxis.
The first translations into Arabic were made in the 9th century, with two separate efforts, one sponsored by the
No Latin translation was made before the 12th century.
In the 15th century, a Greek version appeared in Western Europe. The German astronomer Johannes Müller (known as Regiomontanus, after his birthplace of Königsberg) made an abridged Latin version at the instigation of the Greek churchman Cardinal Bessarion. Around the same time, George of Trebizond made a full translation accompanied by a commentary that was as long as the original text. George's translation, done under the patronage of Pope Nicholas V, was intended to supplant the old translation. The new translation was a great improvement; the new commentary was not, and aroused criticism.[25] The Pope declined the dedication of George's work,[25] and Regiomontanus's translation had the upper hand for over 100 years.[citation needed]
During the 16th century, Guillaume Postel, who had been on an embassy to the Ottoman Empire, brought back Arabic disputations of the Almagest, such as the works of al-Kharaqī, Muntahā al-idrāk fī taqāsīm al-aflāk ("The Ultimate Grasp of the Divisions of Spheres", 1138–39).[26]
Commentaries on the Syntaxis were written by Theon of Alexandria (extant), Pappus of Alexandria (only fragments survive), and Ammonius Hermiae (lost).
Modern assessment
Under the scrutiny of modern scholarship, and the cross-checking of observations contained in the Almagest against figures produced through backwards extrapolation, various patterns of errors have emerged within the work.[27][28] A prominent example is Ptolemy's use of measurements said to have been taken at noon, but which systematically produce readings that are off by half an hour, as if the observations were taken at 12:30pm.[27] However, an explanation for this error was found in 1969.[29][30][31]
The overall quality of Claudius Ptolemy's scholarship and place as "one of the most outstanding scientists of antiquity" has been challenged by several modern writers, most prominently by
Although some have described the charges laid by Newton as "erudite and imposing", others have disagreed with the findings.[27] Bernard R. Goldstein wrote, "Unfortunately, Newton’s arguments in support of these charges are marred by all manner of distortions, misunderstandings, and excesses of rhetoric due to an intensely polemical style."[29] Owen Gingerich, while agreeing that the Almagest contains "some remarkably fishy numbers",[27] including in the matter of the 30-hour displaced equinox, which he noted aligned perfectly with predictions made by Hipparchus 278 years earlier,[32] rejected the qualification of fraud.[27][33] John Phillips Britton, Visiting Fellow at Yale University, wrote of R.R. Newton, "I think that his main conclusion with respect to Ptolemy’s stature and achievements as an astronomer is simply wrong, and that the Almagest should be seen as a great, if not indeed the first, scientific treatise." He continued, "Newton’s work does focus critical attention on the many difficulties and inconsistencies apparent in the fine structure of the Almagest. In particular, his conclusion that the Almagest is not a historical account of how Ptolemy actually derived his models and parameters is essentially the same as mine, although our reasons for this conclusion and our inferences from it differ radically."[31]
Modern editions
The Almagest under the Latin title Syntaxis mathematica, was edited by J. L. Heiberg in Claudii Ptolemaei opera quae exstant omnia, vols. 1.1 and 1.2 (1898, 1903).
Three translations of the Almagest into English have been published. The first, by
A direct French translation from the Greek text was published in two volumes in 1813 and 1816 by
Gallery
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Ptolemy's catalogue of stars; a revision of the Almagest by Christian Heinrich Friedrich Peters and Edward Ball Knobel, 1915
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Epytoma Ioannis de Monte Regio in Almagestum Ptolomei, Latin, 1496
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Almagestum, Latin, 1515
See also
- Abū al-Wafā' Būzjānī(who also wrote an Almagest)
- Book of Fixed Stars
- Star cartography
- Euclid's Elements
References
Notes
- ^ The catalogue actually contained 1,028 entries, but three of these were deliberate duplicates, because Ptolemy regarded certain stars as being shared between adjacent constellations. Three other entries were non-stellar, i.e. the Double Cluster in Perseus, M44 (Praesepe) in Cancer, and the globular cluster Omega Centauri.[5] Ptolemy states that the longitudes (which increase due to precession) are for the beginning of the reign of Antoninus Pius (138 AD), whereas the latitudes do not change with time (but see the star catalog). The constellations north of the zodiac and the northern zodiac constellations (Aries through Virgo) are in the table at the end of Book VII, while the rest are in the table at the beginning of Book VIII. The brightest stars were marked first magnitude (m = 1), while the faintest visible to the naked eye were sixth magnitude (m = 6). Each numerical magnitude was considered twice the brightness of the following one, which is a logarithmic scale. (The ratio was subjective as no photodetectors existed.) This system is believed to have originated with Hipparchus. The stellar positions too are of Hipparchan origin, despite Ptolemy's claim to the contrary. Ptolemy identified 48 constellations: The 12 of the zodiac, 21 to the north of the zodiac, and 15 to the south.[6]
- 62 Orioniswhich are now around ecliptic longitude 91° are attributed longitudes in the Almagest of 66° and 64°20' respectively.
- ^ These modern stick figures as a reconstruction of the historical constellations of the Almagest are available in the free planetarium software Stellarium since 2019.[citation needed]
Citations
- ^ Tomarchio 2022, p. xv.
- ^ Hamilton & Swerdlow 1987, p. [pages needed].
- ^ Kunitzsch 2008, pp. 140–141.
- ^ Lichtenstein 1515, p. [pages needed].
- ^ Ridpath 2023, "Ptolemy’s Almagest".
- ^ Ridpath 2023, Ptolemy’s 48 constellations.
- ^ a b Toomer 1984, p. [pages needed].
- ^ Ptolemy 1952, Book I, Chapter 5, p.9.
- ^ Lichtenstein 1515, p. 79.
- ^ a b c d e f g h i Hoffmann 2017, p. [pages needed].
- ^ a b Hoffmann 2018, p. [pages needed].
- ^ a b c d e Graßhoff 1990, p. [pages needed].
- ^ Peters & Knobel 1915, p. 15.
- ^ Dreyer 1917, p. 528.
- ^ a b Vogt 1925, pp. 17–54.
- ^ Dambis & Efremov 2000, pp. 115–134.
- ^ Peters & Knobel 1915, pp. 9–14.
- ^ Peters & Knobel 1915, p. 14.
- ^ Peters & Knobel 1915, p. 112.
- ^ Ridpath 2023, "How Ptolemy’s spare stars became new constellations".
- ^ Hoskin 1999, p. 44.
- ^ Angelo 2006, p. 78.
- ^ Toomer 1984, p. 3.
- ^ Kunitzsch 1986, p. 89.
- ^ a b Shank 2020, pp. 305–307.
- ^ Saliba 2011, pp. 217–221.
- ^ a b c d e f g Wade 1977.
- ^ a b Lewis 1979.
- ^ a b Goldstein 1978.
- ^ Britton 1969.
- ^ a b Britton 1992.
- ^ Gingerich 1980.
- ^ Gingerich 1981.
- ^ Toomer 1984.
- ^ Ptolemy 2014.
- ^ Jodra 2013.
- ^ Halma 1813.
- ^ Halma 1816.
Sources
Books
- Angelo, Joseph A. Jr. (2006). Encyclopedia of Space and Astronomy (1st ed.). New York: Facts on File. ISBN 978-0-8160-5330-8– via books.google.com.
- Britton, John Phillips (1992). Models and Precision: The Quality of Ptolemy's Observations and Parameters. New York: Garland. ISBN 0-8153-0215-0.
- Graßhoff, Gerd (1990). The History of Ptolemy's Star Catalogue. Studies in the History of Mathematics and Physical Sciences. Vol. 14. Berlin: Springer. ISBN 3-540-97181-5.[pages needed]
- Halma, Nicolas (1813). Composition mathématique de Claude Ptolémée (PDF) (in French). Vol. 1. Paris: J. Hermann – via Bibliothèque nationale de France.
- — (1816). Composition mathématique de Claude Ptolémée (PDF) (in French). Vol. 2. Paris: H. Grand – via Bibliothèque nationale de France.
- Hamilton, N. T.; Swerdlow, N. M. (1987). "The Canobic Inscription: Ptolemy's Earliest Work". In Berggren, J. L.; Goldstein, B. R. (eds.). From Ancient Omens to Statistical Mechanics. ]
- Hoffmann, Susanne M. (2017). Hipparchs Himmelsglobus (in German). Berlin: Springer. ]
- Hoskin, Michael (1999). "2. Astronomy in Antiquity". In Hoskin, Michael (ed.). The Cambridge Concise History of Astronomy (1st ed.). ISBN 978-0-521-57291-0.
- Kunitzsch, Paul (2008) [1997]. "Almagest: Its Reception and Transmission in the Islamic World". In Selin, Helaine (ed.). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures (2nd ed.). Berlin: Springer. ISBN 978-1-4020-4559-2.
Around AD 150, Ptolemy wrote his great handbook of astronomy called Mathematike Syntaxis...
- Lichtenstein, Petrus (1515). Claudius Ptolemaeus Almagestum (in Latin). Venice. OCLC 644484399. Retrieved 31 May 2014 – via Astronomy Library of the Vienna University.
- Carnegie Institution of Washington.
- Ptolemy, Claudius (1952). "The Almagest". In Hutchins, Robert Maynard; Adler, Mortimer J. (eds.). Ptolemy, Copernicus, Kepler. Chicago: Encyclopaedia Brittanica, Inc.
- — (2014). Donahue, William H. (ed.). The Almagest: Introduction to the Mathematics of the Heavens. Translated by Perry, Bruce M. ISBN 978-1-88800-943-9.
- ISBN 978-0-262-51615-0.
- Shank, Michael H. (2020). "Regiomontanus versus George of Trebizond on Planetary Order, Distances, and Orbs (Almagest 9.1)". In Juste, David; van Dalen, Benno; Hasse, Dag Nikolaus; Burnett, Charles (eds.). Ptolemy's Science of the Stars in the Middle Ages. Ptolemaeus Arabus et Latinus. Turnhout: Brepols. pp. 305–307. ISBN 978-2-503-58639-7.
- Tomarchio, John (2022). A Sourcebook for Ancient Greek: Grammar, Poetry, and Prose. Washington, D.C.: ISBN 978-1-949822-20-5.
- ISBN 978-0-387-91220-2.
Journals and magazines
- Britton, John Phillips (Dec 1969). "Ptolemy's Determination of the Obliquity of the Ecliptic". doi:10.1111/j.1600-0498.1969.tb00132.x. Reprinted as Chapter 1 of.[1]
- Dambis, A. K.; Efremov, Yu. N. (2000). "Dating Ptolemy's Star Catalogue through Proper Motions: The Hipparchan Epoch". .
- Dreyer, J. L. E. (1917). "On the Origin of Ptolemy's Catalogue of Stars". OCLC 10340650.
- Bibcode:1980QJRAS..21..253G.
- Gingerich, Owen (1981). "Ptolemy Revisited - Reply to R.R. Newton". Quarterly Journal of the Royal Astronomical Society. 22: 40–44.
- PMID 17757580.
- Hoffmann, Susanne M. (2018). "The Genesis of Hipparchus' Celestial Globe". Mediterranean Archaeology and Archaeometry. 18 (4): 281–287. .
- Kunitzsch, Paul (1986). "The Star Catalogue Commonly Appended to the Alfonsine Tables". Journal for the History of Astronomy. 17 (49): 89–98. .
Gerard of Cremona's Latin translation made in Toledo about 1175 from the Arabic, ...
- Lewis, H. A. G. (1979). "Review of The Crime of Claudius Ptolemy, by R. R. Newton". Imago Mundi. 31: 105–107. JSTOR 1150735.
- Vogt, H. (1925). "Versuch einer Wiederherstellung von Hipparchs Fixsternverzeichnis" [Attempting a restoration of Hipparchus' fixed-star catalog]. .
- .
Websites
- Jodra, Serge (2013). "L'Almageste". cosmovisions.com (in French) (Online ed.) – via Imago Mundi.
- Ridpath, Ian (2023). "Star Tales – Ptolemy's Almagest". ianridpath.com (Revised, online ed.).
Further reading
- Evans, James (1998). The History and Practice of Ancient Astronomy. ISBN 978-0-19-509539-5.
- .
- ISBN 3-540-06995-X.
- Hanson, Norwood Russell (1960). "The Mathematical Power of Epicyclical Astronomy". Isis. 51 (2): 150–158. JSTOR 226846.
- ISBN 978-0-7188-9478-8.
- ISBN 978-0-521-40899-8.
- Pedersen, Olaf (2011) [1974]. A Survey of the Almagest (2nd ed.). Berlin: Springer. ISBN 978-1-4939-3922-0.
- OCLC 767751182. Retrieved 10 April 2023 – via MDZ/München, Bayerische Staatsbibliothek.
- Shank, Michael H. (2009). "Islamic Science and the Making of European Renaissance by George Saliba". Aestimatio (Book review). 6: 63–72.
External links
- Syntaxis Mathematica (Almagest), original Greek, edited by Johan Ludvig Heiberg, 1898.
- Syntaxis mathematica in J.L. Heiberg's edition (1898–1903)
- Ptolemy's De Analemmate. PDF scans of Heiberg's Greek edition, now in the public domain (Koine Greek)
- Toomer's English translation Duckworth, 1984.
- Ptolemy. Almagest. Latin translation from the Arabic by State Library of Victoria.
- University of Vienna: Almagestum (1515) PDFs of different resolutions. Edition of Petrus Liechtenstein, Latin translation of Gerard of Cremona.
- Almagest Ephemeris Calculator by Robert Van Gent. Positions for any date, translation of dates in calendars used by Ptolemy. Extensive list of references and articles.
- Online luni-solar and planetary ephemeris calculator based on the Almagest
- A podcast discussion by Prof. M Heath and Dr A. Chapman of a recent re-discovery of a 14th-century manuscript in the university of Leeds Library
- Star catalog in ASCII (in Latin)
- Animation of Ptolemy's model of the universe by Andre Rehak (YouTube)
- (in French) French translation, with some diagrams animated, interactive, or random
- (in Hebrew) Maimonides explaining why you need to learn Almagest first to understand science