Almagest (/ˈælməˌdʒɛst/) is a 2nd-century Greek-language
mathematical and astronomical treatise on the apparent motions of the
stars and planetary paths, written by Claudius
Ptolemy (c. AD 100 –
c. 170). One of the most influential scientific texts of all time,
its geocentric model was accepted for more than 1200 years from its
origin in Hellenistic Alexandria, in the medieval
Islamic worlds, and in Western Europe through the
Middle Ages and
Renaissance until Copernicus.
Almagest is the critical source of information on ancient Greek
astronomy. It has also been valuable to students of mathematics
because it documents the ancient Greek mathematician Hipparchus's
work, which has been lost.
Hipparchus wrote about trigonometry, but
because his works appear to have been lost, mathematicians use
Ptolemy's book as their source for Hipparchus's work and ancient Greek
trigonometry in general.[dubious – discuss]
An edition in
Latin of the Almagestum in 1515
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 it cannot have been completed before about 150, a
Ptolemy began observing.
2.2 Ptolemy's cosmos
2.3 The star catalog
2.4 Ptolemy's planetary model
4 Modern editions
6 See also
9 External links
The work was originally titled "Μαθηματικὴ
Σύνταξις" (Mathēmatikē Syntaxis) in Ancient Greek, and also
called Syntaxis Mathematica or Almagestum in Latin. The treatise was
later titled Hē Megalē Syntaxis (Ἡ Μεγάλη Σύνταξις,
"The Great Treatise"; Latin: Magna Syntaxis), and the superlative form
of this (Ancient Greek: μεγίστη, megiste, "greatest") lies
behind the Arabic name al-majisṭī (المجسطي), from which the
Almagest derives. The Arabic name is important due to the
popularity of a
Latin re-translation made in the 12th century from an
Arabic translation, which would endure until original Greek copies
resurfaced in the 15th century.
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.
Book I contains an outline of Aristotle's cosmology: on the spherical
form of the heavens, with the spherical Earth lying motionless as the
center, with the fixed stars and the various 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
Sun through the stars); and an introduction to spherical
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
Sun is vertical, the shadows of the gnomon at the equinoxes and
solstices, and other observations that change with the spectator'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 Sun.
Ptolemy explains Hipparchus' discovery of the precession of the
equinoxes and begins explaining the theory of epicycles.
Books IV and V cover the motion of the Moon, lunar parallax, the
motion of the lunar apogee, and the sizes and distances of the
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 star catalogue of
1022 stars, described by their positions in the constellations,
together with ecliptic longitude and latitude.
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 below, under 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.
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
Venus as well as the outer planets.
Book XIII covers motion in latitude, that is, the deviation of planets
from the ecliptic.
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.
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.
The Earth does not move.
The star catalog
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", and that the ecliptic
longitudes are for the beginning of the reign of
Antoninus Pius (138
AD). But calculations show that his ecliptic longitudes correspond
more closely to around 58 AD. He states that he found that the
longitudes had increased by 2° 40' since the time of Hipparchos. This
is the amount of axial precession that occurred between the time of
Hipparchos and 58 AD. It appears therefore that
Ptolemy took a star
Hipparchos and simply added 2° 40' to the longitudes.
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
1175, put 300° for the latitude of several stars. He had apparently
learned from Moors, who used the letter "sin" for 300, but the
manuscript he was translating came from the East, where "sin" was used
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 very accurate, with
errors of 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. A series of stars in Centaurus
are off by a couple 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.
Ptolemy's planetary model
16th-century representation of Ptolemy's geocentric model in Peter
Apian's Cosmographia, 1524
Ptolemy assigned the following order to the planetary spheres,
beginning with the innermost:
Sphere of fixed stars
Other classical writers suggested different sequences.
Plato (c. 427
– c. 347 BC) placed the
Sun second in order after the Moon.
Martianus Capella (5th century AD) put Mercury and
Venus in motion
around the Sun. Ptolemy's authority was preferred by most medieval
Islamic and late medieval European astronomers.
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.
Apollonius of Perga
Apollonius of Perga (c. 262 – c. 190 BC) had
introduced the deferent and epicycle and the eccentric deferent to
Hipparchus (2nd century BC) had crafted mathematical models
of the motion of the
Sun and Moon.
Hipparchus had some knowledge of
Mesopotamian astronomy, and he felt that Greek models should match
those of the Babylonians in accuracy. He was unable to create accurate
models for the remaining five planets.
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": 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,
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.
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
Hipparchus comes from references in the Syntaxis.
Almagest became an authoritative work for many centuries.
The first translations into Arabic were made in the 9th century, with
two separate efforts, one sponsored by the caliph Al-Ma'mun. Sahl ibn
Bishr is thought to be the first Arabic translator. By this time, the
Syntaxis was lost in Western Europe, or only dimly remembered. Henry
Aristippus made the first
Latin translation directly from a Greek
copy, but it was not as influential as a later translation into Latin
Gerard of Cremona
Gerard of Cremona from the Arabic (finished in 1175).
Gerard translated the Arabic text while working at the Toledo School
of Translators, although he was unable to translate many technical
terms such as the Arabic Abrachir for Hipparchus. In the 12th century
a Spanish version was produced, which was later translated under the
patronage of Alfonso X.
Picture of George of Trebizond's
Latin translation of the Syntaxis
Mathematica or Almagest
In the 15th century, a Greek version appeared in Western Europe. The
German astronomer Johannes Müller (known, from his birthplace of
Königsberg, as Regiomontanus) made an abridged
Latin version at the
instigation of the Greek churchman Johannes, Cardinal Bessarion.
Around the same time,
George of Trebizond
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. The Pope declined the dedication of
George's work, and Regiomontanus's translation had
the upper hand for over 100 years.
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",
Commentaries on the Syntaxis were written by Theon of Alexandria
Pappus of Alexandria
Pappus of Alexandria (only fragments survive), and Ammonius
Almagest 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
R. Catesby Taliaferro of St. John's College in
Annapolis, Maryland, was included in volume 16 of the Great Books of
the Western World in 1952. The second, by G. J. Toomer, Ptolemy's
Almagest in 1984, with a second edition in 1998. The third was a
partial translation by Bruce M. Perry in The Almagest: Introduction to
the Mathematics of the Heavens in 2014.
A direct French translation from the Greek text was published in two
volumes in 1813 and 1816 by Nicholas Halma, including detailed
historical comments in a 69-page preface. The scanned books are
available in full at the
Gallica French national library.
Ptolemy's cataloque of stars; a revision of the
Almagest by Christian
Heinrich Friedrich Peters and Edward Ball Knobel, 1915
Epytoma Ioannis de Monte Regio in Almagestum Ptolomei, Latin, 1496
Almagestum, Latin, 1515
Abū al-Wafā' Būzjānī
Abū al-Wafā' Būzjānī (who also wrote an Almagest)
Book of Fixed Stars
^ NT Hamilton, N. M. Swerdlow, G. J. Toomer. "The Canobic Inscription:
Ptolemy's Earliest Work". In Berggren and Goldstein, eds., From
Ancient Omens to Statistical Mechanics. Copenhagen: University
^ "Almagestum (1515)". Universität Wien. Retrieved 31 May 2014.
^ Ley, Willy (December 1963). "The Names of the Constellations". For
Your Information. Galaxy Science Fiction. pp. 90–99.
^ a b Toomer, G. J. (1998), Ptolemy's
Almagest (PDF), Princeton
University Press, ISBN 0-691-00260-6
^ Ptolemy. Almagest. , Book I, Chapter 5.
Christian Peters and
Edward Knobel (1915). Ptolemy's Catalogue of
the Stars – A Revision of the Almagest. p. 15.
^ Peters and Knobel, pp. 9-14.
^ Peters and Knobel, p. 14.
^ Peters and Knobel, p. 112.
^ Michael Hoskin. The Cambridge Concise History of Astronomy.
Chapter 2, page 44.
^ See p. 3 of Introduction of the Toomis translation.
^ Islamic science and the making of European Renaissance, by George
Saliba, p. 218 ISBN 978-0-262-19557-7
^ Perry, Bruce M. (2014), The Almagest: Introduction to the
Mathematics of the Heavens, Green Lion Press,
^ Halma, Nicolas (1813). Composition mathématique de Claude
Ptolémée, traduite pour la première fois du grec en français, sur
les manuscrits originaux de la bibliothèque impériale de Paris, tome
1 (in French). Paris: J. Hermann. p. 608.
^ Halma, Nicolas (1816). Composition mathématique de Claude
Ptolémée, ou astronomie ancienne, traduite pour la première fois du
grec en français sur les manuscrits de la bibliothèque du roi, tome
2 (in French). Paris: H. Grand. p. 524.
James Evans (1998) The History and Practice of Ancient Astronomy,
Oxford University Press
Oxford University Press ISBN 0-19-509539-1
Michael Hoskin (1999) The Cambridge Concise History of Astronomy,
Cambridge University Press
Cambridge University Press ISBN 0-521-57291-6
Olaf Pedersen (1974) A Survey of the Almagest, Odense University Press
Alexander Jones &
Olaf Pedersen (2011) A Survey of the Almagest,
Springer ISBN 9780387848259
Olaf Pedersen (1993) Early Physics and Astronomy: A Historical
Introduction, 2nd edition, Cambridge University Press
Wikimedia Commons has media related to Almagest.
Ptolemy's Almagest. PDF scans of Heiberg's Greek edition, now in the
public domain (Koine Greek)
Toomer's English translation, 1984.
Latin translation from the Arabic by Gerard of
Cremona. Digitized version of manuscript made in Northern Italy c.
1200–1225 held by the State Library of Victoria.
University of Vienna: Almagestum (1515) PDFs of different resolutions.
Edition of Petrus Liechtenstein,
Latin translation of Gerard of
Almagest Planetary Model Animations
Online luni-solar and planetary ephemeris calculator based on the
A podcast discussion by Prof. M Heath and Dr A. Chapman of a recent
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Star catalog in
The 48 constellations listed by
Ptolemy after 150 AD
Ancient Greek astronomy
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Medieval European science
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Ancient Greek mathematics
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Theon of Smyrna
Zeno of Elea
Zeno of Sidon
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