The work known as the ALMAGEST (/ˈælməˌdʒɛst/ ), originally
titled "Μαθηματικὴ Σύνταξις" (Mathēmatikē
Ancient Greek , and also called SYNTAXIS MATHEMATICA or
Latin , 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
Byzantine and Islamic
worlds, and in Western Europe through the
Middle Ages and early
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
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.
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 English name
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. An edition in
Latin of the Almagestum in 1515
Ptolemy set up a public inscription at
Canopus, Egypt , in 147 or
148. The late 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 quarter century after
Ptolemy began observing.
* 1 Contents
* 1.1 Books
* 1.2 Ptolemy\'s cosmos
* 1.3 Ptolemy\'s planetary model
* 2 Impact
* 3 Modern editions
* 4 Gallery
* 5 See also
* 6 Footnotes
* 7 References
* 8 External links
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
* 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 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
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 Sun
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 . 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 twice the brightness of the following one,
which is a logarithmic scale . This system is believed to have
originated with Hipparchus. The stellar positions too are of
Hipparchan origin, despite Ptolemy's claim to the contrary.
* 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
* Book XI covers the motions of
* 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.
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 (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. Ptolemy's
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 made by
Gerard of Cremona from the Arabic. 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
of the Syntaxis Mathematica or
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 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
Commentaries on the Syntaxis were written by Theon 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 (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 Library, 1987.
* ^ "Almagestum (1515)". Universität Wien. Retrieved 31 May 2014.
* ^ A B Toomer, G. J. (1998), Ptolemy's Almagest, Princeton
University Press, ISBN 0-691-00260-6
* ^ Ptolemy. Almagest. , Book I, Chapter 5.
* ^ Michael Hoskin. The Cambridge Concise History of Astronomy.
Chapter 2, page 44.
* ^ 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, ISBN 978-188800943-9
* ^ 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, The History and Practice of Ancient Astronomy, Oxford
University Press, 1998 (ISBN 0-19-509539-1 )
* Michael Hoskin, The Cambridge Concise History of Astronomy,
Cambridge University Press, 1999 (ISBN 0-521-57291-6 )
* Olaf Pedersen, A Survey of the Almagest, Odense University Press,
1974 (ISBN 87-7492-087-1 . A revised edition, prepared by Alexander
Jones, is due to be published by Springer on November 29, 2010.
* Olaf Pedersen, Early Physics and Astronomy: A Historical
Introduction, 2nd edition, Cambridge University Press, 1993 (ISBN
Wikimedia Commons has media related to ALMAGEST .
* Ptolemy. Almagest.