Almagest is the
Latin form of the
Arabic name (
,
, in
English The Great Book) of a
mathematical and
astronomical treatise proposing the complex motions of the
stars and
planetary paths, originally written in
Greek as (
,
Mathematical Treatise; later titled
,
The Great Treatise) by
Ptolemy of
Alexandria,
Egypt, written in the 2nd century. Its
geocentric model was accepted as correct for more than a thousand years in
Islamic and
European societies through the
Middle Ages and early
Renaissance. The
Almagest is the most important source of information on ancient
Greek astronomy. The
Almagest 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 have been lost mathematicians use Ptolemy's book as their source for Hipparchus' works and ancient Greek trigonometry in general.
Dating the Almagest
The date of
Almagest has recently been more precisely established. 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
Almagest. Hence
Almagest cannot have been completed before about 150, a quarter century after Ptolemy began observing.(Reference: Introduction, Toomer's translation, Princeton University Press, 1998)
Contents
Books
The
Almagest consists of thirteen sections, called books, totalling 152 pages in a printed edition of 1515.
- 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 a set of chord tables; 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 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 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, as well as the motion of Mercury.
- 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
Almagest 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 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.
Ptolemy's planetary model
Ptolemy assigned the following order to the
planetary spheres, beginning with the innermost:
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 A.D.) 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 astronomy. 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
Almagest 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
Almagest 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
Almagest, the
Planetary Hypotheses is sometimes described as a book of cosmology.
Impact
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
Almagest.
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. By this time, the
Almagest was lost in Western
Europe, or only dimly remembered in
astrological lore. Consequently,
Western Europe rediscovered Ptolemy from translations of Arabic versions. In the twelfth century a Spanish version was produced, which was later translated into
Latin under the patronage of
Frederick II, Holy Roman Emperor.
Gerard of Cremona translated the
Almagest into Latin directly from the Arabic version. Gerard found the Arabic text in
Toledo, Spain. Gerard of Cremona was unable to translate many technical terms; he even retained the Arabic
Abrachir for Hipparchus.
In the 15th century, a Greek version appeared in Western Europe. The German astronomer Johannes Müller (known 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 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 work, and Regiomontanus's translation had the upper hand for over 100 years.
Commentaries on the
Almagest were written by
Theon of Alexandria (extant),
Pappus of Alexandria (only fragments survive), and
Ammonius Hermiae (lost).
Modern editions
Three translations of the
Almagest into English have been published . The first, by R. Catesby Taliaferro, was included in volume 16 of the
Great Books of the Western World. G. J. Toomer's later translation,
Ptolemy's Almagest, Princeton University Press, 1998 (ISBN 0-691-00260-6), is almost universally thought to be superior. Bruce M. Perry, a tutor at
St. John's College in
Annapolis, Maryland, made the most recent translation.
An older French translation (facing the Greek text), published in two volumes in 1813 and 1816 by
Nicholas Halma, is available online at the Gallica web site and
Footnotes
See also
