Almagest

Almagest is the Latin form of the Arabic name (الكتاب المجسطي, al-kitabu-l-mijisti, i.e. "The Great Book") of a mathematical and astronomical treatise proposing the complex motions of the stars and planetary paths, originally written in Greek as μαθηματικἠ σύνταξις (Mathematike Syntaxis, "Mathematical Treatise"; later titled Hè Megalè Syntaxis, "The Great Treatise") by Ptolemy of Alexandria, Egypt, written in the 2nd century. Its geocentric model was accepted as correct for over a thousand years in Arab and European societies^{[citation needed]}. 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 provides information on the ancient Greek mathematician Hipparchus' work, which has been lost. Hipparchus wrote about trigonometry, but since his works have been lost mathematicians use Ptolemy's book as their source for information on 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 in Egypt in 147/148 A.D. 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 A.D. 150, a quarter century after Ptolemy began observing.^{[dead link]}

Contents

The Almagest consists of thirteen books. Their subject matter can be summarized as follows:

• Book I contains an outline of Aristotelian 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; 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, and 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 things which 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 of the first magnitude (m = 1), while the faintest were of sixth magnitude (m = 6), the limit of human visual perception (without the aid of a telescope). Each grade of magnitude was considered to be twice the brightness of the following grade (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 X covers the motions of Venus and Mars.
• Book XI covers the motions of Jupiter and Saturn.
• Book XII covers stations and retrogradations, which occur 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 (the deviation of planets from the ecliptic, the apparent path of the Sun through the stars).

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 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.^[1]
• The earth does not move.

Ptolemaic Planetary Models

16th-century representation of the Ptolemaic geocentric 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) made the Sun next in order after the Moon, while Martianus Capella (5th century AD) put Mercury and Venus in motion around the Sun. Ptolemy's authority was preferred by most 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.

In the Almagest, Ptolemy adopted Hipparchus' solar model, which consisted of a simple eccentric deferent. For the Moon, he 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.

The Almagest was written by Ptolemy as a textbook of mathematical astronomy. It explained geometrical models of the planets based on combinations of circles, that 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.

In the Middle Ages and Renaissance

Ptolemy's Almagest became an authoritative work for many centuries, as this 16th-century portrait of him as a Renaissance mathematician shows

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 work was lost in 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, later turned into Latin under the patronage of Emperor Frederick II. Another Latin version, this time directly from the Arabic, was produced by Gerard of Cremona, who found his text in Toledo in Spain. Gerard of Cremona was unable to translate many technical terms, even retaining the Arabic Abrachir for Hipparchus.

In the 15th century, a Greek version appeared in Western Europe, and Johannes Müller, better known as Regiomontanus, made an abridged Latin version at the instigation of the brilliant Greek churchman Johannes, Cardinal Bessarion. At the same time, a full translation was made by George of Trebizond. It included a commentary that was as long as the original. The work of translation, done under the patronage of Pope Nicholas V was intended to supplant the old translation. The new manuscripts were a great improvement; the new commentary was not, and aroused much heated criticism. The Pope declined the dedication of the translation, and Regiomontanus' translation had the upper hand for the next century and more.

Commentaries on Almagest were written by Theon of Alexandria (extant), Pappus of Alexandria (fragments), and Ammonius Hermiae (lost).

Modern editions

• Two translations of the Almagest have been published in English. The first, by R. Catesby Taliaferro, was included in volume 16 of the Britannica Great Books series. A more recent translation, by G. J. Toomer, Ptolemy's Almagest, Princeton University Press, 1998 (ISBN 0-691-00260-6), is almost universally thought to be superior. A third translation has been recently made by Bruce M. Perry, a tutor at St. John's College,_U.S.

• An older French translation (facing the Greek text), published in two volumes (1813 and 1816) by Nicholas Halma, is available online at the Gallica web site.[1]

Footnotes

See also

• Star cartography

References

• James Evans, The History and Practice of Ancient Astronomy, Oxford University Press, 1998 (ISBN 0-19-509539-1)
• Olaf Pedersen, A Survey of the Almagest, Odense University Press, 1974 (ISBN 87-7492-087-1)
• Olaf Pedersen, Early Physics and Astronomy: A Historical Introduction, 2nd edition, Cambridge University Press, 1993 (ISBN 0-521-40340-5)

External links

• University of Vienna: Almagestum (1515) PDF:s of different resolutions
• Online copy of the star catalog in the Almagest
• Almagest Planetary Model Animations
• Online luni-solar & planetary ephemeris calculator based on the Almagest
• Ptolemy's Almagest. PDF scans of Heiberg's Greek edition, now in the public domain (Classical Greek)

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