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 the
Almagest. Hence the
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 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
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.
- The Earth does not move.
Ptolemy's planetary model
Ptolemy assigned the following order to the
planetary spheres, beginning with the
innermost:
- Moon
- Mercury
- Venus
- Sun
- Mars
- Jupiter
- Saturn
- 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 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
[22877] and
[22878]
Footnotes
- http://www.univie.ac.at/hwastro/rare/1515_ptolemae.htm
- , Book I, Chapter 5.
- Chapter 2, page 44.
See also
References
- 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)
- Olaf Pedersen, Early Physics and Astronomy: A Historical
Introduction, 2nd edition, Cambridge University Press, 1993
(ISBN 0-521-40340-5)
External links