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Claudius Ptolemy
(100 - 170)
The Greek astronomer, astrologer, and geographer Claudius
Ptolemy (ca. 100-ca. 170) established the system of mathematical
astronomy that remained standard in Christian and Moslem
countries until the 16th century.
Ptolemy is known to have made astronomical observations at
Alexandria in Egypt between 127 and 141, and he probably lived
on into the reign of Marcus Aurelius (161-180). Beyond the fact
that his On the Faculty of Judgment indicates his adherence to
Stoic doctrine, nothing more of his biography is available.
The
Almagest
The earliest and most influential of Ptolemy's major writings is
the Almagest. In 13 books it establishes the kinematic models
(purely mathematical and nonphysical) used to explain solar,
lunar, and planetary motion and determines the parameters which
quantify these models and permit the computation of longitudes
and latitudes; of the times, durations, and magnitudes of lunar
and solar eclipses; and of the times of heliacal risings and
settings. Ptolemy also provides a catalog of 1, 022 fixed stars,
giving for each its longitude and latitude according to an
ecliptic coordinate system.
Ptolemy's is a geocentric system, though the earth is the actual
centre only of the sphere of the fixed stars and of the "crank
mechanism" of the moon; the orbits of all the other planets are
slightly eccentric. Ptolemy thus hypothesizes a mathematical
system which cannot be made to agree with the rules of
Aristotelian physics, which require that the centre of the earth
be the centre of all celestial circular motions.
In solar astronomy Ptolemy accepts and confirms the eccentric
model and its parameters established by Hipparchus. For the moon
Ptolemy made enormous improvements in Hipparchus's model, though
he was unable to surmount all the difficulties of lunar motion
evident even to ancient astronomers. Ptolemy discerned two more
inequalities and proposed a complicated model to account for
them. The effect of the Ptolemaic lunar model is to draw the
moon close enough to the earth at quadratures to produce what
should be a visible increase in apparent diameter; the increase,
however, was not visible. The Ptolemaic models for the planets
generally account for the two inequalities in planetary motion
and are represented by combinations of circular motions:
eccentrics and epicycles. Such a combination of eccentric and
epicyclic models represents Ptolemy's principal original
contribution in the Almagest.
Canobic Inscription
This brief text was inscribed on a stele erected at Canobus near
Alexandria in Egypt in 146 or 147. It contains the parameters of
Ptolemy's solar, lunar, and planetary models as given in the
Almagest but modified in some instances. There is also a section
on the harmony of the spheres. The epoch of the Canobic
Inscription is the first year of Augustus, or 30 B.C.
Planetary Hypotheses
In the two books of Planetary Hypotheses, an important
cosmological work, Ptolemy "corrects" some of the parameters of
the Almagest and suggests an improved model to explain planetary
latitude. In the section of the first book preserved only in
Arabic, he proposes absolute dimensions for the celestial
spheres (maximum and minimum distances of the planets, their
apparent and actual diameters, and their volumes). The second
book, preserved only in Arabic, describes a physical
actualization of the mathematical models of the planets in the
Almagest. Here the conflict with Aristotelian physics becomes
unavoidable (Ptolemy uses Aristotelian terminology but makes no
attempt to reconcile his views of the causes of the inequalities
of planetary motion with Aristotle's), and it was in attempting
to remove the discrepancies that the "School of Maragha" and
also Ibn al-Shatir in the 13th and 14th centuries devised new
planetary models that largely anticipate Copernicus's.
The Phases
This work originally contained two books, but only the second
has survived. It is a calendar of the parapegma type, giving for
each day of the Egyptian year the time of heliacal rising or
setting of certain fixed stars. The views of Eudoxus, Hipparchus,
Philip of Opus, Callippus, Euctemon, and others regarding the
meteorological phenomena associated with these risings and
settings are quoted. This makes the Phases useful to the
historian of early Greek astronomy, though it is certainly the
least important of Ptolemy's astronomical works.
The Apotelesmatica
Consisting of four books, the Apotelesmatica is Ptolemy's
contribution to astrological theory. He attempts in the first
book to place astrology on a sound scientific basis. Astrology
for Ptolemy is less exact than astronomy is, as the former deals
with objects influenced by many other factors besides the
positions of the planets at a particular point in time, whereas
the latter describes the unswerving motions of the eternal stars
themselves. In the second book, general astrology affecting
whole states, societies, and regions is described; this general
astrology is largely derived from Mesopotamian astral omina. The
final two books are devoted to genethlialogy, the science of
predicting the events in the life of a native from the horoscope
cast for the moment of his birth. The Apotelesmatica was long
the main handbook for astrologers.
The Geography
In the eight books of the Geography, Ptolemy sets forth
mathematical solutions to the problems of representing the
spherical surface of the earth on a plane surface (a map), but
the work is largely devoted to a list of localities with their
coordinates. This list is arranged by regions, with the river
and mountain systems and the ethnography of each region also
usually described. He begins at the West in book 2 (his prime
meridian ran through the "Fortunate Islands, " apparently the
Canaries) and proceeds eastward to India, the Malay Peninsula,
and China in book 7.
Despite his brilliant mathematical theory of map making, Ptolemy
had not the requisite material to construct the accurate picture
of the world that he desired. Aside from the fact that,
following Marinus in this as in much else, he underestimated the
size of the earth, concluding that the distance from the
Canaries to China is about 180° instead of about 130°, he was
seriously hampered by the lack of all the gnomon observations
that are necessary to establish the latitudes of the places he
lists. For longitudes he could not utilize astronomical
observations because no systematic exploitation of this method
of determining longitudinal differences had been organized. He
was compelled to rely on travellers' estimates of distances,
which varied widely in their reliability and were most uncertain
guides. His efforts, however, provided western Europe,
Byzantium, and Islam with their most detailed conception of the
inhabited world.
Harmonics and Optics
These, the last two works in the surviving corpus of Ptolemy's
writings, investigate two other fields included in antiquity in
the general field of mathematics. The Harmonics in three books
became one of the standard works on the mathematical theory of
music in late antiquity and throughout the Byzantine period. The
Optics in five books discussed the geometry of vision,
especially mirror reflection and refraction. The Optics survives
only in a Latin translation prepared by Eugenius, Admiral of
Sicily, toward the end of the 12th century, from an Arabic
version in which the first book and the end of the fifth were
lost. The doubts surrounding its authenticity as a work of
Ptolemy seem to have been overcome by recent scholarship.
His Influence
Ptolemy's brilliance as a mathematician, his exactitude, and his
masterful presentation seemed to his successors to have
exhausted the possibilities of mathematical astronomy and
geography. To a large extent they were right. Without better
instrumentation only minor adjustments in the Ptolemaic
parameters or models could be made. The major "improvements" in
the models - those of the School of Maragha - are designed
primarily to satisfy philosophy, not astronomy; the lunar theory
was the only exception. Most of the deviations from Ptolemaic
methods in medieval astronomy are due to the admixture of
non-Greek material and the continued use of pre-Ptolemaic
elements. The Geography was never seriously challenged before
the 15th century.
The authority of the astronomical and geographical works carries
over to the astrological treatise and, to a lesser extent, to
the Harmonics and Optics. The Apotelesmatica was always
recognized as one of the works most clearly defending the
scientific basis of astrology in general, and of genethlialogy
in particular. But Neoplatonism as developed by the pagans of
Harran provided a more extended theory of the relationship of
the celestial spheres to the sublunar world, and this theory was
popularized in Islam in the 9th century. The Harmonics ceased to
be popular as Greek music ceased to follow the classical modes,
and the Optics was rendered obsolete by Moslem scientists.
Ptolemy's fame and influence, then, rest primarily on the
Almagest, his most original work, justly subtitled The Greatest.
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This web page was last updated on:
09 March, 2009
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