Ptolemaic astronomy, that is, the astronomy of Claudius
Ptolemy's *Mathematical Compilation, *(Μαθηματικη
Συνταξις) synthesized some five
hundred years' effort to account for the observed motions of the stars,
sun, and planets on the assumption that their proper motions were uniform
and circular and that the earth lay immobile at the center of the rotating
universe. Composed around the middle of the second century C.E. and known
later to Arabic and Latin readers as the *Almagest,
*Ptolemy's
grand system had neither successor nor rival until the publication of Nicholas
Copernicus' *De revolutionibus orbium coelestium *in 1543. The
bulk of the technical astronomy during the intervening 1400 years, both
in the Middle East and in Europe, was devoted to the computation of tables
and the design of instruments that translated Ptolemy's theorems and calculations
into almanacs, horoscopes, and planetaria. While Islamic astronomers carried
out some systematic observations aimed at filling gaps left in Ptolemy's
work, especially in his treatment of such long-term motions as precession,
Europeans concentrated on making the system accessible and useful to a
variety of users.

Before the establishment of the university curriculum in Europe, Ptolemaic
astronomy circulated separately from the geocentric world-picture on which
it was predicated and from which it had initially taken its task. In the
*Timaeus
(ca. *350 B.C.) Plato had first sketched out the kinetic model of a
spherical earth resting immobile at the center of a vast rotating sphere
containing the fixed stars and encompassing a nested series of concentric
spheres each carrying one of the "wandering stars", or planets (including
the sun), along its own path through the stars. Although each sphere rotated
uniformly, the combination of their separate gyrations gave rise to the
appearance of irregularity in the motions of the sun and planets as viewed
from the earth. Able to give a rough, qualitative account of the sun's
combined daily and annual motions, Plato left to astronomers the task of
articulating the model for all the planets and of fitting it
mathematically to the data that Babylonian and Greek observers had been
accumulating over several centuries. That was the task that Ptolemy finally
completed.

Yet, from Plato's time on, practically no one doubted the geocentric
model itself, whatever its precise fit with observational data. As Aristotle
showed in greater detail in his *On
the Heavens, *reason and common experience confirmed it. Philosophers,
poets, Church Fathers, educators, and encyclopedists all spoke of the universe
much as Plato had described it, embellishing his picture on occasion with
the nomenclature and simpler mathematical features of technical astronomy
as it was developing. Although such embellishments pointed to the astronomers'
more intricate version of the model, they did not provide sufficient detail
to supplant the technical literature. They did, however, make access to
that literature necessary for full understanding of the general accounts.

A socially fragile enterprise, mathematical and observational astronomy
did not survive the ferment of the late Empire in the west. Until the translation
of the *Almagest *into Latin -- from the Greek in 1160, from the Arabic
in 1175 -- Europeans readers drew their picture of the world from the encyclopedists
and the poets and hence, in the absence of any ongoing technical tradition,
had neither the need for a work as sophisticated as Ptolemy's nor the basis
for understanding it. Over the next three centuries the *Almagest *itself
circulated among a quite small number of mathematicians, while simplified
versions of its contents served the wider learned audience, especially
at the universities. These versions took two basic forms, *De spera *and
*Theorica
planetarum.*

Treatises on
the sphere, of which Johannes
de Sacrobosco's *(ca.
*1220) became the standard, set out for
students the structural elements of the geocentric universe and the rudiments
of the mathematical model that accounted for its astronomical phenomena.
Although the texts varied in detail, they generally opened with mathematical
definitions of the sphere and with the basic metaphysical and empirical
arguments that made it the shape of the earth and heavens. They turned
then to the major circles that provide lines and points of reference in
the sky: equator or equinoctial circle, celestial poles, zodiacal or sign-bearing
circle (ecliptic), *coluri *(meridians through the equinoctial and
solstitial points), horizon, zenith, and so on. As might be expected in
a university text, the definitions were accompanied by synonyms and etymologies,
the expounding of which accomplished one of the evident tasks of the sphere
literature, to wit, exegesis of passages in classical and patristic literature
where the various terms appear or are alluded to. For example, before explaining
the rising and setting of the zodiacal constellations (and hence of the
sun with them) in terms of a uniformly rotating sphere cut by a fixed,
oblique horizon, Sacrobosco briefly treated three other measures of the
phenomenon "according to the poets", and even in his main discussion quoted
frequently from Virgil, Ovid, and Lucan.

The motion of the sun eastward along the ecliptic combined with the
rotation of the stars westward along the equator to account for seasonal
changes in the length of daylight, while moving the circle of the sun's
motion slightly off-center toward Gemini adjusted for the inequality of
the seasons. The resulting extremes of apogee and perigee of the sun also
explained for writers on the sphere why the arctic regions are too cold,
and the southern hemisphere is too hot, to be habitable; the intermediate
region of habitation was divided into seven climes according to half-hour
differences in the length of the solstitial day. Yet another very slow
motion of the celestial sphere about the poles of the ecliptic produced
the gradual drift, or precession, of the equinoctial and solstitial points
eastward along the zodiac; in some accounts, e.g. Robert Grosseteste's
*(ca.
*1215-1230),
this Ptolemaic device was supplanted by Thâbit b. Qurra's more intricate
mechanism for non-uniform precession, or trepidation (see below).

With the kinetic model established for the sun and stars, treatises on the sphere turned briefly to the moon and planets, the several different cycles of which require more sophisticated arrangements of moving spheres and the use of two new devices, the epicycle and the equant. These lay at the heart of Ptolemaic astronomy, constituting both the basis of its precision and the point of its departure from strict geocentrism. Yet, precisely here writers on the sphere hurried through their presentations. "Every planet except the sun has an epicycle", wrote Sacrobosco, "and an epicycle is a small circle along the circumference of which the planet is borne, and the center of the epicycle is always carried along the circumference of the deferent." Simply introducing the names of the devices and their components in this manner, he could do no more than suggest vaguely how they were related to the phenomena they saved, in particular to the retrograde motion of the planets and to eclipses of the moon and sun.

As part of the arts curriculum, the tracts *de spera *represent
what most educated people knew -- or were supposed to know -- about Ptolemaic
astronomy. They set out the vocabulary and conveyed a general, qualitative
sense of how the basic mathematical devices explained the celestial appearances.
But they provided neither demonstrations of the mathematics nor instructions
for linking the devices to the observational data contained in the various
astronomical tables. For the demonstrations the curious student of the
thirteenth or fourteenth century still had to seek out the *Almagest
*itself;
for instructions he could turn to readily accessible abridgements generically
titled, "theory of the planets".

Following the pattern of the *Almagest, *then, each model of the
*theorica
planetarum *analyzed the "true" appearances from the earth into a composite
of mean motions and compensating equations and conversely showed how such
parameters translated into actually observable measurements. But while
the *Almagest *also provided the apparatus for calculating those parameters
from the observational data combined with the mathematics of the models
(and thus, incidentally, for tinkering with the models), the *theorica
*assumed
that readers had access to on e of the various tables that by the Middle
Ages circulated separately from their prototype in the *Almagest
*and
that reflected in the mixed provenance of their data the subsequent touch
of Italian and Islamic hands.

Belonging to an independent genre, a set of tables (called a *zîj*
in Arabic) had its own accompanying instructions, or canons, and could
be used without reference to the models. The first tables to enter Europe
stemmed from the ninth-century Arabic astronomer and mathematician al-Khwarazmi;
rendered into Latin by Adelard of Bath in 1126, they were subsequently
adjusted for the Christian Era and for various European meridians. Somewhat
later they were joined by another set, the Toledan Tables, generally (but
uncertainly) ascribed to the eleventh-century astronomer al-Zarqal; (Arzachel),
whose translated canons were particularly popular. In the 1260s Alfonso
X of Spain ordered the compilation of tables designed to be universal;
preliminary calculations allowed the user to adjust for meridian and epoch.
Extant only in the form given them by Johannes de Lineriis and his student
Johannes de Saxonia in Paris in the 1320s, and generally accompanied by
the canons of one or the other editor, the Alfonsine Tables remained the
standard for European astronomy until the sixteenth century.

Using the tables with an understanding of the models behind them was
made easier by versions of the *theorica planetarum *that translated
the models directly into calculating instruments. The earliest of these
in the west was Campanus of Novara's equatorium*(ca.
*1260),
which gave instructions for assembling sets of graduated disks into physical
models of the planets circles. With each disk then set from the tables
to the appropriate mean *motus,
*a planet's true place appeared under
a string stretched from the center of the instrument, through the point
marking the planet on the epicycle disk, and onto the ecliptic scale etched
on the rim. Inspired perhaps by Arabic instruments, the equatorium underwent
improvement in the fourteenth and fifteenth centuries; in particular, Campanus'
separate models were brought together into a single mechanism allowing
for all possible combinations of circles.

The replacement of mathematics by mechanics in medieval Europeans' general
understanding and use of Ptolemaic astronomy placed an emphasis on its
coherence as a total structure, an emphasis reinforced by knowledge of
Ptolemy's own attempt at unification in his *Planetary Hypotheses *and
of similar efforts by Arabic cosmologers such al-Farghani (Alfraganus)
al-Bitruji (Alpetragius). Of a piece with such structural concerns, but
generally critical of them, were the writings of later European cosmologers
who worried about the incompatibility of Ptolemaic astronomy with Aristotelian
physics. The title of a popular work of this genre by Henry of Langenstein
reveals the source of the concern: *De reprobatione ecentricorum et epiciclorum,
*also
referred to in some manuscripts as simply *Contra theoricam planetarum.
*Ptolemaic
astronomy in the Middle Ages served practical and pedagogical ends rather
than theoretical ones. Writers aimed at designing tables and instruments
rather than carrying out systematic observations aimed at articulating
and improving the system. For the most part, it was only the astrologer
who need astronomy at the time, in order to be free of the vagaries of
weather and location in determining the positions of the planets. Not until
the later fifteenth century, with the work of Johannes
Regiomontanus (in particular his completion of George
Peurbach's *Epitome Almagesti), *did theoretical mathematical
astronomy begin to attract scholarly interest for its own sake and bring
a return to the *Almagest
*itself. When it did, the Ptolemaic system,
pressed perhaps precisely by the mechanical and cosmological concerns noted
above, had only a short future.