Düring (1932); Barker (1989); Mathiesen (1999); NP 10.571–572, R. Harmon; NDSB 6.172–173,
E. Rocconi.
David Creese
Ptolemy (“Claudius Ptolemaeus,” 127 – after 146 CE)
Ptolemy (Ptolemaios) was the most important author working in the mathematical and phys-
ical sciences during the Roman Empire. His extant writings are devoted to astronomy,
astrology, cartography, harmonic theory, and optics. A central concern of his work was the
deduction of systems of models representing physical causes of various categories of phe-
nomena, whether in the heavens or in our more immediate environment. From his own
works we know that he made astronomical observations between 127 and 141 CE at
Alexandria, and erected an inscription reporting the numerical details of his astronomical
models at Kanobos (“Canopus,” a suburb of Alexandria) in 146 or 147 CE. The order of
several of his books is known from cross-references, and most were completed after the
inscription. Authentic tradition may be behind O A’s asser-
tion that Ptolemy lived for 40 years in an isolated place called the “Wings” at Kanopos; the
few medieval sources attesting Ptolemy’s biography are untrustworthy or fictitious.
Astronomy: Among Ptolemy’s several works on astronomy, occupying a central place is
the Almagest – the medieval nickname derived from the Greek megistos (“greatest”) by way of
Arabic and Latin; Ptolemy entitled it Mathematical Composition (Suntaxis Mathe ̄matike ̄). This
treatise in 13 books attempts to use mathematics – by which Ptolemy means the rational
study of shape, number, size, position, and time in physical bodies – to establish models for
the motions of the Sun, Moon, planets, and stars. The fundamental assumption is that these
motions are combinations of uniform circular revolutions representing the spinning of
spherical bodies of aithe ̄r. Starting from appropriately selected observations, subjected to
mathematical analysis, Ptolemy demonstrates first the qualitative arrangement and then the
quantitative details such as radii and rates of revolution in the various circles.
The opening chapters of Book 1 give empirical arguments for Ptolemy’s basic cosmo-
logical framework, most of which would not have been controversial among contemporary
astronomers. The Earth is spherical, stationary, and located at the center of the kosmos.
The Earth’s size is negligible relative to the heavens, which taken as a whole revolve uni-
formly in an east-to-west direction around the Earth, causing the daily risings and settings
of the visible heavenly bodies. The complex secondary motion of the Sun, Moon, and
planets occurs from west to east along the ecliptic circle.
To account for the apparent irregularity in the motions of the heavenly bodies, Ptolemy
employs two devices, introduced into Greek astronomy by the time of H
N: eccentric motion and epicycles. A uniform circular motion, when seen from a
point off center, appears to vary in speed, and is called an eccenter; likewise a uniform
circular motion, the center of which is carried uniformly in a circular path around the
observer, will appear non-uniform, and is called an epicycle. Any periodic variation in
apparent speed explainable by an eccentric model can equivalently be explicated by an
epicyclic model, though the circles involved have different physical meanings. Ptolemy uses
a simple eccenter for the Sun, but his models for the Moon and planets combine the two
principles since the apparent motions of these bodies exhibited two intertwined periodici-
ties. Moreover, in his models for the Moon and planets, Ptolemy considers that a motion is
uniform if it sweeps out equal angles as seen from some fixed point which need not be the
PTOLEMY