## Greek Cosmology The Second Stage

Greek rational cosmology emerged in an intellectual milieu dominated by a geometrical conception of mathematics, and it was natural that geometrical modeling was integral to the Greek astronomical outlook. The astronomy of Eudoxus and Aristotle was theoretical and qualitative, based on highly idealized models of how the planets move. During the second century b.c., the Greeks came into contact with a large body of observational data compiled by the Babylonians. Although the details of how this contact occurred are not known, it is believed that the acquisition of some of the Babylonian data and the associated numerical methods transformed Greek astronomy, eventually leading to the mature geocentric theory of the universe that would endure unchallenged as the dominant cosmology until the sixteenth century.

The legacy of ancient mathematical astronomy is contained in Ptolemy of Alexandria's masterpiece, The Mathematical Syntaxis, a work that is customarily known by its Arabic title, the Almagest (or "greatest"). Written around 150 a.d., the Almagest is, along with Euclid's Elements, one of the two or three most significant works of Greek exact science. Perhaps the greatest astronomical book ever written, it is a comprehensive exposition of the methods and theory needed to produce empirically reliable tables of motion for the Sun, Moon, and planets. In addition to the Almagest, Ptolemy composed a work on geography and some comparatively minor treatises on cosmology and astrology as well as some specialized studies of mathematical subjects.

Among his predecessors, Ptolemy credited the work of Hipparchus of Nicaea, an astronomer who lived around 140 b.c. and who appears to have been the most important figure in astronomy before Ptolemy. It is believed that the Almagest solar theory and some of the lunar theory were due to Hipparchus, as were many of the observations cited by Ptolemy in the Almagest. The star catalog presented by Ptolemy in book seven of the Almagest was originally compiled by Hipparchus.

Hipparchus initiated the basic methodology that would characterize advanced Hellenistic astronomy. One began by devising a geometrical model to explain the motion of a given celestial body. Observations were then used to compute the parameters of the model, that is, the constants that precisely specify the orientation and relative dimensions of the model. For this purpose Hipparchus drew upon the detailed and very accurate ephemeridae produced by the Seleucid Babylonians. The model as so calibrated could then be made the basis for predictive schemes giving the positions of the body for a sequence of future times. These predictive schemes were the basis for a table giving the planet's position as a function of time. It was Ptolemy who systematized and refined the methodology involved in the second stage of this project.

The essential difference between the Babylonians and the Greeks was the fundamental place occupied by geometric models in Greek astronomy. As far as cosmology is concerned, the main question is to understand the relationship between Ptolemy's geometrical models and the physical conception he held of the heavens. As we shall see, this question is not entirely straightforward.

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