## Historical Significance in Numerical Details

Plodding through mathematical details in the Almagest is tiresome for those not imbued with a love of learning for its own sake, but the effort occasionally yields a more tangible reward.

In his discussion of the synodic month (the period of revolution of the Moon with respect to the Sun; a sidereal month is measured with respect to the stars), Ptolemy noted that there are 4,267 synodic months in 126,007 days and 1 hour. He then concluded that the mean synodic month is therefore 29, 31, 50, 8, 20 days (29 plus 31/60 plus 50/3600, etc., days).

Dividing 126,007 days and 1 hour by 4,267 does not, however, produce this number. See if you don't get, instead: 29, 31, 50, 8, 9.

It so happens that the Babylonian value of the mean synodic month is 29, 31, 50, 8, 20. Obviously, Ptolemy did not do the division implied but instead borrowed the Babylonian value.

Also obvious is that there was an exchange of astronomical information between the Babylonians and the Greeks, an exchange hinting at a more general pattern of mutual influences between Hellenistic and Oriental civilizations.

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