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Details of Ptolemy's procedures can be found in Pedersen (1974) and Katz (1998) as well as in the Almagest itself.

See, for example, Smart (1960).

A is the vernal equinox and the Sun is at B.

As an example, consider Ptolemy's determination of the declination S and right ascension a of the Sun for a given ecliptic longitude X. In Figure 3.9, A is the vernal equinox, the Sun is at B, and the angle s is the obliquity of the ecliptic, which Ptolemy took to be 23° 51' 20".24 The first and last of the four formulas listed above then show that sin S = sin s sin X, tan a = tan X cos s.

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