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show that | OE| should be 10; 19 and the radius of the epicycle was 5; 15. In

The claim that Ptolemy never made any lunar observations, in support ofthe general thesis of Newton (1977), is made by Goldstein (1982). Details can be found in Pedersen (1974).

the first version of his lunar theory, the Moon M was made to rotate around its epicycle at a uniform rate with respect to the line ECB (see Figure 3.12) once in each anomalistic month, exactly as in Hipparchus' theory. The angle BCM thus was a given linear function of time. In order to calculate the longitude of the Moon for a given time, Ptolemy had first to compute the longitude of the point C (the mean moon) from the mean lunar motion. Then he could calculate the angle CES, since the solar theory provided the longitude of the mean sun. Next, the distance |CE| can be computed by solving the triangle EOC and, finally, LCEM (the prosthaphaeresis angle for the Moon) can be found by

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