But the angular radius of the moon being 15′, its distance is necessarily about 220 times its radius,
and ∴ distance of the moon
= 60 (1 + 1∕n) (radius of the earth),
which is roughly Hipparchus’s result, if n be any fairly large number.
[26] Histoire de l’Astronomie Ancienne, Vol. I., p. 185.
[27] The chief MS. bears the title μεγάλη σύνταξις or great composition though the author refers to his book elsewhere as μαθηματικὴ σύνταξις (mathematical composition). The Arabian translators, either through admiration or carelessness, converted μεγάλη, great, into μεγίστη, greatest, and hence it became known by the Arabs as Al Magisti, whence the Latin Almagestum and our Almagest.
[28] The better known apparent enlargement of the sun or moon when rising or setting has nothing to do with refraction. It is an optical illusion not very satisfactorily explained, but probably due to the lesser brilliancy of the sun at the time.
[29] In spherical trigonometry.
[30] A table of chords (or double sines of half-angles) for every 1∕2° from 0° to 180°.
[31] His procedure may be compared with that of a political economist of the school of Ricardo, who, in order to establish some rough explanation of economic phenomena, starts with certain simple assumptions as to human nature, which at any rate are more plausible than any other equally simple set, and deduces from them a number of abstract conclusions, the applicability of which to real life has to be considered in individual cases. But the perfunctory discussion which such a writer gives of the qualities of the “economic man” cannot of course be regarded as his deliberate and final estimate of human nature.
[32] The equation of the centre and the evection may be expressed trigonometrically by two terms in the expression for the moon’s longitude, a sinθ + b sin (2φ-θ), where a, b are two numerical quantities, in round numbers 6° and 1°, θ is the angular distance of the moon from perigee, and φ is the angular distance from the sun. At conjunction and opposition φ is 0° or 180°, and the two terms reduce to (a-b) sinθ. This would be the form in which the equation of the centre would have presented itself to Hipparchus. Ptolemy’s correction is therefore equivalent to adding on