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The excerpt represents the core issue or deciding factor on which you must meditate, and is drawn from Alexandria and her Schools by Charles Kingsley: Ptolemy, not however without making a few important additions to his
knowledge; for Aboul Wefa discovered a third inequality of the moon's
motion, in addition to the two mentioned by Ptolemy, which he did,
according to Professor Whewell, in a truly philosophic manner--an
apparently solitary instance, and one which, in its own day, had no
effect; for the fact was forgotten, and rediscovered centuries after by
Tycho Brahe. To Albatani, however, we owe two really valuable
heirlooms. The one is the use of the sine, or half-chord of the double
arc, instead of the chord of the arc itself, which had been employed by
the Greek astronomers; the other, of even more practical benefit, was
the introduction of the present decimal arithmetic, instead of the
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