By AD 150, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for zero (—°) in his work on mathematical astronomy called the Syntaxis Mathematica, also known as the Almagest. This Hellenistic zero was perhaps the earliest documented use of a numeral representing zero in the Old World. Ptolemy used it many times in his Almagest (VI. for the magnitude of solar and lunar eclipses. It represented the value of both digits and minutes of immersion at first and last contact. Digits varied continuously from 0 to 12 to 0 as the Moon passed over the Sun (a triangular pulse), where twelve digits was the angular diameter of the Sun. Minutes of immersion was tabulated from 0′0″ to 31′20″ to 0′0″ where 0′0″ used the symbol as a place holder in two positions of his sexagesimal positional numeral system,[b] while the combination meant a zero angle. Minutes of immersion was also a continuous function 1/12 31′20″ √d(24−d) (a triangular pulse with convex sides), where d was the digit function and 31′20″ was the sum of the radii of the Sun’s and Moon’s discs. Ptolemy’s symbol was a place holder as well as a number used by two continuous mathematical functions, one within another, so it meant zero, not none.
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