sides), where d was the digit function and 3120 was the sum of the radii of the Sun's and Moon's discs. Ptolemy's symbol was a placeholder as well as a number used by two continuous mathematical functions, one within another, so it meant zero, not none. The earliest use of zero in the calculation of the Julian Easter occurred before AD311, at the first entry in a table of epacts as preserved in an Ethiopic document for the years AD311 to 369, using a Ge'ez word for "none" (English translation is "0" elsewhere) alongside Ge'ez numerals (based on Greek numerals), which was translated from an equivalent table published by the Church of Alexandria in Medieval Greek. This use was repeated in AD525 in an equivalent table, that was translated via the Latin nulla or "none" by Dionysius Exiguus, alongside Roman numerals. When division produced zero as a remainder, nihil, meaning "nothing", was used. These medieval zeros were used by all future medieval calculators of Easter. The initial "N" was used as a zero symbol in a table of Roman numerals by Bede—or his colleagues—around AD 725. China The Sūnzĭ Suànjīng, of unknown date but estimated to be dated from the 1st to , and Japanese records dated from the 18th century, describe how the Chinese counting rods system enabled one to perform decimal calculations. As noted in Xiahou Yang's Suanjing (425–468 AD) that states that to multiply or divide a number by 10, 100, 1000, or 10000, all one needs to do, with rods on the counting board, is to move them forwards, or back, by 1, 2, 3, or 4 places, According to A History of Mathematics, the rods "gave the decimal representation of a number, with an empty space denoting zero". The counting rod system is considered a positional notation system. In AD 690, Empress Wǔ promulgated Zetian characters, one of which was "〇"; originally meaning 'star', it subsequently came to represent zero. Zero was not treated as a number at that time, but as a "vacant position". Qín Jiǔsháo's 1247 Mathematical Treatise in Nine Sections is the oldest surviving Chinese mathematical text using a round symbol for zero. Chinese authors had been familiar with the idea of negative numbers by the Han Dynasty , as seen in The Nine Chapters on the Mathematical Art. India Pingala (c. 3rd/2nd century BC), a Sanskrit prosody scholar, used binary numbers