Meton of Athens approximated the cycle to a whole number ( 6, 940 ) of days, obtained by 125 long months of 30 days and 110 short months of 29 days . During the next century, Callippus developed the Callippic cycle of four 19-year periods for a 76-year cycle with a mean year of exactly 365.25 days.
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The Babylonian calendar used a cycle of 235 lunar months in 19 years since 499 BC ( with only three exceptions before 380 BC ), but it did not use a specified number of days . The Metonic cycle ( 432 BC ) assigned 6, 940 days to these 19 years producing an average year of 365 + 1 / 4 + 1 / 76 or 365.26316 days . The Callippic cycle ( 330 BC ) dropped one day from four Metonic cycles ( 76 years ) for an average year of 365 + 1 / 4 or 365.25 days . Hipparchus dropped one more day from four Callipic cycles ( 304 years ), creating the Hipparchic cycle with an average year of 365 + 1 / 4 " 1 / 304 or 365.24671 days, which was close to his tropical year of 365 + 1 / 4 " 1 / 300 or 365.24667 days.
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