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The proleptic Julian calendar is produced by extending the Julian calendar to dates preceding AD 4 when its quadrennial leap year stabilized. The leap years actually observed between its official implementation in 45 BC and AD 4 were erratic, see the Julian calendar article for details.
A calendar obtained by extension earlier in time than its invention or implementation is called the "proleptic" version of the calendar, and thus we obtain the proleptic Julian calendar. Likewise, the proleptic Gregorian calendar is occasionally used to specify dates before its official introduction in 1582. Because the Julian calendar was actually used before that time, one must explicitly state that a given date is in the proleptic Gregorian calendar when that is used.
Historians since Bede have traditionally represented the years preceding AD 1 as "1 BC", "2 BC", etc. Bede and later Latin writers chose not to place the Latin zero, nulla, between BC and AD years. In this system the year 1 BC would be a leap year. To determine an interval in years across the BC/AD boundary, it is more convenient to include a year zero and represent earlier years as negative. This is the convention used in the "astronomical Julian calendar". In this system the year 0 is equivalent to 1 BC and is a leap year.
- Julian date