The proleptic Gregorian calendar is produced by extending the Gregorian Calendar to dates preceding its official introduction in 1582.
Bede and later historians decided not to use the Latin zero, nulla, as a year, so the year preceding AD 1 is 1 BC. In this system the year 1 BC is a leap year (likewise in the proleptic Julian calendar).
Mathematically, it is more convenient to include a year zero and represent earlier years as negative. This is the convention used in the "astronomical" Gregorian calendar and in the international standard date system, ISO 8601. In these systems, the year 0 is a leap year.
Note that because the Julian calendar was in actual use between 4 and 1582, historians and astronomers prefer to use it. Likewise, the proleptic Julian calendar is used to specify dates before AD 4, its first quadrennial leap year (leap years between 45 BC and AD 4 were irregular). But when seasonal dates are important, the proleptic Gregorian calendar is sometimes used, especially when discussing cultures that did not use the Julian calendar.
The prolepticGregoriancalendar is produced by extending the Gregoriancalendar to dates preceding its official introduction in 1582.
From 1 March 200 to 28 February 300 it corresponds to the Julian calendar.
Note that the Julian calendar was in actual use after AD 4, until 1582 or later (see From Julian to Gregorian), so historians and astronomers prefer to use the actual Julian calendar during that period.
The GregorianCalendar was devised both because the mean year in the Julian Calendar was slightly too long, causing the vernal equinox to slowly drift backwards in the calendar year, and because the lunar calendar used to compute the date of Easter had grown conspicuously in error as well.
The Gregorian solar calendar is an arithmetical calendar.
Gregorian reform of the calendar: Proceedings of the Vatican conference to commemorate its 400th anniversary, 1582-1992, ed.
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