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<h1 align="CENTER"><a name="Astronomical">4. Astronomical Year
Numbering</a></h1>
Astronomers designate years prior to 1 A.D. by means of zero and
negative numbers, according to the sequence of numbers ..., -2,
-1, 0, 1, 2, .... Between the year 1 and the year -1 there
occurs the year 0. Thus astronomers adopt the following
convention:
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<td><font face="Trebuchet
MS,Arial,Tahoma,Verdana,Sans-serif,Helvetica">1 A.D.
= 1 C.E. = year 1</font></td>
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<td><font face="Trebuchet
MS,Arial,Tahoma,Verdana,Sans-serif,Helvetica">1 B.C.
= 1 B.C.E. = year 0</font></td>
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<td><font face="Trebuchet
MS,Arial,Tahoma,Verdana,Sans-serif,Helvetica">2 B.C.
= 2 B.C.E. = year -1 and so on</font></td>
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<p>
More generally, a year popularly designated <i>n</i> B.C. or
<i>n</i> B.C.E. is designated by astronomers as the year <i>-(n-1)</i>.</p>
<p>
The rules for leap years work for years prior to 1 C.E. only
if those years are expressed according to the astronomical
system, not if expressed as years B.C.E. 4 C.E. is a leap
year in both calendars, 1 B.C.E. = astronomical year 0,
5 B.C.E. = year -4, 9 B.C.E. = year -8, and so on, are all
leap years. 101 B.C.E. = year -100 is a leap year in the (<a
href="https://www.hermetic.ch/cal_stud/cal_art.html#Proleptic">proleptic</a>)
Julian Calendar but not in the (proleptic) Gregorian Calendar.
These statements, however, are only theoretically true,
because (as noted above) prior to 4 C.E. the leap years were
not observed correctly by the Roman calendrical authorities.</p>
<p>
The choice of which system of numbering years to use is
relevant to the question: <a
href="https://www.hermetic.ch/cal_stud/newmill.htm">When
Does the New Millennium Begin?</a> as can be seen from the
following:</p>
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<pre>Gregorian Religiously Common Era
Calendar Neutral Calendar
3 BC 3 BCE -2 CE
2 BC 2 BCE -1 CE
CE millennium begins 0-01-01 CE
1 BC 1 BCE 0 CE
Gregorian millennium usually taken to begin 1-1-1 AD
1 AD 1 CE 1 CE
2 AD 2 CE 2 CE
... ... ...
1998 AD 1998 CE 1998 CE
1999 AD 1999 CE 1999 CE
CE millennium ends 1999-12-31 CE
CE millennium begins 2000-01-01 CE
2000 AD 2000 CE 2000 CE
Gregorian millennium usually taken to end 2000-12-31 AD
Gregorian millennium usually taken to begin 2001-1-1 AD
2001 AD 2001 CE 2001 CE</pre>
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<p>
January 1st, 1 AD is usually taken to be the start of the
first Christian millennium,
but a case could be made for January 1st, 1 BC (see the
comment above concerning
<a
href="https://www.hermetic.ch/cal_stud/cal_art.html#Dionysius">the
Incarnation</a>), which would imply that the third Christian
millennium began on January 1st, 2000 AD.</p>
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