Metonic
Table
of Leap Years
The lunar year is eleven days shorter than
the solar year, requiring the addition of an extra month
approximately every third year. To reconstruct the priestly
courses from AD 70 to the ministration of Zechariah, father of John
the Baptist, we must consult the Metonic table, named after the
Greek mathematician who discovered it. An extra month (“bet
Adar”) is added seven times in nineteen years. Leap years are
ascertained by adding the year Anno Domini to the year 747 Anno
Nepolassar (after the Babylonian monarch), then dividing by
nineteen. The remainder is the year in the cycle; a remainder
of zero is the last year in the cycle. In the table above, we
see that the years 26, 7 BC, AD 13, AD 32, and AD 70 (indicated by
yellow) were the 19th year in their respective cycles.
Leap years occupied the 3rd, 6th, 8th, 11th, 14th, 17th, and 19th
positions in each cycle (indicated by green/yellow).
Metonic Table of
Leap Years
|
Anno Nepolassar
|
Anno Domini
|
Quotient
|
Divisor
|
Numerator
|
Remainder
|
|
747 +
|
70
|
= 817
|
÷ 19
|
= 43
|
R 0
|
|
747 +
|
69
|
= 816
|
÷ 19
|
= 42
|
R 18
|
|
747 +
|
68
|
= 815
|
÷ 19
|
= 42
|
R 17
|
|
747 +
|
67
|
= 814
|
÷ 19
|
= 42
|
R 16
|
|
747 +
|
66
|
= 813
|
÷ 19
|
= 42
|
R 15
|
|
747 +
|
65
|
= 812
|
÷ 19
|
= 42
|
R 14
|
|
747 +
|
64
|
= 811
|
÷ 19
|
= 42
|
R 13
|
|
747 +
|
63
|
= 810
|
÷ 19
|
= 42
|
R 12
|
|
747 +
|
62
|
= 809
|
÷ 19
|
= 42
|
R 11
|
|
747 +
|
61
|
= 808
|
÷ 19
|
= 42
|
R 10
|
|
747 +
|
60
|
= 807
|
÷ 19
|
= 42
|
R 9
|
|
747 +
|
59
|
= 806
|
÷ 19
|
= 42
|
R 8
|
|
747 +
|
58
|
= 805
|
÷ 19
|
= 42
|
R 7
|
|
747 +
|
57
|
= 804
|
÷ 19
|
= 42
|
R 6
|
|
747 +
|
56
|
= 803
|
÷ 19
|
= 42
|
R 5
|
|
747 +
|
55
|
= 802
|
÷ 19
|
= 42
|
R 4
|
|
747 +
|
54
|
= 801
|
÷ 19
|
= 42
|
R 3
|
|
747 +
|
53
|
= 800
|
÷ 19
|
= 42
|
R 2
|
|
747 +
|
52
|
= 799
|
÷ 19
|
= 42
|
R 1
|
|
747 +
|
51
|
= 798
|
÷ 19
|
= 42
|
R 0
|
|
747 +
|
50
|
= 797
|
÷ 19
|
= 41
|
R 18
|
|
747 +
|
49
|
= 796
|
÷ 19
|
= 41
|
R 17
|
|
747 +
|
48
|
= 795
|
÷ 19
|
= 41
|
R 16
|
|
747 +
|
47
|
= 794
|
÷ 19
|
= 41
|
R 15
|
|
747 +
|
46
|
= 793
|
÷ 19
|
= 41
|
R 14
|
|
747 +
|
45
|
= 792
|
÷ 19
|
= 41
|
R 13
|
|
747 +
|
44
|
= 791
|
÷ 19
|
= 41
|
R 12
|
|
747 +
|
43
|
= 790
|
÷ 19
|
= 41
|
R 11
|
|
747 +
|
42
|
= 789
|
÷ 19
|
= 41
|
R 10
|
|
747 +
|
41
|
= 788
|
÷ 19
|
= 41
|
R 9
|
|
747 +
|
40
|
= 787
|
÷ 19
|
= 41
|
R 8
|
|
747 +
|
39
|
= 786
|
÷ 19
|
= 41
|
R 7
|
|
747 +
|
38
|
= 785
|
÷ 19
|
= 41
|
R 6
|
|
747 +
|
37
|
= 784
|
÷ 19
|
= 41
|
R 5
|
|
747 +
|
36
|
= 783
|
÷ 19
|
= 41
|
R 4
|
|
747 +
|
35
|
= 782
|
÷ 19
|
= 41
|
R 3
|
|
747 +
|
34
|
= 781
|
÷ 19
|
= 41
|
R 2
|
|
747 +
|
33
|
= 780
|
÷ 19
|
= 41
|
R 1
|
|
747 +
|
32
|
= 779
|
÷ 19
|
= 41
|
R 0
|
|
747 +
|
31
|
= 778
|
÷ 19
|
= 40
|
R 18
|
|
747 +
|
30
|
= 777
|
÷ 19
|
= 40
|
R 17
|
|
747 +
|
29
|
= 776
|
÷ 19
|
= 40
|
R 16
|
|
747 +
|
28
|
= 775
|
÷ 19
|
= 40
|
R 15
|
|
747 +
|
27
|
= 774
|
÷ 19
|
= 40
|
R 14
|
|
747 +
|
26
|
= 773
|
÷ 19
|
= 40
|
R 13
|
|
747 +
|
25
|
= 772
|
÷ 19
|
= 40
|
R 12
|
|
747 +
|
24
|
= 771
|
÷ 19
|
= 40
|
R 11
|
|
747 +
|
23
|
= 770
|
÷ 19
|
= 40
|
R 10
|
|
747 +
|
22
|
= 769
|
÷ 19
|
= 40
|
R 9
|
|
747 +
|
21
|
= 768
|
÷ 19
|
= 40
|
R 8
|
|
747 +
|
20
|
= 767
|
÷ 19
|
= 40
|
R 7
|
|
747 +
|
19
|
= 766
|
÷ 19
|
= 40
|
R 6
|
|
747 +
|
18
|
= 765
|
÷ 19
|
= 40
|
R 5
|
|
747 +
|
17
|
= 764
|
÷ 19
|
= 40
|
R 4
|
|
747 +
|
16
|
= 763
|
÷ 19
|
= 40
|
R 3
|
|
747 +
|
15
|
= 762
|
÷ 19
|
= 40
|
R 2
|
|
747 +
|
14
|
= 761
|
÷ 19
|
= 40
|
R 1
|
|
747 +
|
13
|
= 760
|
÷ 19
|
= 40
|
R 0
|
|
747 +
|
12
|
= 759
|
÷ 19
|
= 39
|
R 18
|
|
747 +
|
11
|
= 758
|
÷ 19
|
= 39
|
R 17
|
|
747 +
|
10
|
= 757
|
÷ 19
|
= 39
|
R 16
|
|
747 +
|
9
|
= 756
|
÷ 19
|
= 39
|
R 15
|
|
747 +
|
8
|
= 755
|
÷ 19
|
= 39
|
R 14
|
|
747 +
|
7
|
= 754
|
÷ 19
|
= 39
|
R 13
|
|
747 +
|
6
|
= 753
|
÷ 19
|
= 39
|
R 12
|
|
747 +
|
5
|
= 752
|
÷ 19
|
= 39
|
R 11
|
|
747 +
|
4
|
= 751
|
÷ 19
|
= 39
|
R 10
|
|
747 +
|
3
|
= 750
|
÷ 19
|
= 39
|
R 9
|
|
747 +
|
2
|
= 749
|
÷ 19
|
= 39
|
R 8
|
|
747 +
|
1
|
= 748
|
÷ 19
|
= 39
|
R 7
|
|
747 +
|
1 BC
|
= 747
|
÷ 19
|
= 39
|
R 6
|
|
747 +
|
2 BC
|
= 746
|
÷ 19
|
= 39
|
R 5
|
|
747 +
|
3 BC
|
= 745
|
÷ 19
|
= 39
|
R 4
|
|
747 +
|
4 BC
|
= 744
|
÷ 19
|
= 39
|
R 3
|
|
747 +
|
5 BC
|
= 743
|
÷ 19
|
= 39
|
R 2
|
|
747 +
|
6 BC
|
= 742
|
÷ 19
|
= 39
|
R 1
|
|
747 +
|
7 BC
|
= 741
|
÷ 19
|
= 39
|
R 0
|
|
747 +
|
8 BC
|
= 740
|
÷ 19
|
= 38
|
R 18
|
|
747 +
|
9 BC
|
= 739
|
÷ 19
|
= 38
|
R 17
|
|
747 +
|
10 BC
|
= 738
|
÷ 19
|
= 38
|
R 16
|
|
747 +
|
11 BC
|
= 737
|
÷ 19
|
= 38
|
R 15
|
|
747 +
|
12 BC
|
= 736
|
÷ 19
|
= 38
|
R 14
|
|
747 +
|
13 BC
|
= 735
|
÷ 19
|
= 38
|
R 13
|
|
747 +
|
14BC
|
= 734
|
÷ 19
|
= 38
|
R 12
|
|
747 +
|
15 BC
|
=733
|
÷ 19
|
= 38
|
R 11
|
|
747 +
|
16 BC
|
= 732
|
÷ 19
|
= 38
|
R 10
|
|
747 +
|
17 BC
|
= 731
|
÷ 19
|
= 38
|
R 9
|
|
747 +
|
18 BC
|
= 730
|
÷ 19
|
= 38
|
R 8
|
|
747 +
|
19 BC
|
= 729
|
÷ 19
|
= 38
|
R 7
|
|
747 +
|
20 BC
|
= 728
|
÷ 19
|
= 38
|
R 6
|
|
747 +
|
21 BC
|
= 727
|
÷ 19
|
= 38
|
R 5
|
|
747 +
|
22 BC
|
= 726
|
÷ 19
|
= 38
|
R 4
|
|
747 +
|
23 BC
|
= 725
|
÷ 19
|
= 38
|
R 3
|
|
747 +
|
24 BC
|
= 724
|
÷ 19
|
= 38
|
R 2
|
|
747 +
|
25BC
|
= 723
|
÷ 19
|
= 38
|
R 1
|
|
747 +
|
26 BC
|
= 722
|
÷ 19
|
= 38
|
R 0
|
|
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