Appendix I

FINDING
THE FIRST DAY OF AN ARABIC MONTH

There are various methods for finding what the first day of an Arabic (lunar) month is. The most valid of them is the one written by Uluğ Bey. According to his method, initially the first day of Muharram, the first month of the Hijrî year is found. To find the first day of Muharram, the year in question is always divided by 210. The last digit of the remainder of this division is subtracted from the remainder and this second remainder is looked up in the first colaumn of the first table [below left.]. In the other columns of the same table, the number corresponding to the first digit of the remainder written in the first line of the table is obtained to be the number corresponding to the day of the week beginning from Sunday. And it is the first day of Muharram. Let’s find the first day of Muharram of the Hijrî year 1316, for example:

  1316          56

¾¾¾¾ = 6 ¾¾¾

   210          210

The first digit, 6, is subtracted from 56, the remainder, and thus 50 is obtained. Across from the number 50 in the first column, 1 is written in the column headed by 6, the first digit. Thus, the first day of the year is found to be Sunday. After finding the first day of the year, the first day of a mounth is found by the use of the second table. In the line containing Muharram, the number corresponding to the first day of the year is found. The number below this and across from the month in question is the day, as numbered from Sunday, of the month in question. Let’s find, for example, the first day of Ramadân in 1316: the first day of this year is Sunday, i.e. the first day of the week, and, in the column headed by 1 in the first line of the second table, 6 is written across from Ramadân. Thus, the first day of Ramadân is the sixth day of the week, i.e. Friday.

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