1 [Rosh Chodesh is generally instituted on the day of the conjunction. Nevertheless,] Rosh Chodesh Tishrei should never be established on a Sunday, a Wednesday, or a Friday - in symbols, אד"ו - although, according to these calculations, [the conjunction for the month will occur on these days]. Instead, when the conjunction for the month of Tishrei occurs on any of these three days, Rosh Chodesh should be established on the following day.
What is implied? When the conjunction occurs on Sunday, Rosh Chodesh Tishrei should be established on Monday. When the conjunction occurs on Wednesday, Rosh Chodesh Tishrei should be established on Thursday. When the conjunction occurs on Friday, Rosh Chodesh Tishrei should be established on the Sabbath.
2 Similarly, if the conjunction [for the month of Tishrei] takes place at noon or after noon, Rosh Chodesh should be established on the following day.
What is implied? When the conjunction takes place on Monday, six hours after daybreak or later, Rosh Chodesh is established on Tuesday. If, however, the conjunction takes place before noon, even if only a single unit prior, Rosh Chodesh is established on the day of the conjunction, provided that day is neither Sunday, Wednesday, nor Friday.
3 When the conjunction takes place at noon or after noon, and [Rosh Chodesh Tishrei would be] postponed to the following day - if that following day is either Sunday, Wednesday, or Friday, Rosh Chodesh is postponed again, and is established on the third day after the conjunction.
What is implied? If the conjunction takes place on the Sabbath after noon (in numbers, 7 - 18), in such a year Rosh Chodesh should be established on Monday. Similarly, if the conjunction takes place on Tuesday at noon or after noon, Rosh Chodesh should be established on Thursday.
4 In an ordinary year, when the conjunction [of the month] of Tishrei falls on the night of the third day, nine hours and 204 units (in numbers, 3 - 9 - 204) or more after nightfall, Rosh Chodesh is postponed, and instead of being established on Tuesday, it is established on Thursday.
5 A similar situation [may arise] in a year that follows a leap year: If the conjunction for Tishrei takes place on Monday, three hours and 589 units or more after daybreak (in numbers, 2 - 15 - 589), Rosh Chodesh is not established on Monday, but on Tuesday.
6 If, however, the conjunction of an ordinary year occurs [even] one unit earlier - i.e., were it to be 3 - 9 - 203 or earlier - [Rosh Chodesh] should be established on Tuesday, [rather than postponed until Thursday as mentioned above].
Similarly, if the conjunction of a year following a leap year occurs [even] one unit earlier - i.e., were it to be 2 - 15 - 588 or earlier - [Rosh Chodesh] should be established on Monday.
Thus, the way to determine [the day on which] Rosh Chodesh Tishrei will be established according to these calculations is as follows: One should first determine the day [of the week], the hour of the day - or night - and the number of units of the hour when the conjunction takes place. The day of the conjunction will be the day of Rosh Chodesh, except in the following instances:
a) [The conjunction] takes place on Sunday, Wednesday, or Friday;
b) The conjunction takes place at noon or after noon;
c) In an ordinary year, [the conjunction] takes place on the night of the third day, after 204 units of the tenth hour have passed, or later [that day];
d) In an ordinary year that follows a leap year, the conjunction takes place on Monday past 589 units of the fourth hour after daybreak has passed or later [that day].
If the conjunction occurs in one of these four instances, [Rosh Chodesh] is not established on the day of the conjunction, but rather on the day that follows, or on the day following that, as explained.
7 Why is [Rosh HaShanah] not established [on the day of the conjunction] when it falls on Sunday, Wednesday, or Friday? Because these calculations determine the conjunction of the sun and the moon only according to their mean [rate of] progress, and do not [necessarily] reflect the true position [of the sun and the moon in the celestial sphere], as explained. Therefore, they instituted that [on] one day [Rosh Chodesh] would be established and on the following day it would be postponed, so that they would ascertain the day when the true conjunction takes place.
What is implied? [When according to our calculations, the conjunction occurs on] Tuesday, we establish [Rosh Chodesh]. [When it occurs] on Wednesday, we postpone it. [When it occurs] on Thursday, we establish [Rosh Chodesh]. [When it occurs] on Friday, we postpone it. [When it occurs] on the Sabbath, we establish [Rosh Chodesh]. [When it occurs] on Sunday, we postpone it. [When it occurs] on Monday, we establish [Rosh Chodesh].
8 This same principle, that the calculations are based on the mean rate of progress, is also the motivating factor for the other four reasons for the postponement [of Rosh Chodesh]. As proof of this, there are times when [according to the calculations] the conjunction takes place on Tuesday, and [Rosh Chodesh] is postponed until Thursday, and yet the moon will not be seen Thursday night, nor even Friday night. This indicates that the true conjunction of the sun and the moon did not take place until Thursday.
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