[San 10b: We begin at the two dots on the fourth line of the text. The lunar month (on which the Jewish calendar is based) is 29:12:44:3.3 (days:hours:minutes:seconds) long. But halakhically, the month must consist of full days. Therefore, some months are 29 days, and some months are 30 days. Intercalation (`ibur") is the addition of a thirtieth day to the month. Generally, the court's proclamation of a new month is based on the testimony of witnesses who saw the new moon, but under some circumstances (e.g., if there were several cloudy nights towards the end of the month, when new moon could not be seen), the court could declare a new month based on astronomical calculations.]
[Citing our mishna:] "Intercalation to the month is by a court of three."
It (the mishna) does not refer to calculation or to sanctification but to intercalation.
[As we will see, the distinction between intercalation and .sanctification is ambiguous. Rashi distinguishes between sanctification, i.e.,hearing the testimony of witnesses and proclaiming that a new month has been sanctified, and intercalation, i.e., the court's declaration that a day has been added to the month. According to Hameiri, intercalation is the actual addition of the day, whereas sanctification requires no additional declaration.]
[The gemara asks:] (Even) if it is not sanctified [on the thirtieth day] it will automatically be intercalated. [If the court does not declare the new month on the thirty-first day, we know that no month can have more than thirty days even without the formal declaration.]
Abbaye said: Learn it [i.e., revise our mishnaic text] to "Sanctification of the month " [so that the court must sanctify the new month explicitly]. This was taught in a b'raita as well: The sanctification of the month and the intercalation of the month must be by a court of three. These are the words of R. Meir.
Rava said: But it says "intercalation" [and we cannot so readily change the words of the mishnaic text]. Rather, Rava said, sanctification on the intercalated day [i.e., the thirtieth day] requires a court of three. After the intercalary [the thirtieth] day, there is no sanctification [i.e., it is automatic.] And whose opinion is this? R. Elazar b. R. Zadok, as it says in a b'raita: R. Elazar b. R. Zadok says: If the new moon was not seen at its time, we do not sanctify it, because it has already been sanctified in Heaven.
Rav Nachman said: Sanctification after the intercalary [the thirtieth] day is by a court of three, but there is no sanctification on the intercalary day And whose opinion is this? Plimo, as we learned in a b'raita: Plimo says: At its time [i.e., if the new moon was sighted by witnesses] we do not sanctify, but after its time [i.e., on the thirty-first day] we do sanctify.
Rav Ashi said: Actually the mishna is referring to calculation. And what is meant by "intercalation"? -- the calculations required for intercalation. But since the mishna wanted to teach [in the mishna's next line] about intercalation to a year [adding an entire month], it uses the term "intercalation to a month" (here). Calculation (for adding a day) to a month is indeed referred to (in our mishna), but sanctification of the month is not. Whose opinion is this? R. Eliezer, for we learned in a b'raita: Whether or not it [the moon] is sighted on time, we do not sanctify it, as it says (Lev 25:10) "And ye shall hallow the fiftieth year" -- we sanctify years, not months.
[Sanctification of the new month is discussed at greater length on Rosh Hashanah 24a, where halakhah is fixed according to R. Elazar b. R. Zadok.]
[Our mishna, on proclaiming a leap year:] Rabban Shimon b. Gamliel says: They begin with three [judges].
We learned in a b'raita: How (does the court proclaim a leap year) Rabban Shimon b. Gamliel said: They start with three, and they discuss it with five, and they finalize it with seven. If one judge says that they must sit (as a court to consider whether a leap year should be declared) and two say that they do not have to sit, the single judge's opinion is rejected as a minority opinion. If two say that it is necessary to sit, and one says that it is not, they add two more (for a total of five) and discuss the matter. If (after the deliberation by the court of five) two say that it [the leap year] is necessary and three say that it is not, the two are nullified as a minority. If three say that it [the leap year] is necessary and two say it is not, we add another two judges (for a total of seven), because the quorum (for declaring a leap year) is not less than seven.
These are (Rabban Shimon b. Gamliel's) three, five, and seven. To what do they correspond? R. Yitzchak b. Nahmani and one who was with him disagree. And who was with him? R. Shimon b. Pazi. Others say that R. Shimon b. Pazi and one who was with him disagree. And who was with him? R. Yitzchak b. Nahmani. One says that they correspond to the number of words in the Priestly Blessings [Num. 6:24 has three words, 6:25 has five, 6:26 has seven], and one says that the three correspond to the keepers of the door (of the Temple) and five of them that saw the king's face (i.e., courtiers) and seven to those that saw the king's face .
[The three and five refereed to were those taken captive with King Zedekiah and put to death {2 Kings 25:18-21} by the King of Babylon. Rashi and Tosafot disagree as to the identity of the seven. Rashi: the seven princes mentioned in Esther 1:10 who served King Ahasuerus. Tosafot: Why should the Jewish court be modeled after that of an evil king. Instead, they are the seven attendants of KIng Zedekiah who were taken captive, as related in to Jer 52:25.]
Rav Yosef taught a b'raita: To what do these courts of three, five, and seven correspond? Three correspond to the three keepers of the door, and five from those who saw the king's face, and seven to those who saw the king's face.
Abbaye [evidently while he was still a student] said to Rav Yosef: Why haven't you explained this to us until now? He [Rav Yosef] said: I did not know that you needed it. Did you ever ask me about anything and I did not tell you?
[We end at the next to the last line of 10b.]