1)

(a)Ninety-one days comprise a Tekufah (sun season).

(b)Rav Yehudah Amar Shmuel maintains that - the majority of the month of Tishri must belong to the old Tekufah, to justify fixing a leap-year.

(c)According to Rebbi Yehudah, this means that the day of the Tekufah falls on the seventeenth of Tishri (the first day of Chol-ha'Mo'ed). Rebbi Yossi says - on the twenty-second of Tishri.

(d)According to Shmuel, both Tana'im learn their respective opinions from the Pasuk in Ki Sisa "ve'Chag ha'Asif Tekufas ha'Shanah". According to ...

1. ... Rebbi Yehudah - the Pasuk requires the entire Chag (meaning Chol-ha'Mo'ed, as we will explain at the end of the Sugya) to belong to the new Tekufah.

2. ... Rebbi Yossi - it requires at least part of the Chag to belong to the new Tekufah.

2)

(a)We ask whether 'Yom Tekufah Maschil' or 'Yom Tekufah Gomer' - meaning whether 'the day of the Tekufah' refers to the first day of the new Tekufah or the last day of the old one.

(b)We know that ...

1. .. Rebbi Yehudah holds 'Yom Tekufah Maschil', - because if he held 'Yom Tekufah Gomer', then even if there were only fifteen days in the old Tekufah, and not sixteen, (and the day of the Tekufah fell on the sixteenth) he would not have the entire Chag in the new Tekufah.

2. ... Rebbi Yossi holds 'Yom Tekufah Maschil' - because if he held 'Yom Tekufah Gomer', even if there were only twenty days in the old Tekufah, and not twenty-one, (and the day of the Tekufah fell on the twenty-first day) he would not have even a little bit of the Chag in the new Tekufah.

3)

(a)Beis-Din need to declare a leap-year for that reason. They cannot simply declare Elul a full month instead - because Chazal were very careful never to declare Elul Me'ubar, to avoid Rosh Hashanah falling on one of the days that it cannot fall (as we learned in Rosh Hashanah 'Since the days of Ezra, Elul was never Me'ubar').

(b)The problem in postponing Rosh Chodesh Tishri (Rosh Hashanah), if Elul fell on Tuesday, Thursday or Shabbos, is that - it would then inevitably fall on 'Adu' (Sunday, Wednesday or Friday), which it cannot do, since then Yom Kipur would fall on Friday or Sunday, or Hosha'ana Rabah on Shabbos, as we explained above).

(c)Neither do we even ask why, if Tishri was destined to fall on Monday, we would not rather postpone it until Tuesday, by being Me'aber Elul, rather than fix a leap-year - because it rarely happens, so we do not contend with it.

(d)Nor do we ask why Beis-Din should not then make two extra full months, thereby delaying Rosh Chodesh Tishri by two days - because seeing as a year usually comprises six full months and six short ones, this would entail arranging a year of eight full months, which is not permitted, as we learned earlier.

4)

(a)We query Shmuel however, from a Beraisa where Rebbi Yehudah specifically states 'Yom Tekufah Gomer'. Rebbi Yossi says -'Yom Tekufah Maschil'.

(b)We also query him from another Beraisa, where the Tana Kama echoes Rebbi Yehudah's first opinion, and where Rebbi Yehudah says 'Sh'tei Yados ba'Chodesh', by which he means - twenty days (and the day of the Tekufah falls on the twenty-first).

(c)This poses two Kashyos on Shmuel - 1. because Rebbi Yehudah here says twenty days (and not sixteen); 2. because here again, he holds 'Yom Tekufah Gomer', and not 'Yom Tekufah Maschil.

(d)We conclude with a Kashya on Shmuel.

5)

(a)Rebbi Yossi says 'Me'abrin Shishah-Asar Yom Lifnei ha'Pesach' - because then, if one adds the 192 days of the two Tekufos until Succos, Tekufas Tishri will fall on the twenty-second of Tishri, which warrants a leap-year according to Rebbi Yossi, as we learned above.

(b)He says 'Shishah-Asar Lifnei ha'Chag - Ein Me'abrin'.

(c)He says 'sixteen', despite the fact that even twenty days will not warrant a leap-year - in order to balance the 'sixteen days before Pesach' with which he began.

(d)In spite of the fact that Rebbi Yehudah too, requires only a little bit of Chol ha'Mo'ed in the new Tekufah, the bone of contention between him and Rebbi Yossi is now - whether 'Yom Tekufah Maschil' (Rebbi Yossi) or 'Yom Tekufah Gomer' (Rebbi Yehudah).

6)

(a)Rebbi Shimon says 'Shishah-Asar Lifnei ha'Chag, Me'abrin', which appears to mimic the opinion of the Tana Kama. In fact. Their Machlokes is whether 'Yom Tekufah Maschil', and they only declare a leap-year if it occurs on the seventeenth of Tishri (but if it falls on the sixteenth, the entire Chag falls under the new Tekufah and it is not necessary to do so), and the other, 'Yom Tekufah Gomer', and they declare it even if it falls on the sixteenth.

(b)We know that this is their bone of contention - but we do not know who holds which opinion.

7)

(a)The final opinion in the Beraisa is that of Acherim, who says 'Mi'uto' - meaning (not sixteen, but) even fourteen days (and the Tekufah falls on the fifteenth), Beis-Din may declare a leap-year.

(b)We initially assume that he cannot be referring to the Tekufah of Tishri - because even if he would require the whole Yom-tov to be in the new Tekufah, and even if he wee to hold 'Yom Tekufah Gomer, this would be fulfilled, and there would be no reason to fix a leap-year.

(c)Consequently, based on the Pasuk "Shamor es Chodesh ha'Aviv", Rav Shmuel bar Rav Yitzchak establishes Acherim (not with regard to Tekufas Tishri, but) - to Tekufas Nisan ...

(d)... and he explains the Pasuk to mean that - the new Tekufah must fall whilst the moon is still new (before it reaches its fullness on the fifteenth).

8)

(a)Nisan is called "Chodesh ha'Aviv" - because that is when the produce ripens (and the corn not ripening in the spring is one of the reasons for proclaiming a leap year).

(b)We query Rav Shmuel bar Rav Yitzchak's current explanation however - in that, if the problem was confined to the fourteenth of Nisan, we could have avoided fixing a leap-year, and arranged for Adar to be a full month instead.

(c)Rav Acha bar Ya'akov answers that Acherim reckons from up downwards - by which he means that if Tekufas Teives lacks eighteen, seventeen, sixteen or fifteen days, and Tekufas Nisan falls from the sixteenth, we fix a leap-year (because Acherim holds 'Yom Tekufah Gomer'), if it lacks only fourteen days, and the new Tekufah falls on the fifteenth, then we don't need to fix a leap-year.

(d)We would then avoid Tishri falling on Sunday, Wednesday or Friday - by declaring one of the summer months a short month.

9)

(a)Ravina however, establishes Acherim by Tekufas Tishri, like the other Tana'im, and he resolves the problem - by requiring (not just from the first day of Chol-ha'Mo'ed to fall in the new Tekufah, but) the entire Chag including the first day Yom-tov.

(b)Until now, we have interpreted "Chag ha'Asif" to mean - the part of the Chag when gathering the corn is permitted ...

(c)... such as in a case of 'Davar ha'Avud' when it would otherwise involve a loss]), but not on Yom-Tov itself, when all work not directly concerning food, is forbidden.

(d)Ravina now reinterprets it (according to Acherim) to mean - the Chag that falls during the in-gathering season (Yom-Tov included).

10)

(a)Rebbi Yehudah (in our Mishnah) learns from the plural form of each of the two words "ve'Samchu Ziknei ha'Eidah al Rosh ha'Par" - that Semichah on the head of the Par He'elam Davar requires four Dayanim ...

(b)... and since 'Ein Beis-Din Shakul', five are3 required.

(c)He also learns from the word "Ziknei" - that the Dayanim must be members of the Sanhedrei Gedolah, and not just any three Talmidei-Chachamim.

(d)Rebbi Shimon requires only three Dayanim - because the word "ve'Samchu" is needed for the basic Halachah (as we shall now see).

11)

(a)According to Rebbi Yehudah, the word "ve'Samchu" would be superfluous - since the Torah could just as well have written "Ziknei ha'Eidah al Rosh ha'Par".

(b)And he learns from a 'Gezeirah-Shavah' ("Rosh" "Rosh" from the Korban Olah) that "al Rosh ha'Par" means on the head of the bull. Rebbi Shimon says - that, were it not for "ve'Samchu", we would have interpreted "al Rosh ha'Par" to mean that they place their hands next to the bull. Consequently, we need "ve'Samchu" to teach us that they must place teir hands on its head.

(c)Rebbi Shimon - did not receive the 'Gezeirah-Shavah' from his Rebbes (and one cannot Darshen a 'Gezeirah-Shavah' without a tradition handed down from one's Rebbes.

12)

(a)We learned in a Beraisa 'Semichah u'Semichas Zekeinim bi'Sheloshah'. Rebbi Yochanan interprets 'Semichas Zekeinim' - as giving a potential candidate Semichah, in the sense that we use it.

(b)Abaye cited the Pasuk in Pinchas "va'Yismach es Yadav alav" - written in connection with Moshe giving Semichah to Yehoshua.

(c)Abaye asks from there on what we just learned - that since Moshe gave Yehoshua Semichah on his own, one judge ought to suffice for Semichah; and if we consider Moshe equivalent to the entire Sanhedrin, then it ought to require seven-one.

(d)This problem remains unresolved.

13)

(a)When Rav Acha b'rei de'Rava asked Rav Ashi whether Semichas Zekeinim means that the judges must actually lean their hands on the candidate, he replied that - Semichah in this context means adding the title 'Rebbi' to his name and authorizing him to rule Dinei K'nasos, and that placing his hands on him is not necessary (even though that is what Moshe did to Yehoshua).