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1)

(a) The Tana says that on three occasions in the year the Kohanim Duchen four times (a statement which the Gemara will amend). What are ...

1. ... the three occasions - are on Ta'aniyos, Ma'amados and Yom Kipur.
2. ... the four times - Shachris, Musaf, Minchah and Ne'ilah.

(b) Besides the closing of the gates of the Beis Hamikdash - 'Ne'ilas She'arim' can also mean the closing of the gates of Heaven (which close after Yisrael have Davened Minchah).

(c) We learn from the Pasuk in Pinchas "Tzav es B'nei Yisrael ... es Korbani Lachmi ... " - that Yisrael are the owners of the Korban Tamid, and that (since it is not correct for someone's Korban to be brought in his absence), they should appoint representatives to stand by the Tamid whenever it is brought.

(d) The early prophets (Shmuel and David) - instituted the Ma'amados.

(a) The Ma'amados corresponded to the twenty-four Mishmaros. There were Ma'amados - both in Yerushalayim and in the other towns of Yisrael.

(b) The men of the Ma'amad in the towns used to - Daven that the Korban Tamid should be accepted, fast and Lein.

(c) They would fast from Monday through Thursday.

(d) They would Lein ...

1. ... on Sunday - "Bereishis" and "Yehi Raki'a".
2. ... on Monday - "Yehi Raki'a" and "Yikavu ha'Mayim".
3. ... on Friday - "va'Totzei ha'Aretz" and "va'Yechulu".

(a) They needed to Lein two Parshiyos each day - because they did not have the required number of Pesukim (ten, or at least nine) in either of the prescribed Parshiyos.

(b) They arranged the three Aliyos - by calling up two for the bigger Parshah, and one for the smaller.

(c) They Leined each day - at Shachris, Musaf and Minchah.

(d) The men of the Ma'amad did not gather to Lein - at Minchah on Friday, because of Kevod Shabbos.

(a) On a day when Hallel was recited (i.e. Chanukah - Tosfos DH 'be'Chol') - the men of the Ma'amad would omit the Ma'amad of Shachris (i.e. Davening for their brothers' Korbanos to be accepted).

(b) They would omit ...

1. ... Ma'amados at Ne'ilah, on a day when the Korban Musaf was brought - because they were busy on account of the extra Korbanos that the Musaf comprised (at least two lambs - on Shabbos). It goes without saying that the Ma'amados at Minchah were also omitted.
2. ... Ma'amados at Minchah, on a day when the Korban Eitzim was brought - because the Korban that accompanied the donation of wood kept them busy (they did however, say the Ma'amados at Ne'ilah.

(c) The Kohanim of the Ma'amad (who were apparently chosen from the Mishmar of that week) were Patur - because they were busy bringing the Musafim; the Yisre'eilim - because they were busy chopping wood and drawing water for the needs of the Korban. Note: the Giv'onim performed these tasks for the Kohanim's personal needs, but not for Hashem's (i.e. for the Korbanos) - Tosfos Yom-Tov.

(d) This is the opinion of Rebbi Akiva - ben Azai quoting Rebbi Yehoshua (to whom Rebbi Akiva later concedes) reverses the Halachos: according to him, whenever there was a Korban Musaf, they omitted the Ma'amad at Minchah (but not at Ne'ilah), whereas when there was a Korban Eitzim, they omitted the Ma'amad at Ne'ilah, too.

(a) Z'man Atzei Kohanim ve'ha'Am comprised nine fixed days in the year - on which certain designated families donated wood each year for the Korbanos. Together with their donation they brought a Korban of wood.

(b) Those particular families were chosen - on the basis of their having stepped forward and donated wood (on those same dates) when it was needed (after Yisrael returned from Bavel and re-built the second Beis Hamikdash).

(c) The family of Orach ben Yehudah was the first to bring the Korban Eitzim - and their designated date was the first of Nisan.

(d) The second family to bring the Korban Eitzim (on the twentieth of Tamuz) - was that of David ben Yehudah (alias David Hamelech).

(a) What the B'nei Zeisu ben Yehudah, the B'nei Gonvei Ali and the B'nei Kotz'ei Ketzi'os had in common was - that they were all one and the same.

(b) Kohanim and Levi'im, as well as anyone who did not know to which tribe he belonged - brought the Korban Eitzim together with them on the fifteenth of Av.

(c) The last family on the list was that of Par'osh ben Yehudah, who brought the Korban Eitzim on Rosh Chodesh Teives. The distinction that marked ...

1. ... Par'osh ben Yehudah from all the other families - was the fact that they were the only ones that donated twice.
2. ... Rosh Chodesh Teives from all the other dates - was the fact that (since both the Korban Musaf and a Korban Eitzim were brought on it) no Ma'amados were said.

7)

(a) The two calamities ...

1. ... (besides the smashing of the Luchos, the nullification of the Tamid and the breaching of the walls of Yerushalayim in the time of the first Beis- Hamikdash) that occurred on Shiv'ah-Asar be'Tamuz - were 1. Apostomos (a Greek officer) burned the Torah (possibly the Seifer-Torah that Ezra wrote - see Tif'eres Yisrael), and 2. Menasheh, King of Yehudah in the time of the *first* Beis Hamikdash) placed an image in the Heichal (though some say that it was Apostomus who did so)
2. ... (besides the decree that the generation that left Egypt would not enter Eretz Yisrael and the destruction of both Batei Mikdash) that occurred on Tish'ah be'Av - were 1. Beitar was captured (following the revolt of Bar Kochba, fifty-two years after the Churban of the second Beis Hamikdash), and 2. Turnusrufus turned Yerushalayim into a plowed field (shortly after the destruction of the second Beis-Hamikdash).

(b) When Av enters - we minimize Simchah.

(c) The Tana of our Mishnah forbids - having a hair-cut (and shaving) and washing one's clothes during the week of Tish'ah be'Av.

(d) Washing one's clothes (li'Chevod Shabbos) is permitted on Thursday - when Tish'ah be'Av falls on Friday (because, when it falls earlier in the week, it goes without saying, that everything is permitted afterwards.

(a) The Tana Kama forbids three (additional) things on Erev Tish'ah be'Av - eating two cooked foods, eating meat and drinking wine.

(b) Raban Shimon ben Gamliel requires a change (which will be explained in the Gemara). Rebbi Yehudah adds the obligation of overturning one's bed (and not sleeping on it - as was customary by a mourner in the times of the Gemara). However, the Rabbanan disagree with him.

(a) Raban Shimon ben Gamliel describes Yom Kipur and Chamishah-Asar be'Av as the greatest Yamim-Tovim - on them, he says, the girls would go out to the vineyards and dance.

(b) They would all wear borrowed dresses - so as not to embarrass the poor girls, who could not afford to buy nice dresses.

(c) All the dresses required Tevilah - since one girl did not know for certain that the girl from whom she had borrowed was Tehorah.

(d) The girls would say to the young men who might be watching them - 'See what you are choosing. Don't look for beauty, look at the family! "Sheker ha'Chein ... Ishah Yir'as Hashem Hi Tis'halal" (Mishlei). "T'nu Lah mi'Pri Yadehah ... " (Shir Hashirim).

(a) Much of this is hinted in the Pasuk in Shir ha'Shirim "Tze'enah u'Re'enah B'nos Tzi'on ba'Melech Sh'lomoh ... ". "ha'Melech Sh'lomoh" refers to Hashem ('to whom peace belongs').

(b) The Pasuk there concludes "be'Yom Chasunaso u've'Yom Simchas Libo".

1. ... "be'Yom Chasunaso" - refers to the day on which the Torah was given.
2. ... "u've'Yom Simchas Libo" - the day of the building of the Beis Hamikdash.

(c) "be'Yom Chasunaso", the day on which the Torah was given - refers (not to Shavu'os but) to Yom Kipur, on which the *second* Luchos (which remained with Yisrael) were given to K'lal Yisrael. Consequently, the connection between this Pasuk and the previous section of the Mishnah, which speaks about Yom Kipur and Chamishah-Asar be'Av is self-evident (even more so according to the Bartenura, who points out that the [first] Beis Hamikdash too, was inaugurated on Yom Kipur).

12)

(a) The author of our Mishnah (which says that the Kohanim Duchen both at Minchah of a fast-day and at Ne'ilah), says Rav Nachman quoting Rabah bar Avuha, is Rebbi Meir. But according to the Chachamim (Rebbi Yehudah), they do not Duchen at either of them. Presuming that the reason that there is no Duchening at Minchah throughout the year is because the Kohanim may have drunk wine - Rebbi Meir holds that seeing as this does not apply on a fast- day, there is no reason for them not to Duchen; whereas the Chachamim decree a fats-day because of the rest of the year.

(b) Rebbi Yossi has a third opinion. He holds - that they do not Duchen at Minchah on a fast-day, because he decrees Minchah of a fast-day (like the Chachamim), but they do Duchen at Ne'ilah, seeing as there is no Ne'ilah during the year, there is nothing to decree.

(c) Rav Yehudah quoting Rav, Rebbi Yochanan and Rava all rule like Rebbi Meir (but in varying degrees).

1. ... Halachah ke'Rebbi Meir (Rav) means - that we even Darshen publicly at the Derashah that the Halachah is like Rebbi Meir.
2. ... Minhag ke'Rebbi Meir (Rava) - that we will inform anyone who comes to ask, that the Halachah is like Rebbi Meir, but we will not go so far as to Darshen it publicly.
3. ... Nahagu ke'Rebbi Meir (Rebbi Yochanan) means - that if someone follows Rebbi Meir's opinion, we will not force him to retract, though should he come to ask, we will not rule like him.

(d) The Gemara's conclusion however, is like Rav Nachman - who rules like Rebbi Yossi.

(a) The reason that Kohanim Duchen at Minchah of a fast-day nowadays is - because, since we tend to Daven Minchah late, it is like Ne'ilah (at which the Kohanim Duchen - according to Rebbi Yossi).

(b) We learn from the juxtaposition of ...

1. ... Birchas Kohanim to the Parshah of Nazir - that a Kohen is forbidden to drink wine before Duchening, just like a Nazir is forbidden to drink wine.
2. ... the word "le'Sharso" to "u'le'Varech bi'Shemo" - that he is however, permitted to eat grapes before Duchening, just as he is permitted to do before performing the Avodah.

(c) We nevertheless learn that a Kohen who has a blemish is not invalidated from Birchas Kohanim - from the juxtaposition of Birchas Kohanim to Nazir.

(d) We Darshen these Pesukim leniently (to permit a Kohen who has eaten grapes and a Kohen who has a blemish to Duchen, from a Kohen who performs the Avodah and from a Nazir respectively), and not stringently (to forbid a Kohen who has eaten grapes [from a Nazir], and one who has a blemish [from a Kohen who performs the Avodah]) - on the grounds that the main Halachah (prohibiting a Kohen to drink wine before Duchening) is really Asur mi'de'Rabbanan, and the Derashah from the Juxtaposition next to Nazir is only an Asmachta.