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1)

(a) Our Mishnah rules - that ...

1. ... even a minority (i.e. a 'Kol-she'Hu') of the Kometz, the Isaron (of a Minchah), the Yayin or the Levonah is crucial to the Mitzvah.
2. ... the So'les and the Shemen, and the Kometz and the Levonah - are Me'akev each there.

(b) ... Every grain (or drop) of ...

1. ... the Kometz is crucial, because the Torah repeats "M'lo Kumtzo".
2. ... the Minchah is crucial, because the Torah writes "mi'Soltah" (with an extra 'Hey').
3. ... the wine and the oil of a Minchas Nesachim is crucial, because the Torah writes "Kachah" (both in connection with the wine and with the Minchas Nesachim).
4. ... the oil is crucial, because the Torah writes (in connection with the Minchas Nedavah) "u'mi'Shamnah" (with an extra 'Hey').

(c) And we learn from the Pesukim ...

1. ... "mi'Soltah u'mi'Shamnah" and "mi'Girsah (which also means 'the [ground] flour') u'mi'Shamnah" - that both the flour and the and the oil are crucial to the Minchah i.e. that one cannot bring one without the other).
2. ... "al Kol Levonasah" and "ve'es Kol ha'Levonah Asher al ha'Minchah" - that the same applies to the Minchah and the Levonah.

(a) Our Mishnah also rules that each of ...

1. ... the two goats of Yom Kipur, the two Kivsei Atzeres, the two Chalos (i.e. the Sh'tei ha'Lechem), the two rows of the Lechem ha'Panim and the two Bazichin of Levonah - is Me'akev the other - as is each of ...
2. ... the rows of Lechem ha'Panim and the Bazichin, the two species of the Nazir, the three species of the Parah and the four species of the Todah, of the Lulav and of the Metzora.

(b) The ...

1. ... two species of the Nazir comprise - Chalos and wafers.
2. ... three species of the Parah comprise - the cedar wood, the hyssop and the crimson thread.
3. ... four species of the Metzora - comprise the above three plus the two birds.
4. ... four species of the Todah comprise - the Chalos, wafers and boiled flour (all Matzos), and Chametz loaves.

(c) Finally, the Tana rules that each of the seven Hazayos between the poles (of the Aron), the seven Hazayos towards the Paroches and the Hazayos of the Mizbe'ach ha'Zahav - is Me'akev the Kaparah.

(d) This last ruling pertains - both to the Avodah on Yom Kipur and (with the exception of the seven Hazayos between the poles) to that of the Par He'elam Davar of the Tzibur and the Par Kohen Mashi'ach.

(a) We learn from the fact that the Torah writes ...

1. ... "Ve'haysah Zos Lachem *le'Chukas* Olam" - that the two goats of Yom Kipur are Me'akev each other.
2. ... "Kodesh *Yih'yu* la'Hashem" - that the two Kivsei Atzeres they are Me'akev each other as well, and from the Pasuk ...
3. ... there "So'les Tih'yenah" - that the Sh'tei ha'Lechem are too.

(b) We know that each of the two Sedarim is crucial, as is each of the two Bazichin, from the fact that the Torah writes in Emor "me'Ishei Hashem *Chok* Olam". And we know that they are also Me'akev each other - from the same source.

(c) We also know that the two species of the Nazir are crucial from "Kein Ya'aseh", and the three of the Parah, from "Chukah". And we learn from the Pasuk (with regard to the former) "al Zevach Todas *Shelamav*" (comparing the Korban Nazir to the Todah [and vice-versa]) - that each of the four species of the Todah is crucial too.

(d) And from the Pasuk ...

1. ... "Zos *Tih'yeh* Toras ha'Metzora" we learn - that the four species of the Metzora are Me'akev each other.
2. ... "u'Lekachtem Lachem" - that we require 'Lekichah Tamah' (i.e. that each of the four species is crucial to the Mitzvah).

(a) When Rav Chanan bar Rava says that as long as one has the four species of the Lulav, they are not Me'akev each other, he means - that they do not need to be tied together (see also Tosfos DH 'Lo Shanu' and DH 'u'Lekachtem').

(b) The Beraisa rules that - the two species of the Lulav which produce fruit (i.e. the Lulav and the Esrog), and the two which do not (the Hadas and the Aravah) are Me'akev each other, and that one has not fulfilled the Mitzvah unless one binds them together.

(c) Similarly, he says, based on the Pasuk "ha'Boneh ba'Shamayim Ma'alosav, va'Agudaso al Eretz Yesadah" - that, by the same token, Yisrael do not achieve atonement on their fast-days, unless they are all bound together in one group (the Tzadikim, 'who produce fruit', together with the Resha'im, who do not).

(d) We reconcile the Beraisa's initial ruling with Rav Chanan bar Rava, who just said that the four species of the Lulav do not need to be bound - by citing a Beraisa, where Tana'im argue over this matter.

(a) The Tana who holds that the four species of the Lulav require binding is - Rebbi Yehudah ...

(b) ... and he learns it from "Agudas Eizov" - with a 'Gezeirah-Shavah' "Kichah" "Kichah".

(c) The Rabbanan do not learn this 'Gezeirah-Shavah'. The problem with the Beraisa 'Lulav Mitzvah le'Agdo, ve'Im Lo Agdo, Kasher' is - that 'Mah Nafshach', according to Rebbi Yehudah, why will the Lulav be Kasher even Bedieved, if it is not bound? And according to the Rabbanan, why is it a Mitzvah to bind it?

(d) We nevertheless establish the Beraisa like the Chachamim - and the Tana is referring to the Mitzvah of 'Zeh Keili Ve'anveihu", to beautify a Mitzvah (i.e. 'Hidur Mitzvah').

(a) We learn that the seven Haza'os as well as the various sets of Haza'os of the Par of the Kohen Gadol on Yom Kipur are Me'akev each other - from 'Chukah'.

(b) The problem with the Pasuk "Ve'asah le'Par (He'elam Davar shel Tzibur) Ka'asher Asah le'Par ha'Chatas (shel Kohen Mashi'ach)" is - that everything that is mentioned by the one is mentioned by the other, so what is the point of comparing them?

(c) Nevertheless, the Torah writes it - to teach us that each and every Haza'ah is crucial to the Avodah (nd the same applies to all Matnos Sheva, such as that of the Parah Adumah and the Haza'os of a Metzora).

(d) And we learn from ...

1. ... the word "ha'Chatas" we learn - that the same applies to the Se'eirei Avodas-Kochavim, which also sprinkled towards the Paroches.
2. ... the continuation of the Pasuk "Kein Ya'aseh" - that even the four Matanos on the Mizbe'ach ha'Zahav are Me'akev too (even thought similar Matanos on the Mizbe'ach ha'Chitzon are not Me'akev.

(e) From the second "la'Par" ("ve'Ka'asher Asah le'Par ha'Chatas") we include the Haza'os of the Par shel Yom ha'Kipurim in the Din of Ikuv. We need a special Pasuk for this, despite the fact that the Torah has already written "Chukah", to teach us - that the Shirayim must be poured on to the Yesod of the Mizbe'ach ha'Chitzon.

7)

(a) The Beraisa invalidates the Haza'os of the Parah Adumah (on the Har ha'Zeisim), those she'bi'Fenim and those of a Metzora (by the Sha'ar Nikanor), if they are performed she'Lo li'Shemah. The former is Pasul - because the Torah refers to it as a "Chatas".

(b) The Haza'os 'she'bi'Fenim' incorporates - those of Yom Kipur, of the Kohen Mashi'ach, the Par He'elam Davar and the Se'irei Avodas-Kochavim.

(c) The Tana invalidates the Haza'os of the Parah Adumah that were not 'Mechuvanos' (performed towards the Heichal) - because the Torah writes "el Nochach Ohel Mo'ed" and "Chukah", but validates all the others.

(d) The problem with this is - that in another Beraisa - the Tana validates 'she'Lo Mechuvanos' of the Parah Adumah.

(a) And we establish this as a Machlokes Tana'im, as we shall see shortly. The Beraisa rules that Mechusrei Kaparah or Tevulei-Yom or other Temei'im, who entered the Azarah be'Tum'ah ...

1. ... be'Shogeg - are Chayav Chatas.
2. ... be'Meizid - are Chayav Kareis.

(b) The Pasuk "Mei Nidah Lo Zorak Alav" teaches us that a Tamei who did not Tovel is Chayav Kareis for entering the Azarah, and we learn from ...

1. ... "Od Tum'aso Bo" - that a T'vul-Yom is Chayav too (even though he has already Toveled).
2. ... "ve'Ish Asher Yitma ve'Lo Yischata" - that even a Mechusar Kipurim is Chayav (even though, he has Toveled and night has fallen too), because as long as he has not brought his Kaparah, he remains Tamei.

(c) If Tahor Zarim enter ...

1. ... 'Lifenim mi'Mechitzasan' (meaning beyond the first eleven Amos of the Azarah [see also Chitah Mekubetzes 6]) - they are Chayav Malkos.
2. ... 'el P'nei ha'Kapores' (in front of the lid of the Aron) - they are Chayav Misah.

(d) Rebbi Yehudah and the Rabbanan argue - over "mi'Beis la'Paroches" (the north-eastern or the south-eastern section of the Kodesh Kodshim, which is not in line with the Aron ha'Kodesh).

(a) The Torah writes "ve'al Yavo ve'Chol Eis el ha'Kodesh, mi'Beis la'Paroches, el P'nei ha'Kapores ... ve'Lo Yamus". The Rabbanan disagree with Rebbi Yehudah - because according to him, they claim, the Torah ought to have written "el ha'Kodesh" and "el P'nei ha'Kapores" and omitted "mi'Beis la'Paroches", which we would already know from a 'Kal va'Chomer' from Heichal.

(b) Rebbi Yehudah counters - that, had the Torah omitted "mi'Beis la'Paroches", we would have thought that Kodesh really means 'mi'Beis la'Paroches', but that for entering the Heichal, one is Patur altogether.

(c) The Rabbanan refute this theory however, based on the Pasuk "Ve'hivdilah ha'Paroches Lachem Bein ha'Kodesh u'Vein Kodesh ha'Kodashim" from which they extrapolate - that Kodesh refers to the Heichal, and not to the Kodesh Kodshim.

(d) Rebbi Yehudah on the other hand, disagrees with the Rabbanan, because, in his opinion, the Torah ought then to have omitted - "el P'nei ha'Kapores" (since, according to the Rabbanan, we would know this with a 'Kal va'Chomer' from "mi'Beis la'Paroches").

(a) The Rabbanan counter that - by learning from "el-P'nei ha'Kapores" that 'Derech Meshupash' is Patur, which means either that someone dug a tunnel on the north or the south side of the Kodesh Kodshim, gaining entry from the side, or even if he entered via the curtains on the north-eastern corner, but then proceeded to walk sideways towards the Aron without turning his face towards the Aron.

(b) The root of the word is - 'Meshubash' (crooked), bearing in mind that a 'Beis' and 'Pey' are sometimes interchangeable.

(c) The source for this D'rashah is a Beraisa. Rebbi Eliezer ben Ya'akov there learn from the Pasuk "el-P'nei ha'Kapores Keidmah" - that whenever the Torah writes "P'nei", it means facing the east.

(a) Rebbi Yehudah too, agrees with this D'rashah, only he now learns from the word "el" - that facing east when the Kohen Gadol sprinkles the blood of the Par and the Sa'ir, is crucial to the Avodah.

(b) The Rabbanan however - do not Darshen "el", in which case facing east is not crucial.

(c) This Machlokes reflects on the Pasuk (in connection with sprinkling the blood of the Parah) "Ve'hizah *el* Nochach P'nei Ohel Mo'ed", inasmuch as - there too, Rebbi Yehudah will hold that "*el* Nochach" is crucial, and that when the Kohen sprinkles the blood of the Parah, he must face the Heichal; whereas the Rabbanan maintain that it is not.

(d) We have proved from here - that the author of the Beraisa 'she'Lo Mechuvanos, Pesulos' is Rebbi Yehudah, whereas the author of the Beraisa 'she'Lo Mechuvanos Kesheiros' is the Rabbanan.

(a) The Torah requires the Kohen Gadol to sprinkle the blood of the Par and the Sa'ir "al-P'nei ha'Kapores" (towards the lid of the Aron). According to the Mishnah in Yoma, during the time of the second Beis Hamikdash, when there was no Aron ha'Kodesh, they achieved this - by sprinkling it towards the place where the Aron should have been (and where the Even Shesiyah now stood).

(b) Rav Yosef queries this however, on the grounds that - if "el-P'nei" is crucial (according to Rebbi Yehudah), then surely, "al-P'nei" is crucial, too, in which case they ought not to have sprinkled at all during that period.

(c) Rabah bar Ula answers, based on the Pasuk "Ve'chiper es Mikdash ha'Kodesh" - that the Mitzvah was to sprinkle the blood (not on the Aron, but) on the location of the Aron.

(a) Rava establishes both Beraisos ('she'Lo Mechuvanos, Pesulos' and 'she'Lo Mechuvanos, Kesheiros' according to the Rabbanan), and he establishes the Beraisa which says 'Pesulos' - when the Kohen faced north-south, instead of east-west, which is unacceptable, even according to them.

(b) And he explains that the Beraisa which rules 'Kesheiros' - is speaking when the Kohen faced east, but was not directly in line with the Heichal.