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(a) (Mishnah): A minority of a Kometz is Me'akev the majority (i.e. if any is missing, it is Pasul);
(b) The same applies to an Isaron (of Soles), wine and oil.
(c) Soles and oil are Me'akev each other; Kometz and Levonah are Me'akev each other.
(d) (Gemara) Question: What is the source (that a minority of a each of these is Me'akev?)
(e) Answer: Regarding the Kometz, we learn from "Melo Kumtzo" - this is written twice;
1. We learn Soles from "Mi'Solt*ah*" - if it is missing any, it is Pasul;
2. Regarding wine it says "Kachah" (this always teaches Ikuv);
3. Regarding oil of Minchas Nesachim, it says "Kachah";
4. Regarding oil of Minchas Nedavah it says "Umi'Shamn*ah*".
5. We learn that Soles and oil are Me'akev each other from "Mi'Soltah Umi'Shamnah", and it also says "Mi'Girshah Umi'Shamnah" (and Geresh is Soles);
6. Kometz and Levonah are Me'akev each other, for it says "Al Kol Levonasah", and it is repeated "V'Es Kol ha'Levonah Asher Al ha'Minchah".
(f) (Mishnah): The following are Me'akev each other:
1. The two goats of Yom Kipur, the two Kivsei Atzeres, the two loaves of Shtei ha'Lechem, the two Sedarim (piles of six loaves of Lechem ha'Panim), the two Bazichim (spoons of Levonah on Lechem ha'Panim), the two kinds of bread brought by a Nazir, the four that accompany a Todah, the three species burned with Parah Adumah, the four species used for Taharas Metzora (when he brings birds), the four species (altogether) taken with the Lulav, the seven Haza'os of (blood of) Parah Adumah, the seven Matanos Bein ha'Badim (between the staves of the Aron, on Yom Kipur), the seven towards the Paroches (of inner Chata'os) and the seven on the inner Mizbe'ach (on Yom Kipur). (Rashash - another Mishnah teaches that all *eight* Bein ha'Badim and towards the Paroches are Me'akev - our Tana merely appends the Matanos to our Mishnah, and teaches about the seven (downward) sprinklings to parallel the other sevens.)
(g) The Sedarim and Bazichim are Me'akev each other.
(a) (Gemara): Regarding the following (it is Me'akev because) it says "Chukah" - the two goats, the two Sedarim, the Bazichim, the Sedarim and Bazichim (are Me'akev each other), the three species burned with Parah Adumah; (b) Regarding the two Kivsei Atzeres and the two loaves of Shtei ha'Lechem it says 'Havayah';
(c) Regarding the two breads of a Nazir it says "Ken Ya'aseh";
(d) Todah is Hukash to Nazir - it was taught, "Al Zevach Todas *Shelamav*" includes Shalmei Nazir (its breads are made from the same amounts of Soles and oil as Lachmei Todah)
(e) The four species of Taharas Metzora - "Zos Tihyeh Toras ha'Metzora";
(f) The four species with the Lulav - "Ul'Kach*tem*", the Kichah (taking) must be Tamah (complete);
1. (Rav Chanan bar Rava): This is only if all four species are not in front of him - if they are in front of, him, he need not tie them together (Rashi, R. Tam; Baha''g - he need not take them at the same time).
2. Question (Beraisa): Two of the four species (Esrog and Lulav) come from trees that bear fruit, two do not; each pair requires the other, to fulfill the Mitzvah they must be bound together (except for the Esrog);
i. Similarly, Hash-m does not accept the prayers of Yisrael until they are united - "Ha'Boneh va'Shamayim Ma'alosav va'Agudaso Al Eretz Yesadah".
3. Answer: Tana'im argue about this:
i. (Beraisa): One fulfills the Mitzvah of the four species even if they are not tied together;
ii. R. Yehudah says, if they are tied together they are Kesherim, if not they are Pesulim.
iii. Question: What is R. Yehudah's reason?
iv. Answer: He learns from a Gezerah Shavah "Kichah-Kichah" from the bundle of Ezov (used to put the blood of Pesach Mitzrayim on the doorposts), which must be tied together.
v. Chachamim do not learn the Gezerah Shavah for this.
4. Question: Who is the Tana of the following?
i. (Beraisa): It is a Mitzvah to tie the Lulav (with the Hadasim and Aravos); if it is not tied, it is Kosher.
ii. This is not like R. Yehudah - he is Posel b'Diavad!
iii. This is not like Chachamim - they hold that there is no Mitzvah!
5. Answer: It is like Chachamim, it is a Mitzvah to tie it to beautify the Mitzvah - "Zeh Keli v'Anvehu".
(g) It says 'Chukah' regarding the Haza'os of Parah Adumah, and also regarding the Matanos on Yom Kipur Bein ha'Badim, towards the Paroches and on the inner Mizbe'ach;
(h) The following teaches about those of Par Kohen Mashu'ach, Par He'elam Davar and Se'ir Avodah Zarah:
1. (Beraisa): "V'Asa (he will offer Par He'elam Davar) ka'Asher Asa (like Par Kohen Mashu'ach)" - this is a second command to perform all the Matanos, therefore, all are Me'akev, if one was omitted the Par did not atone at all.

2. ("Ka'Asher Asa *la'Par*" includes Par Mashu'ach, "Ha'Chatas" includes Se'ir Avodah Zarah.)
(a) (Beraisa #1): If the seven Haza'os of Parah Adumah were Lo Lishmah or not facing the Ohel Mo'ed, they are Pesulos;
1. If Haza'os inside (the Heichal) or of a Metzora were Lo Lishmah, they are Pesulos; if they were (Lishmah but) not facing the Ohel Mo'ed, they are Kesheros.
(b) Contradiction (Beraisa #2): If the Haza'os of Parah Adumah were Lo Lishmah, they are Pesulos; if they were not facing the Ohel Mo'ed, they are Kesheros.
(c) Answer #1 (Rav Chisda): Beraisa #1 is like R. Yehudah, Beraisa #2 is Chachamim. (This will be explained below.)
1. (Beraisa): If a Mechushar Kipurim entered the Azarah b'Shogeg, he is Chayav Chatas; if he was Mezid, he is Chayav Kares, all the more so a Tevul Yom or one who is (fully) Tamei;
2. If a Tahor entered past where he is allowed (Rashi - past the 11 Amos of Ezras Yisrael, or; Shitah Mekubetzes - i.e. if he entered) anywhere in the Heichal, he receives 40 lashes; if he entered mi'Beis la'Paroches (the Kodesh ha'Kodoshim), he is Chayav Misah bi'Dei Shamayim;
3. R. Yehudah says, if he entered anywhere in the Heichal or mi'Beis la'Paroches, he receives 40 lashes; if he came El Penei ha'Kapores (in front of the Aron), he is Chayav Misah (bi'Dei Shamayim).
4. Question: What do they argue about?
5. Answer: They argue about "Aharon...v'Al Yavo b'Chol Es El ha'Kodesh mi'Beis la'Paroches El Penei ha'Kapores...v'Lo Yamus":
i. Chachamim explain, going (unnecessarily) El ha'Kodesh is punishable by V'Al Yavo (a Lav, lashes), going Mi'Beis la'Paroches or El Penei ha'Kapores is punishable by V'Lo Yamus;
ii. R. Yehudah explains, going El ha'Kodesh or mi'Beis la'Paroches is punishable by V'Al Yavo, going El Penei ha'Kapores is punishable by V'Lo Yamus.
6. Question: Why don't Chachamim expound like R. Yehudah?
7. Answer: If so, the Torah could have omitted mi'Beis la'Paroches (Rashi - one who goes mi'Beis la'Paroches passes through the Heichal, he is lashed for entering the Heichal; Shitah Mekubetzes [7] - mi'Beis la'Paroches is more Kodesh than the Heichal, all the more a Lav forbids it);
i. Surely, "Mi'Beis la'Paroches" teaches that one is Chayav Misah for going there.
8. R. Yehudah disagrees - had it said only El ha'Kodesh and El Penei ha'Kapores, one might have thought that 'Kodesh' refers to mi'Beis la'Paroches, but one who enters the Heichal is exempt.
9. Chachamim argue, for we know that the entire Heichal is called Kodesh - "V'Hivdilah ha'Paroches Lachem Bein ha'Kodesh u'Vein Kodesh ha'Kodoshim".
10. Question: Why doesn't R. Yehudah expound like Chachamim?
11. Answer: If so, the Torah could have omitted El Penei ha'Kapores (Rashi - to get to El Penei ha'Kapores, one first comes mi'Beis la'Paroches (and is already Chayav Misah); Shitah - El Penei ha'Kapores is more Kodesh than mi'Beis la'Paroches, all the more one is Chayav Misah for this.)
i. Surely, "El Penei ha'Kapores" teaches that one is Chayav Misah for going *there*, but not for (just) mi'Beis la'Paroches.
12. Chachamim say, El Penei ha'Kapores is needed only to exempt for entering abnormally, e.g. through a tunnel or not facing the Kodesh ha'Kodoshim.
13. (Beraisa - d'vei R. Eliezer ben Yakov): "El Penei ha'Kapores Kedmah" - this is a Binyan Av (precedent), it teaches that 'Penei' always refers to the east.
14. R. Yehudah says, we could have learned this from 'Penei', 'El' (is extra, it) limits the Chiyuv Misah to El Penei ha'Kapores.
15. Chachamim do not expound "El" to limit.
16. Culmination of answer: Just like R. Yehudah says here that 'El' limits, he also says so regarding Haza'os of Parah Adumah ("V'Hizah El Nochach"); just like Chachamim say that 'El' does not limit, they say the same regarding Haza'os Parah Adumah.
(d) Objection (Rav Yosef): If R. Yehudah says that 'El' limits, he should also say that "Al (ha'Kapores)" limits, the Haza'os are only when there is an (Aron with a) Kapores, but not in Bayis Sheni (for Yoshiyah hid it towards the end of Bayis Rishon, but we know that R. Yehudah does not say this!)
(e) Answer (Rabah bar Ula): There is different - it says "V'Chiper Es Mikdash ha'Kodesh", he sprinkles on the Kodesh place (even if the Aron is not there.)