TO WHICH ITEMS DOES HA'ALAS CHUTZ APPLY?
(Mishnah): One is liable for Ha'alas Chutz of Kosher Kodshim, and Pasul Kodshim that had Sha'as ha'Kosher.
One is liable for Ha'alah of a k'Zayis (combined) of limbs and Eimurim of an Olah.
(Gemara - Beraisa) Question: "Asher Ya'aleh Olah (Oh Zevach - Shitah Mekubetzes deletes these words from the text)" teaches only that one is liable for (Ha'alas Chutz of) Olah;
What is the source for Eimurim of Asham, Chatas, Kodshei Kodoshim and Kodshim Kalim?
Answer: We learn from "Zevach".
Question: What is the source to Mechayev for Kometz, Levonah, Ketores, Minchas Kohanim, Minchas Chavitim, (or Nisuch of) three Lugim of wine or water?
Answer: "V'El Pesach Ohel Mo'ed Lo Yevi'enu" obligates for offering outside anything that should be brought to Pesach Ohel Mo'ed.
Question: What is the source to include Kodshim that became Pasul through any of the following:
Linah, Yotzei, Tum'ah, intent Chutz li'Zmano or Chutz li'Mkomo, Kabalah or Zerikah of Pesulim, Zerikah above (Chut ha'Sikra) instead of below or vice-versa, or on the inner Mizbe'ach instead of the outer Mizbe'ach or vice-versa, Pesach or Chatas offered Lo Lishmah?
Answer: "Lo Yevi'enu" teaches that anything Kosher for Pesach Ohel Mo'ed (at the least, Im Alah Lo Yered), one is liable for it outside.
(Mishnah): One is liable for Ha'alah of a k'Zayis... (of limbs and Eimurim of an Olah).
Inference: One is exempt for Ha'alah of limbs and Eimurim of Shelamim.
Our Mishnah implicitly teaches the Chidush of a Beraisa;
(Beraisa): Limbs and Eimurim of an Olah join to a k'Zayis to be liable for Ha'alas Chutz, and for Pigul, Nosar and Tamei.
Question: We understand why limbs and Eimurim of Shelamim do not join for Ha'alas Chutz (limbs are not Kosher for Haktarah in the Mikdash), but why don't they join for Pigul, Nosar and Tamei?
(Mishnah): All Pigulim join. All Nosarim join.
The Beraisa implies that Pigulim of Shelamim do not join, and Nosarim of Shelamim do not join!
Answer #1 (regarding Pigul): All Pigulim join to be liable for eating (a k'Zayis). Limbs and Eimurim of Shelamim do not join regarding intent Chutz li'Zmano (since eating and Haktarah do not join).
Answer #2: (We distinguish between 'standard' Nosar (meat that was permitted, but not eaten or offered in the allotted time) and Nosar 'remnants' that were never permitted, i.e. remaining limbs and Eimurim of Shelamim that was partially lost before Zerikah.) All standard Nosar joins (to be liable for eating a k'Zayis). Nosar remnants do not join (if there is not a k'Zayis of Emurim or meat left, we do not Zerikah, even if together there is a k'Zayis. Tosfos - this answer also resolves Pigul. Limbs and Eimurim do not join to allow Zerikah, therefore, Pigul cannot apply.)
This is like R. Yehoshua;
(Beraisa - R. Yehoshua): If a k'Zayis of meat or a k'Zayis of Chelev of a Korban remains, we may throw the blood;
If half a k'Zayis of meat and half a k'Zayis of Chelev remain, we may not throw the blood;
The exception is Olah. Since all is Huktar, even in this case we do Zerikah.
Regarding a Minchah, even if it is totally intact we do not do Zerikah.
Question: There is no Zerikah in a Minchah!
Answer (Rav Papa): It means that (if a k'Zayis of meat or Chelev does not remain,) we may not do Zerikah for the sake of Minchas Nesachim, even all of the Minchah is intact.
(Mishnah): If one offered a k'Zayis of any of the following outside, he is liable:
A Kometz, Levonah, Ketores, the Minchah of a Kohen, Minchas Chavitim, or Minchas Nesachim;
R. Elazar exempts, unless he offered all of it. (This Tana is R. Elazar (ben Shamu'a). It is the same Tana cited in the Mishnah 110b (see Daf 42a), and there the Gemara calls him a Talmid of R. Akiva. Rashi cites 'R. Eliezer' (the Rebbi of R. Akiva); this is a printing mistake (Shitah Mekubetzes 12).)
If any of them was offered inside except for a k'Zayis, and the k'Zayis was offered outside, he is liable;
If any of them became Chaser (it was lost or burned) before Haktarah, and (part or all of) the rest was offered outside, he is exempt.
If one offered (outside) Kodshim with the Eimurim attached, he is liable.
(Gemara - Beraisa): If one is Maktir a k'Zayis outside, he is liable. If he is Maktir half a Pras (i.e. less than the required amount, even though it is more than a k'Zayis) inside, Patur (he is exempt.)
Assumption: The latter clause exempts a Zar for deficient Avodah in the Mikdash.
Question: Why is a Zar exempt? A k'Zayis is considered Haktarah!
Answer #1 (R. Zeira): No, the Seifa teaches that the Tzibur is Patur (from bringing another Korban, for it fulfilled its obligation).
Question (R. Zeira): This is unlike Rav, who taught that even R. Elazar agrees to the Seifa of the Beraisa;
R. Elazar exempts partial Haktarah (b'Chutz), for he holds that it is not considered Haktarah!
Answer #2 (Rabah): All agree that Haktarah of a k'Zayis of the Ketores burned (every morning and afternoon on the inner Mizbe'ach) in the Heichal is considered Haktarah (the Tzibur fulfills its obligation with this, and one is liable for a k'Zayis b'Chutz. In the Mikdash, each time we offer a Pras or Ketores, i.e. half a Maneh (about a quarter kilo) - Kerisus 6a, which we say with Parshas ha'Ketores in Korbanos. This Shi'ur is only mid'Rabanan.)
They argue about Haktarah of a k'Zayis of the Ketores burned Lifnim (in the Kodesh ha'Kodoshim on Yom Kipur). R. Elazar holds that the Shi'ur of a double handful is Me'akev, and Chachamim say that it is not.
Objection (Abaye): The Torah says "Chukah" concerning this! (All agree that it is Me'akev.)
Answer #3 (Abaye): True, all agree that Haktarah of a k'Zayis of 'outer' Ketores (of the Heichal) is considered Haktarah (to fulfill the Mitzvah, and to be liable for Ha'alas Chutz);
They argue about whether we learn Ha'alas Chutz of Ketores Panim from that of Chutz (the Heichal). Chachamim learn (that a k'Zayis is considered Haktarah), and R. Elazar does not. (He holds that only the Shi'ur for the Mitzvah (a double handful) is considered Haktarah.)
Objection (Rava): Chachamim do not learn outer Haktaros (of the outer Mizbe'ach) one from another! (The Shi'ur for Ha'alas Chutz of water is three Lugim. They do not learn from Chelev, for which the Shi'ur is a k'Zayis.) All the more so they do not learn Panim from the Heichal!
(Beraisa) Suggestion: Perhaps one is liable for Ha'alas Chutz of the following: less than a k'Zayis of a Kometz or Eimurim, or less than three Lugim of wine or water.
Rejection: "La'asos" - one is liable for a complete Shi'ur, but not for a partial Shi'ur.
One is exempt for a k'Zayis of wine or water (this is less than three Lugim, even though one is liable for this Shi'ur of Eimurim). This shows that Chachamim do not learn outer from outer.