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1) [line 4] "MILEVAD OLAS HA'BOKER ASHER L'OLAS HA'TAMID, TA'ASU ES ELEH." - "Besides the burnt offering in the morning that is for the continual burnt offering, you shall offer these." (Bamidbar 28:23) - This verse refers to Korbenos Musaf that are offered "besides" the burnt offering of the morning (the Korban Tamid). It therefore shows that Temidim precede Musafim.

2) [line 9] "KA'ELEH TA'ASU LA'YOM SHIV'AS YAMIM..." - "Like these [Korbanos, listed in the previous verses (Bamidbar 28:19-22)] you shall do (offer) each day for seven days..." (ibid. 28:24) - Since the verse uses the word "ka'Eleh" - "like these," the Gemara proves that the Musafim should also follow the rules of the abovementioned Korbanos (ibid. 28:1-22), that is, with the more frequent (Tadir) ones being offered first. These verses list the daily Korban Tamid (ibid. 28:2-8), the Musaf for Shabbos (ibid. 28:9-10), the Musaf for Rosh Chodesh (ibid. 28:11-15) and the Musaf for Pesach (ibid. 19-22).

3) [line 12] ELEH L'SHIV'AS HA'YAMIM - these [Korbanos would be the only Korbenos Musaf offered] for the seven days [of Pesach, dividing the two bulls, one ram and seven sheep among the seven days]

4) [line 15] SHAVOS - equal

5) [line 18] D'HACH DI'SEDIRA TIKDOM (TADIR VESHE'EINO TADIR, TADIR KODEM)
(a) The rule "Tadir veshe'Eino Tadir, Tadir Kodem" means that when we have a choice of performing two actions, the one that is more frequent is the one that is performed first (all other factors being equal).
(b) Our Mishnah quotes as the source for this rule, the verse "Milevad Olas ha'Boker Asher *l'Olas ha'Tamid*, Ta'asu Es Eleh." - "Besides the burnt offering in the morning that is for the *continual* burnt offering, you shall offer these." (Bamidbar 28:23). This verse refers to Korbenos Musaf that are offered "besides," and after, the daily burnt offering of the morning (the Korban Tamid). It implies that *because* the Tamid is continual, it precedes the Musaf.
(c) Another illustration of this rule is when Rosh ha'Shanah falls on Shabbos. The Korban Tamid is offered first, followed by the Musaf of Shabbos. Next, the Musaf of Rosh Chodesh is offered, followed by the Musaf of Rosh ha'Shanah.

6) [line 21] MERATZEH - appeases. The Korban Chatas atones for those people who have repented after having transgressed one of the sins that are liable to the Kares punishment, who need a formidable appeasement to achieve atonement.

7) [line 22] KALIL LA'ISHIM - it was totally burned on the fires of the Mizbe'ach

8) [line 26] TE'UNIN LECHEM - they require [a supplementary offering of loaves of] bread [or Matzah]

9) [line 28] SEMICHAH
Semichah refers to the Mitzvah for a person to press his hands with all his might on the head of his animal sacrifice before it is slaughtered, as described in Vayikra (1:4).

10) [line 30] KEDUSHASO ME'RECHEM - (lit. its sanctity is from the womb) the Kedushah of Bechor rests on every first-born male bull, goat or sheep when it comes out of its mother's womb

11) [line 31] ZEVACH - a sacrifice that is slaughtered using a knife
12) [line 33] MINEI DAMIM - their blood is utilized in the sacrifice

13) [line 33] MINCHAS CHOTEI (KORBAN OLEH V'YORED B'DALEI DALUS)
(a) A person brings a Korban Oleh v'Yored to atone for sins in three specific cases: Shevu'as ha'Edus (see Background to Shevuos 30:1), Tum'as Mikdash v'Kodashav (see Background to Shevuos 2:2) and Shevu'as Bituy (see Background to Shevuos 2:1).
(b) What constitutes a Korban Oleh v'Yored varies based on the means of the penitent. If he is wealthy, he brings a female sheep or goat as a Chatas (Korban Ashir). If he cannot afford this, he brings two Torim or two Benei Yonah, one as an Olah and one as a Chatas (Korban Oleh v'Yored b'Dalus). If he cannot even afford the birds, he brings one tenth of an Eifah of fine flour as a Minchas Chatas (Korban Oleh v'Yored b'Dalei Dalus). (Vayikra 5:6-13)
(c) The Minchas Chatas is not mixed with oil, and Levonah (frankincense) is not sprinkled on top of it (Vayikra 5:11). When a non-Kohen brings a Minchas Chatas, a Kometz of the flour alone is burned on the Mizbe'ach and the Kohanim receive the Shirayim (the rest of the flour, which they must eat before the following sunrise -- RAMBAM Hilchos Ma'aseh ha'Korbanos 10:7).

14) [line 33] MINCHAS NEDAVAH
(a) The Torah records five types of Minchas Nedavah, voluntary flour offerings (Vayikra 2:1-13). They are: Minchas Soles, Minchas Chalos, Minchas Rekikin, Minchas Machavas and Minchas Marcheshes.
(b) All of these Menachos require one Log of olive oil and a Kometz (handful) of Levonah. The oil is used in the kneading and the baking of the flour. A Kometz (separating a handful of the Minchah separated in a process called Kemitzah - see Background to Zevachim 30:8) of the Minchah itself is burned on the Mizbe'ach, and the Sheyarei ha'Minchah (the remainder of the Minchah) are eaten by the Kohanim in the Azarah of the Beis ha'Mikdash by male Kohanim (since they have the status of Kodshei ha'Kodashim). The five types of Menachos differ as follows:

1. The MINCHAS SOLES is the only Minchah in which the Kometz is removed before the Minchah is baked (hence the Minchah is still in the state of Soles, fine flour, from which this Minchah receives its name). The oil and flour are mixed and Levonah is placed on one side of the mixture, and then the Kohen performs HAGASHAH, KEMITZAH and HAKTARAH. In Hagashah, the owner brings the Minchah to a Kohen who touches the southwest corner of the Mizbe'ach with the utensil that contains the Minchah. In Kemitzah, the Kohen removes a Kometz (handful) from the Minchah, puts it into another utensil and places the Kometz of Levonah upon it. In Haktarah, the Kohen walks up to the top of the Mizbe'ach, salts the Kometz and burns it on the bonfire. The Sheyarei ha'Minchah are eaten by the Kohanim (Vayikra 2:1).
2. The MINCHAS CHALOS is one type of Minchas Ma'afeh Tanur, the Menachos that are baked upon the floor of a metal oven without a pan. A dough of flour and oil is kneaded with lukewarm water (TOSFOS Menachos 47a DH Minchas, RAMBAM Hilchos Ma'aseh ha'Korbanos 12:21, CHAZON ISH Menachos 34:1). It is then divided into ten Chalos (which are not Chametz) and baked. Next, the Chalos are folded and broken into pieces (Pesisah). Levonah is added, and Hagashah, Kemitzah and Haktarah are performed, as above. The Sheyarei ha'Minchah are eaten by the Kohanim (Vayikra 2:4).
3. The MINCHAS REKIKIN is the other type of Michas Ma'afeh Tanur. It differs from the Minchas Chalos in that the Rekikin are smeared with oil after the baking, before the Pesisah. Otherwise, its preparation is exactly like the Minchas Chalos (Vayikra 2:4).
4. The MINCHAS MACHAVAS consists of ten Matzos baked in an oven on a pan called a Machavas, which has ten raised sections. The portions of dough lie on the elevated parts of the pan so that most of the olive oil drains off, causing the dough to bake into brittle Matzos. Levonah is added, Hagashah, Kemitzah and Haktarah are performed. The Sheyarei ha'Minchah are eaten by the Kohanim (Vayikra 2:5).
5. The MINCHAS MARCHESHES consists of ten Matzos baked in an oven in a pan called a Marcheshes, which has ten deep sections filled with olive oil. The portions of dough lie in the deep parts of the pan and are baked in the olive oil, causing the dough to bake into soft Matzos. Levonah is added, and Hagashah, Kemitzah and Haktarah are performed. The Sheyarei ha'Minchah are eaten by the Kohanim (Vayikra 2:7).

16) [line 1] D'TANU RABANAN [REBBI OMER] U'FAR... - (this is the Girsa of TORAS KOHANIM Parshas Vayikra)

17a) [line 11] MATANAH KAMAISA DI'MECHAPRAH TIKDOM - the first application [of blood of the Korban Chatas on one of the corners of the Mizbe'ach] should take precedence [over the limbs of the Korban Olah] because it is the one that achieves atonement (Daf 38a)
b) [line 12] V'HANACH LO [NIKDEMU] - but the other ones (the three other applications of blood of the Korban Chatas) should not [take precedence over the limbs of the Korban Olah]!

18) [line 12] CHATAS HA'LEVIYIM - the Korban Chatas brought in the Sinai desert to sanctify the Leviyim
(a) Until the sin of the golden calf (that occurred three months after the Exodus from Egypt), the Divine service was performed by the Bechoros (first born males). After the sin, HaSh-m chose the Leviyim, who did not sin, to replace the Bechoros as his servants (Bamidbar 8:16-19). HaSh-m commanded Moshe to initiate them into the Divine service with a Taharah process (ritual cleansing) consisting of sprinkling Mei Chatas (see Background to Avodah Zarah 46:19) upon them, shaving off all of their hair and immersing themselves and their clothes in a Mikvah (ibid. 8:7).
(b) In addition, when the Divine service was transferred to the Leviyim, two Korbanos were sacrificed on their behalf. The first was a bull as a Korban Chatas and the second was a bull as a Korban Olah, along with its Minchas Nesachim.
(c) Before the Korbanos were brought, Benei Yisrael performed Semichah upon the Leviyim, Aharon ha'Kohen performed Tenufah (waving in the air) upon them, and then the Leviyim performed Semichah upon their Korbanos (ibid. 8:8-12).

19) [line 14] B'MA'ARAVA - (lit. in the west) in Eretz Yisrael
20) [line 25] D'KA'ASI MI'KO'ACH KALIL - (lit. that comes from the power, strength of a [sacrifice that is burned] entirely) that originates from a Korban that is completely burned

21) [line 31] AVAL DAM ASHAM, LO - that is, the blood of the Asham is not cast on the Mizbe'ach before the blood of the Olah

22) [line 37] KITZVAH - a fixed amount [of money] (Ashamos were usually rams that cost two Sela'im, which were much more expensive that Chata'os. A Chatas could be a small sheep or goat that could cost as little as one Danka, which is one sixth of a Dinar, or one forty-eighth of the price of an Asham.)

23) [line 37] RIBUY D'MIZBE'ACH ADIF - the Korban that has the more applications of blood for the Mizbe'ach is the preferable Korban (that takes precedence)

24) [line 39] YESHNAN B'TZIBUR KIV'YACHID - it is offered by the public as well as by individuals

25) [line 41] 4 MINEI LECHEM - four types of loaves (KORBAN TODAH)
(a) The Todah (thanksgiving offering) is a form of Shelamim that is eaten for only one day and one night (Vayikra 7:15). Korbenos Shelamim that are offered by an individual may be brought from male or female sheep, cows or goats. They are Kodshim Kalim, and may therefore be slaughtered in the entire Azarah (and not only in its northern part). Before its slaughter, the owner presses his hands on the head of the animal (Semichah). The blood of the Shelamim is cast on the northeastern and southwestern corners of the Mizbe'ach (Shenayim she'Hen Arba). Nesachim (a meal offering consisting of flour and oil and a wine libation) are brought as part of the Korban (Bamidbar 15:3-12). The meal offering is completely burned on the Mizbe'ach and the wine is poured into one of the Sefalim (the silver libation pipes located at the top of the southwest corner of the Mizbe'ach) (RAMBAM and RA'AVAD Hilchos Ma'aseh ha'Korbanos 2:1). The amount of flour, oil and wine needed depends upon the animal offered, as specified in Bamidbar ibid.
(b) An animal that was sacrificed as a Todah was brought together with forty loaves of bread, ten each of the following:

1. Chalos Matzos - Matzos mixed with oil;
2. Rekikin - flat Matzos saturated with oil;
3. Soles Murbeches - Matzos made of boiled flour mixed with oil;
4. Loaves of leavened bread. (Vayikra 7:12-13)

26) [line 42] DAMIM ACHERIM - (lit. other types of blood) the Nazir is required to offer a Korban Chatas and a Korban Olah as well as the Eil Nazir, which is his Korban Shelamim (Bamidbar 6:14)

27) [line 44] MITZVOS YESEIROS - the extra Mitzvos [of casting the blood on the two corners of the Mizbe'ach ("Shenayim she'Hen Arba"), Semichah, Nesachim and Tenufas Chazeh v'Shok] (see above, entry #24:a)

28) [line 45] MEKADESH LEFANAV UL'ACHARAV - it (the law of Ma'aser Behemah) can consecrate [animals] before and after [the Ma'aser Behemah (tenth) animal] (MA'ASER BEHEMAH)
(a) Every year, a person must collect all of the Kosher animals that were born during that year into a corral. As they leave the corral through a narrow opening, one by one, the owner counts them and marks every tenth one as Ma'aser Behemah. The Mitzvah of Ma'aser Behemah is stated in Vayikra (27:32), "v'Chol Ma'asar Bakar va'Tzon, Kol Asher Ya'avor Tachas ha'Shavet, ha'Asiri Yiheyeh Kodesh la'Sh-m." - "And all of the herds and flocks shall be tithed as they are counted under the rod, every tenth one being consecrated to HaSh-m."
(b) Ma'aser Behemah is eaten by its owner. If it has no Mum (blemish or defect), it is offered as a Korban on the Mizbe'ach and eaten by its owner in Yerushalayim. If it has a Mum, the owner may slaughter and eat it anywhere.
(c) If one designated the tenth animal as Ma'aser Behemah, no other animal can become Ma'aser Behemah afterwards. However, if two animals exited the corral at the same time and the owner designated both as Ma'aser (the tenth animal), both become Kodesh (one is considered Ma'aser Behemah, and the other must be brought as a Shelamim; see RASHI to Kidushin 51a DH v'Achad Asar). In addition, Ma'aser Behemah has the feature that it takes effect even in error. If the tenth animal was not called "tenth" but the animals that were next to the tenth animal were called "tenth," then they, too, become consecrated, according to all opinions. Beis Shamai cites a case where the owner called the ninth animal "tenth," the tenth, "ninth" and the eleventh, "tenth." The ninth animal is put out to pasture and may be eaten after it develops a Mum (blemish). The tenth animal is brought as the Korban Ma'aser Behemah. The eleventh animal is brought as a Korban Shelamim (Mishnah Bechoros 60a).

29) [line 47] EIMUREI KODSHIM KALIM - the fats and other parts of the Kodshim Kalim (EIMURIN)
The Eimurim are the fats and other parts of the Korban that are burned on the Mizbe'ach. They consist of: 1. the layer of fat covering the stomachs; 2. all other fat attached to the stomachs; 3. the two kidneys; 4. the fat on the kidneys; 5. The Yoseres, which is either the diaphragm (RASHI, RADAK) or a lobe of the liver (RAV HAI GA'ON) (Vayikra 3:3-4).

30) [line 47] SHE'YATZ'U - that went out [of the Azarah of the Beis ha'Mikdash]

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