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1) [line 1] HEVEI RIBUY ACHAR RIBUY, VE'IN RIBUY ACHAR RIBUY ELA L'MA'ET - it is a case of "Ribuy Achar Ribuy," one extension of the law that occurs in the Torah after an identical extension of the law, which limits the scope of the law [rather than extending it]
(a) This rule of Biblical interpretation interprets the occurrence of two Ribuyim (inclusive words) regarding an identical point as *limiting* the Halachah they describe, rather than extending it to include more items or to apply in more cases. That is, even though a single Ribuy extends the Halachah to additional items or cases to which one would have thought that the Halachah does not apply, a double Ribuy teaches *not* to extend the Halachah but rather to interpret it in a limited sense.
(b) The logical derivation for this rule is as follows: If we already know to apply the Halachah under discussion to a particular item (or case), it would not be necessary for the Torah to again teach that the Halachah applies even to that item. It is therefore evident from the second Ribuy that the first one was *not* meant to include that item. Likewise, the second Ribuy cannot have been written to include that item, for the Torah could have taught to include that item by writing *only* the first Ribuy. It must therefore be concluded that the double Ribuy means to teach that we should *not* learn to include the item in the Halachah under discussion. (This rule is closely related to the rule of "Shenei Chesuvim ha'Ba'im k'Echad Ein Melamdim" -- see Background to Zevachim 24:1 and to the converse rule of "Ein Mi'ut Achar Mi'ut Ela l'Rabos -- see Yoma 43a and Background to Shevuos 7:8)
(c) In all cases of Ribuy Achar Ribuy, the obvious question is why did the Torah write even a single Ribuy? Let the Torah write neither Ribuy and we would know by ourselves not to include the item, since there is no Ribuy to include it! (Obviously the item would not be included without a Ribuy, since we originally found it necessary to interpret the first Ribuy as including that item.) TOSFOS (to Yoma 60a DH Trei) asks a similar question (with regard to Mi'ut Achar Mi'ut) and answers that perhaps we would have included that item (or excluded it, in the case of Mi'ut Achar Mi'ut) without the first Ribuy, through a Binyan Av (see Background to Menachos 56:1) or a Kal va'Chomer (see Background to Avodah Zarah 46:22). The first Ribuy was not really necessary, but we would have justified the Ribuy as "Milsa d'Asya b'Kal va'Chomer Tarach v'Chasav Lah Kra" - "the Torah troubles itself to write out explicitly that which can be learned from a Kal va'Chomer" (see Kidushin 4a, Chulin 118b). The second Ribuy teaches not only to ignore the first Ribuy, but also to ignore the Binyan Av or Kal va'Chomer as well.
(d) In other instances (such as the one recorded in our Sugya) it is more obvious why a double Ribuy is necessary. The second Ribuy does not entirely negate the first, but rather it limits the first Ribuy (or it limits itself) to a narrower interpretation.

2) [line 10] HAGASHAH
When Korbenos Minchah (flour offering) are offered (many of them but not all of them, as our Mishnah specifies), the owner brings the Minchah to a Kohen who touches the southwest corner of the Mizbe'ach ha'Chitzon with the utensil that contains the Minchah.

3) [line 11] TENUFAH
Waving portions of certain Korbanos and meal-offerings is called Tenufah; the Kohen, together with the owner of the Korban (when it is not a Korban Tzibur), waves them in all four directions and up and down (RASHI to Menachos 62a DH Molich. TOSFOS to Sukah 37b DH Kedei, ponders whether all Tenufos were done in this fashion, or whether some Tenufos only required lifting and lowering).

4) [line 23] "V'HEVEISA... ASHER YE'ASEH ME'ELEH LA'SH-M, V'HIKRIVAH EL HA'KOHEN V'HIGISHAH [EL HA'MIZBE'ACH]" - "And you shall bring [the Minchah offering] that shall be made from these to HaSh-m, and you shall give it to the Kohen, and he shall bring it close (lit. offer it) [to the Mizbe'ach.]" (Vayikra 2:8)

5) [last line] "[V'HEVEISA ES HA']MINCHAH [ASHER YE'ASEH...]" - see previous entry

6) [last line] NE'EMAR (HACHA MINCHAS CHOVAH) ["HAVEI" B'MINCHAS CHOVAH]... - it states the word "v'Hevi'ah," "and he shall bring it," in the verse that deals with the Minchas Chotei (Vayikra 5:12)

7) [line 1] MINCHAS CHOVAH (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 Chotei (Korban Oleh v'Yored b'Dalei Dalus). (Vayikra 5:6-13)
(c) The Minchas Chotei 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 Chotei, 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).
(d) Our Gemara intends to prove that the Minchas Chotei requires Hagashah from the words "*Es* ha'Minchah."

8) [line 1] V'NE'EMAR (HACHA MINCHAS NEDAVAH) ["HAVEI" B'MINCHAS NEDAVAH] - and it states the word "v'Heveisa," "and you shall bring," in the verse that deals with the Minchas Nedavah (Vayikra 2:8)

9) [line 1] MINCHAS NEDAVAH - voluntary Menachos (see Background to Menachos 59:1-2)

10) [line 6] V'CHAZAR HA'DIN, LO RE'I ZEH KI'RE'I ZEH... HA'TZAD HA'SHAVEH SHE'BAHEN... - and the argument returns, this subject is not exactly like that subject... the common denominator between them... (TZAD HA'SHAVEH)
(a) The method of learning that is being used by our Gemara is called a comparison, or "Meh Matzinu" - "What we have found [in one subject, applies to another subject, also.]" Among the rules of this method is the rule of a "Pirchah" (a question), where even a slight difference between the subjects causes the comparison to collapse, and no connection may be made.
(b) If a Pirchah is asked, the Gemara will bring a "Yochi'ach" or "Tochi'ach" (fem.) (a proof), where another subject, which fulfills the requirements of the Pirchah, is used to rebuild the comparison. A second Pirchah usually follows, where the Yochi'ach subject is brought into question. Then the original subject becomes the Yochi'ach.
(c) The conclusion is "v'Chazar ha'Din" - "the argument goes back and forth," "Lo Re'i Zeh k'Re'i Zeh" - "this subject is not exactly like that subject and vice versa," but the "Tzad ha'Shaveh" - "common denominator" may be used to connect the Halachos of the two subjects, and we may learn a new Halachah from them. The common denominator may also be brought into question, which inhibits learning the new Halachah from the two subjects.

11a) [line 10] SHE'KEN HUCHSHERU LAVO B'ASHIR KIV'ANI - since they (Minchas Nedavah and Minchas Sotah) are fit to be brought by a wealthy person as well as a poor person
b) [line 11] TOMAR B'MINCHAS CHOTEI, SHE'LO HUCHSHERAH LAVO B'ASHIR KIV'ANI - would you say that same in the case of a Minchas Chotei, which is not fit to be brought by a wealthy person as well as a poor person (rather, it is *only* brought by a poor person)

12a) [line 27] LO HUCHSHERU LAVO KEMACH - since they (the Minchas Chotei and the Minchas ha'Omer) are not fit to be brought as "Kemach," ordinary flour (rather they are brought from Soles, fine flour)
b) [line 28] TOMAR MINCHAS SOTAH SHE'HUCHSHERAH LAVO KEMACH - would you say that same in the case of a Minchas Sotah, which is not fit to be brought from Kemach

13) [line 32] MI'DINA KA ASYA - it is learned from a "Meh Matzinu" argument (see above, entry #10), as the Gemara presently shows

14) [line 37] SHE'KEN BA'AH L'VARER AVON (D'MAZKERES AVON HI) - since it comes to clarify [the matter as to whether] a sin [took place] (see Background to Menachos 59:10) (the SHITAH MEKUBETZES #3 removes the words d'Mazkeres Avon Hi, which are superfluous)

15) [line 42] U'MAI PARACHT? - And what did you ask? i.e. what Pirchah can you ask with regard to the Tzad ha'Shaveh?

16) [last line] V'HA APIKTEI? - But have you not used it [to teach that Minchas Sotah requires Hagashah -- line 15]?

17) [last line] V'HIKRIV V'HIKRIVAH - Rebbi Shimon teaches two Halachos from this word. One from the fact that it was written at all, and one from the fact that it could have been written "v'Hikriv" instead of "v'Hikrivah"

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