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1)
(a) According to the Tana Kama of the Beraisa, one is not permitted to render the Sh'tei ha'Lechem or the Lachmei Todah Chametz, using apples - because it is not proper Chametz.
(b) Rebbi Chanina ben Gamliel (according to Rav Kahana, Rebbi Chanina ben T'radyon) - permits it.
(c) When the Mishnah in Terumos rules 'Tapu'ach she'Risko ve'Nasno be'Soch ha'Isah ve'Chimtzah, Harei Zu Asurah' - it is forbidding to Zarim, a Chulin dough which was made Chametz using apples of Terumah.
(d) We reconcile this Mishnah with the Tana Kama of the Beraisa - since, even if apples do not render a dough real Chametz, they do render it Chametz Nukshah (which is sufficient to render the dough forbidden to Zarim).

2)
(a) Rebbi Ila maintains that the most difficult Minchah from which to take Kemitzah from is the Minchas Chotei - because it is dry and a lot of the flour drops from the Kohen's fist as he smoothens the flour that protrudes from the fist containing the Kometz.
(b) Rav Yitzchak bar Avdimi - disagrees, since the Kohen is permitted to add water to the Kometz.
(c) Initially, we explain the basis of their Machlokes as - whether we go after the Kometz as it is at the time of measuring (Rav Yitzchak bar Avdimi), or whether we reckon it as if it was flour, in which case the Kohen is forbidden to add water, in case he makes the dough too thick, making the Chometz Chaser, or too thin, making it Yeser (similar to what we explained in our Mishnah).
(d) We conclude that both opinions go after the way the flour is now, and the basis of their Machlokes lies in the Pasuk "ve'Chol Minchah Belulah va'Shemen va'Chareivah". The latter pertains to a Minchas Chotei, which contained no oil. Rebbi Ila however, takes it literally, forbidding even water, whereas Rav Yitzchak bar Avdimi confines the Pasuk to oil, since that is what most Menachos contain, but not to water.

3)
(a) When the Mishnah in Uktzin refers to ...
1. ... 'Basar ha'Eigel she'Nispach' - it is referring to the flesh of a calf that was initially, less than a k'Beitzah (the Shi'ur to be Metamei Tum'as Ochlin), but then expanded to obtain the Shi'ur.
2. ... 'u'Basar Zekeinah she'Nisma'ech' - it is referring to the flesh of an old cow that initially had a Shi'ur k'Beitzah, but then contracted to less.
(b) The Tana concludes 'Mishta'arin li'Kemos she'Hein, which Rav, Rebbi Chiya and Rebbi Yochanan interpret to mean 'Mishta'arin K'mos she'Hein', meaning - that one reckons them as they are now (and not as they were).
(c) Whereas Shmuel, Rebbi Shimon bar Rebbi and Resh Lakish explain - that we reckon them as they originally were ('Mishta'arin li'Kemos she'Hayu').

4)
(a) The Beraisa rules that if the flesh of a calf that did not have a Shi'ur of a k'Beitzah, but which subsequently expanded to a k'Beitzah, it is Tahor retroactively, but Tamei from now on - a proof that we assess the flesh as it is now (like the opinion of Rebbi Yochanan).
(b) According to Resh Lakish - this Beraisa speaks mi'de'Rabbanan (since min ha'Torah, it remains Tahor from now on, too).
(c) The problem with this from the Seifa of the Beraisa 've'Chein be'Pigul ve'Chein be'Nosar' is - that this implies that someone who eats them is Chayav Kareis, which would make no sense if the Tana was talking about Pigul and Nosar mi'de'Rabbanan.
(d) We answer by amending the Seifa to 've'Chein be'Tum'as Pigul ve'Chein be'Tum'as Nosar' (which is mi'de'Rabbanan) - and the Tana is speaking, not about a Chiyuv Kareis, but about being Metamei the hands (as we learned in the Mishnah in Pesachim).
(e) And the Tana is coming to teach us - that the current Chumra extends even to Tum'as Pigul and Tum'as Nosar, which are only mi'de'Rabbanan to begin with.

5)
(a) Another Beraisa says that the flesh of an old animal that originally had a Shi'ur, but shrunk to less than the Shi'ur, is Tamei retroactively, but not from now on - a proof that we reckon the Shi'ur of meat as it is now, and according to how it was originally, posing once again a Kashya on Resh Lakish.
(b) Rabah therefore concludes that there is no Machlokes there where the animal originally had a Shi'ur but then contracted, or where it originally had no Shi'ur, but now has. The Halachah ...
1. ... in the former case is - that it is Tahor.
2. ... in the latter case is - that it is Tamei mi'de'Rabbanan.

6)
(a) And Rebbi Yochanan and Resh Lakish argue in a case - where the flesh was originally a k'Beitzah, but then contracted, before expanding again.
(b) And when the Tana, in the source Mishnah in Uktzin, refers to ...
1. ... 'Basar ha'Eigel she'Nispach', he is speaking about a case - where it had first contracted.
2. ... 'u'Basar Ziknah she'Nisma'ech is speaking about a case - where it subsequently expanded once more.
(c) The basis of their Machlokes is - whether 'Ein Dichuy be'Isurin' (Rebbi Yochanan), or 'Yesh Dichuy be'Isurin' (Resh Lakish).
(d) 'Yesh Dichuy be'Isurin' means - that since, at one stage, the Isur lacked the Shi'ur, it is as if it never had a Shi'ur, and cannot become Asur once more. Consequently, since the piece of flesh contracted, it can no longer be Metamei mi'd'Oraysa, even if it later regains its original Shi'ur.

7)
(a) The Shi'ur Tum'ah of food is a k'Beitzah, of ...
1. ... Meis and Neveilah - a k'Zayis.
2. ... Sheretz - a k'Adashah (the size of a lentil).
(b) According to the Mishnah in Taharos, if someone places ...
1. ... a k'Beitzah of food, a k'Zayis from a Meis or a Neveilah, or a k'Adashah from a Sheretz in the sun and they contract - they become Tahor.
2. ... a k'Zayis of Pigul, Nosar, Tamei or Cheilev in the sun and they contract - they are not subject to Malkos.
(c) The Tana then rules however, that if one someone subsequently placed them in the sun and they expanded again - the former become Tamei once more, and the latter become subject to Malkos.
(d) That proves conclusively - that 'Ein Dichuy be'Isurin'.

8)
(a) Te'einim are ripe figs - whereas G'rogros are dried figs that are considerably smaller (by as much as fifty per-cent).
(b) The Beraisa rules 'Tormin Te'einim al ha'Gerogros - 'be'Minyan' (by number [ten fresh figs per ninety dried ones]). 'Tormin' in this case refers to - taking Ma'aser and not Terumah.
(c) The reason for this ruling is because (bearing in mind that the Te'einim are larger than the G'rogros) if one gave according to the weight, one would be giving less than one in ten as far as numbers are concerned.

9)
(a) We try to prove from the Beraisa that the Tana holds 'li'K'mos she'Hayu' (a Kashya on Rebbi Yochanan [see Shitah Mekubetzes 2), because if he held 'Km's she'Hu' - then he would be giving more (in weight) than a tenth as Ma'aser, and we have learned in a Beraisa 'ha'Marbeh be'Ma'asros, Peirosav Mesukanim, u'Ma'asrosav Mekulkalim' (if someone gives more than a tenth as Ma'aser, his fruit is rectified, but the Ma'aser that he gave still needs rectification.
(b) We counter this however, from the Seifa of the Beraisa 'G'rogros al ha'Te'einim, be'Midah', because if we hold 'li'K'mos she'Hayu' (as we just suggested) - we will be faced with the same problem, seeing as the G'rogros originally weighed more, what is one tenth now, will have been more than one tenth originally.

10)
(a) So we try to establish the Beraisa by Terumah (as the Lashon implies). This alleviates the problem - because by Terumah, the Torah is not particular about the Shi'ur ('Afilu Chitah Achas Poteres Kol ha'K'ri'), so that one cannot give too much (nor too little [min ha'Torah]).
(b) And the Mishnah is then coming to teach us - that one should always give Terumah generously (according to the number in the Reisha, and according to the measure in the Seifa).
(c) We reject this explanation however, on the basis of the Beraisa, where Rebbi Elazar b'Rebbi Yossi cited his father, who used to take ten G'rogros from the Miktzo'a (the vessel in which they had been dried) on ninety Te'einim in the basket. The problem with that is - that if the Beraisa is talking about Terumah (and not Ma'aser), why did Rebbi Yossi give specifically one in ten.
(d) On the one hand, we now have a problem with establishing the Beraisa by Ma'aser, and on the other, we have a problem with establishing it by Terumah. We finally establish it - by Terumas Ma'aser.

11)
(a) And the author of the Beraisa is Aba Elazar ben Gomel, who Darshens the Pasuk "Ve'nechshav Lachem Terumaschem". When he says ...
1. ... 'bi'Shetei Terumos ha'Kasuv Medaber", he means - that the Torah is referring to Terumas Ma'aser, as well as to Terumah Gedolah (in fact, the Torah is comparing the former to the latter).
2. ... 'Terumas Ma'aser Niteles a. be'Omed'; b. be'Machshavah', he means - that it can be taken a. by assessment alone (without needing to measure it), and b. with Machshavah alone (as we have learned 'Nosen Einav be'Tzad Zeh, ve'Ochel be'Tzad Acher'), without even having separated it yet.
(b) These two constitute two of the three things that Aba Elazar ben Gomel learns with regard to Terumas Ma'aser from Terumah Gedolah. The third is - that one should separate it generously (one in forty, rather than one in sixty, or even fifty).
(c) We nevertheless try to prove from Rebbi Elazar b'Rebbi Yossi's testimony (regarding his father taking ten G'rogros from the Miktzo'a on ninety Te'einim in the basket - that we assess 'li'Kemos sha'Hayu'. Otherwise, he would have given less than a tenth (seeing as G'rogros are smaller than Te'einim.
(d) When Rav Dimi came from Eretz Yisrael, he cited Rebbi Elazar, who refutes the proof from there however, on the grounds that G'rogros are different than meat - inasmuch as they can be boiled and returned to their former size (whereas meat cannot.

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