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1)
(a) The problem with our Mishnah 'she'Ein Mechanchin ... Mizbe'ach ha'Olah Ela be'Tamid shel Shachar' is - that this statement does not go with anything that the Tana said previously.
(b) We therefore amend the previous statement 'Lo Hikrivu Keves ba'Boker, Lo Yakrivo bein ha'Arbayim' adding - 'Bameh Devarim Amurim, she'Lo Nischanech ha'Mizbe'ach, Aval Nischanech ha'Mizbe'ach, Yakrivo bein ha'Arbayim'.

2)
(a) The Beraisa learns the above from the Pasuk in Tetzaveh "es ha'Keves ha'Echad Ta'aseh ba'Boker, ve'es ha'Keves ha'Sheini Ta'aseh bein ha'Arbayim" - from which he Darshens 've'Lo Rishon bein ha'Arbayim'.
(b) The Tana knows that the Pasuk is talking specifically about the inauguration of the Mizbe'ach - because the previous Parshah ("ve'Zeh Asher Ta'aseh al ha'Mizbe'ach") specifically refers to that.
(c) And from the Pasuk in Pinchas "ve'es ha'Keves ha'Sheini Ta'aseh bein ha'Arbayim, ke'Minchas ha'Boker" (which is not preceded by 'es ha'Keves Echad Ta'aseh be'Boker) - the Tana learns - that once the Mizbe'ach has been inaugurated, even the Tamid shel bein ha'Arbayim may be the first Tamid of the day.
(d) As for the earlier Pasuk there "es ha'Keves Echad Ta'aseh ba'Boker, ve'es ha'Keves ha'Sheini Ta'aseh bein ha'Arbayim" - that teaches us that the Korban Tamid comprises two lambs and not four (the two of the inauguration [in Parshas Tetzaveh], plus the two mentioned in this Parshah).

3)
(a) Rebbi Shimon learned in our Mishnah that if the Kohanim deliberately failed to bring the Tamid shel Shachar, they can no longer bring the Tamid shel bein ha'Arbayim. The problem with that is - why the Mizbe'ach should be left idle, on account of the Kohanim's negligence.
(b) Rava solves the problem - by interpreting Rebbi Shimon to mean that the Tamid shel bein ha'Arbayim is brought, not by the Kohanim who were negligent, but by other Kohanim.
(c) Rebbi Shimon does not penalize the Kohanim who failed to bring the Ketores shel Shachar in the same manner - because a. unlike the Tamid, which is an Olah, of which many are brought each day, the Ketores is brought only twice daily, and b. it enriches whoever performs it, the Kohanim are unlikely to take their cue from those who have been lax on one occasion, in which case there is no reason to penalize the sinners.

4)
(a) We learned in our Mishnah that the Mizbe'ach ha'Zahav is inaugurated with the Ketores shel bein ha'Arbayim (see Shitah Mekubetzes 3). The problem with this - lies in a Beraisa, which specifically states that it is inaugurated with the Ketores shel Shachar.
(b) Abaye proves from the Pasuk "ba'Boker ba'Boker be'Heitivo es ha'Neiros Yaktirenah" - that the Menorah must be inaugurated with the Hadlakas Neiros of bein ha'Arbayim, because otherwise what would they clean out in the morning (since that is what ''be'Heitivo ... " means)?
(c) And we learn the Ketores from the Menorah (seeing as the Torah compares them).
(d) The source of the Tana who holds that the Mizbe'ach ha'Zahav is inaugurated with the Ketores shel Shachar is - the inauguration of the Mizbe'ach shel Olah, which is done through the Tamid shel Shachar.

5)
(a) We extrapolate from the Mishnah's ruling 've'Lo es ha'Shulchan Ela be'Lechem ha'Panim be'Shabbos' that the Lechem ha'Panim will become sanctified even if they are placed on the Shulchan during the week. The problem with that - lies in a Mishnah in 'Sh'tei ha'Lechem', which confines the Kedushah taking effect to Shabbos.
(b) We answer that the Tana maintains that the Lechem too, is sanctified only on Shabbos, and we prove this from the Seifa, 've'Lo es ha'Menorah Ela be'be'Shiv'ah Neirosehah bein ha'Arbayim' - where everything to do with the Menorah becomes Kadosh at the time stated in the Mishnah, likewise the Shulchan.

6)
(a) Rav Papa explains that the Beraisa's statement 'Zehu Ketores she'Alsah le'Yachid al Mizbe'ach ha'Chitzon; ve'Hora'as Sha'ah Haysah' - refers to the Nesi'im (by the Chanukas ha'Mizbe'ach).
(b) We might have thought that ...
1. ... a Yachid is obligated to bring a Nedavah of Ketores on the Mizbe'ach ha'Zahav - in order not to transgress the Mitzvah of "Motzei Sefasecha Tishmor ve'Asisa".
2. ... the Tzibur is obligated to keep their word, even if a Yachid is not - seeing as they bring the obligatory Ketores.
(c) We know that neither of these suppositions is correct, form the Pasuk - "Lo Sa'alu Alav Ketores Zarah (which is written in the plural to include a Tzibur).
(d) And we learn from the Pasuk there "es Shemen ha'Mishchah ve'es Ketores ha'Samim la'Kodesh, ke'Chol Asher Tzivisicha Ya'asu" - that one may only bring on the Mizbe'ach ha'Chitzon (i.e. ha'Olah) what is listed in that Parshah (but not Ketores).

7)
(a) We can extrapolate two things from the statement 'Eizehu Ketores she'Alsah le'Yachid al Mizbe'ach ha'Chitzon'. One of them is that a Yachid may donate Ketores to bring on the Mizbe'ach ha'Penimi; the other - that a Yachid is not permitted to bring Ketores on the Mizbe'ach ha'Chitzon, but a Tzibur may.
(b) The problem with both of these inferences is that - we just learned from Pesukim in Ki Sisa to the contrary.
(c) So to counter the inferences, Rav Papa explains the Beraisa 'Lo Miba'i ka'Amar', by which he means - that not only may a Tzibur not bring Ketores on the Mizbe'ach ha'Chitzon and a Yachid on the Mizbeach ha'Penimi (for neither of which we have a precedence). But even for a Yachid to bring Ketores on the Mizbe'ach ha'Chitzon, for which we have a precedence in the form of the Nesi'im), is forbidden, since that was a Hora'as Sha'ah.

8)
(a) Our Mishnah describes the Chavitei Kohen Gadol (the Minchas Chavitin), so called - because it was baked on a flat-pan (Machavas).
(b) It comprised - one Isaron of flour mixed with oil.
(c) It was ...
1. ... burned on the Mizbe'ach - in two lots, half in the morning and half in the afternoon.
2. ... brought to the Azarah - in one go, and divided afterwards.

9)
(a) The Tana discusses the Din of a Kohen Gadol who died after bringing the first half of his Minchah, and a new Kohen Gadol was appointed in his place - before the Tamid shel bein ha'Arbayim (for the Mishnah's ruling to be relevant).
(b) The new appointee does not bring half an Isaron from his house, and the second half of his predecessor's Minchah. He brings a fresh Isaron from home, which he divides into two halves, one of which he brings in the afternoon. (c) The two remaining halves must be burned.

10)
(a) In the event that they did not appoint another Kohen Gadol, Rebbi Shimon maintains that the Tzibur is obligated to bring the afternoon Minchas Chavitin. According to Rebbi Yehudah - the onus lies on the Kohen Gadol's heirs to bring it.
(b) Either way, the Halachah differs between where the Kohen Gadol brings the afternoon Minchas Chavitin, and where somebody else brings it - in that, in the latter case, it is brought on the Mizbe'ach in its entirety, without being divided (nd if it is brought in the morning, then they bring one Isaron in the morning amd one in the afternoon).
(c) We learn that the Kohen Gadol brings the full Isaron for the Minchas Chavitin before dividing into two halves, from the Pasuk "Machtzisah ba'Boker ... ". The Beraisa learns that the same applies in a case where ...
1. ... the second half of the Minchas Chavitin became Tamei or lost - from the 'Vav' in "u"Machtzisah ba'Erev", and where ...
2. ... the Kohen Gadol died after bringing the first half of his Minchah and they appointed a replacement before the Tamid shel bein ha'Arbayim has been brought - from the same source.

11)
(a) The problem Rav Nachman had with the Beraisa cited by a Beraisa expert - 'Mechtzah Rishon u'Mechtzah Sheini, Te'ubar Tzurasan ve'Yeitz'u le'Beis ha'Sereifah' is - why the second half, which was initially designated to be burned, requires Ibur Tzurah.
(b) He had no problem with the first half - because it is fit to be brought on the Mizbe'ach.
(c) So he established the Beraisa like Tana de'Bei Rabah bar Avuhah, who holds - that even Pigul requires Ibur Tzurah (even though it is Pasul min ha'Torah), and the same will therefore apply in our case.
(d) Rav Ashi concludes that the Beraisa can even go like the Rabbanan, and the second half requires Ibur Tzurah - because when the two halves were divided, both halves were fit to be brought on the Mizbe'ach, and were therefore initially Kasher.

12)
(a) According to Rebbi Chiya bar Aba Amar Rebbi Chanina, the Minchas Chavitin was first baked and then fried. Rav Asi Amar Rebbi Chanina says - the other way round (first fried and then baked).
(b) They argue over how to Darshen the acronym of the word "Tufinei". Rebbi Chiya bar Aba Darshens 'Te'afenah Na'ah' - meaning that it should look nice when it is baked. Now if the Minchas Chavitin was fried first (like Rav Asi maintains), it would turn black, and not look very pretty at the time of baking.
(c) Rav Asi Darshens "Tufinei" - 'Tufinei Na' (meaning 'bake it when it is already partially cooked' [referring to fried]).
(d) Their Machlokes also appears in a Beraisa, where Rebbi Darshens like Rav Asi. When Rebbi Dosa says there 'Te'afenah Rabah', he means - baked many times i.e. baked, fried and baked again (to fulfill both 'Na'eh' and 'Na'). Alternatively, the text reads 'Te'afenah Rakah', meaning that one softens it first with a lot of oil, which prevents it from turning black, following which the frying makes it look nice. Then it is baked.

13)
(a) The Mishnah in Sh'tei ha'Lechem discusses the kneading, the shaping and the baking of the Minchas Chavitin. The Tana rules there that ...
1. ... they must be performed - inside the Azarah.
2. ... these Melachos override Shabbos.
(b) Rav Huna learns the latter Halachah from "Tufinei" - which he Darshens 'Te'afenah Na'eh', whereas if they were baked on Erev Shabbos, they would swell.
(c) Rav Yosef refutes Rav Huna's proof on the grounds that the swelling could be prevented - by covering the loaves with vegetables, so that the air cannot get to them.

14)
(a) Tana de'Bei Rebbi Yishmael Darshens from "al Machavas ba'Shemen Te'aseh" - 'Afilu be'Shabbos, va'Afilu be'Tum'ah'.
(b)
1. Abaye learn this from the Pasuk "So'les Minchas Tamid" - comparing the Minchas Chavitin to the Tamid, which we know over-rides Shabbos.
2. Rava, who has the support of a Beraisa, learns it from "al Machavas" - which is a K'li Shareis. If it was baked on Erev Shabbos, it would therefore become Pasul be'Linah (like anything that is placed inside a K'li Shareis).

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