1) THE LOCATION OF THE "LISHKAS HA'TELA'IM" IN THE "BEIS HA'MOKED"
OPINIONS: The Gemara addresses a contradiction between the Mishnah in Tamid (3:3) and the Mishnah in Midos (1:6). The Mishnah in Tamid says that the Lishkas ha'Tela'im was on the northwest side of the Beis ha'Moked, while the Mishnah in Midos says that it was on the southwest side.
The Gemara offers several answers. Rav Huna answers that the Mishnah is Midos expresses the opinion of Rebbi Eliezer ben Yakov, who indeed argues with the Mishnah in Tamid.
Rav Ada brei d'Rav Yitzchak (17a) answers that the Lishkas ha'Tela'im was "Aktzuyei Mekatzya." When one stood in the south, the Lishkas ha'Tela'im appeared to be in the northwest. When one stood in the north, it appeared to be in the southwest. The Rishonim explain this in different ways.
(a) RASHI (DH Rav Ada), the RA'AVAD (in Tamid), and the ROSH (in Midos) explain that the Lishkas ha'Tela'im was "elongated" and occupied almost the entire western side of the Beis ha'Moked. Consequently, when one looked from the north it appeared that more of the Lishkah was in the south, and when one looked from the south it appeared that more of it was in the north.
The VILNA GA'ON in Tamid (3:3) suggests that the Lishkas ha'Tela'im was elongated for an important reason. The southern part of the Beis ha'Moked (the side closer to the Azarah) was not sanctified, according to the Mishnah in Midos (1:6; see Rashi to 15b, DH Shtayim), while the northern half was sanctified. If the entrance to the Lishkas ha'Tela'im would have been in the south, opening into the Azarah, the entire Lishkah would have been sanctified because it was accessed from a sanctified area (the Azarah). However, it would have been inappropriate for the Lishkas ha'Tela'im to be sanctified, because live animals were kept there and the presence of their excrement would have been disrespectful to a holy area. Therefore, the Lishkas ha'Tela'im was extended to the north, so that its entrance opened into a non-sanctified area (the northern side of the Beis ha'Moked). Since it opened into a non-sanctified area, the entire Lishkah itself had no sanctity.
(b) RABEINU CHANANEL (in his first explanation) and the ARUCH in the name of RABEINU MOSHE HA'DARSHAN suggest that "Aktzuyei Mekatzya" means that the Lishkas ha'Tela'im was "set away" from the corner of the Beis ha'Moked, positioned nearly in the center of the western side of the Beis ha'Moked (but slightly towards the south, as the Gemara concludes). Therefore, when one looked from the north, the Lishkas ha'Tela'im appeared as though it was in the southwest corner, since it was still a considerable distance away. When one looked from the south, it appeared to be in the northwest corner.
(c) The BA'AL HA'ME'OR seems to understand that the Lishkas ha'Tela'im indeed was in the southwest corner of the Beis ha'Moked, but the southern wall of the Lishkas ha'Tela'im was not the southern wall of the Beis ha'Moked. Rather, the Lishkah's southern wall began at the corner of the Beis ha'Moked and protruded north into the Beis ha'Moked at an angle as it extended towards the east. Therefore, to one who entered from the south it seemed as though the Lishkas ha'Tela'im's main area was more towards the north, and to one who entered from the north the Lishkah's main area appeared to be more towards the south.
(d) The RAMBAM (Perush ha'Mishnayos to Midos 1:6) explains that the Lishkas ha'Tela'im was in the southwest corner of the Beis ha'Moked, and the Beis ha'Moked was in the northwest of the Azarah. He understands that the Mishnah in Tamid which positions the Lishkas ha'Tela'im in the northwest does not refer to an area in the Beis ha'Moked, but rather to an area in the Azarah.
While this explanation brilliantly resolves the contradiction between the Mishnayos, it is a novel explanation of which the Gemara makes no mention. (In fact, the RIVA (cited by Tosfos to 17b, DH v'Ha) asks why the Gemara does not offer this answer.)
RABEINU CHANANEL here proposes the same explanation as the Rambam. (Some words seem to be missing in our edition of his commentary.) Rabeinu Chananel apparently understands that this is the intention of the words, "Aktzuyei Mekatzya." The Lishkah was "set into a corner" from two different perspectives. (See CHAZON ISH OC 126:16.)
Alternatively, the Rambam and Rabeinu Chananel may understand that when the Gemara continues and says, "u'Mistavra...," it rejects the answer of "Aktzuyei Mekatzya" and asserts that the Lishkas ha'Tela'im was entirely in the southeast part of the Beis ha'Moked. Since the Gemara does not explicitly address how this assertion can be reconciled with the Mishnah in Tamid, the Rambam and Rabeinu Chananel propose their explanation for what the Gemara must mean.