(a) RASHI and the RA'AVAD (in Tamid) and ROSH (in Midos) explain that the
Lishkas ha'Tela'im was "elongated." Since it occupied almost the entire
western side of the Beis ha'Mokad, if one looked from the north, there
appeared to be more of it to the south, and vice versa.
The VILNA GAON (Tamid 3:3) suggests that there was an important reason for
extending the Lishkas ha'Tela'im. The southern part of the Beis ha'Moked
(i.e. the side closer to the Azarah) was Chol, according to the Mishnah
(Midos 1:6; see Rashi 15b DH Shetayim), while the northern half was Kodesh.
If the entrance to the Lishkas ha'Tela'im would have been in the south,
since it was entered from an area of Kodesh the entire Lishkah would have
been Kodesh. But the excrement deposited by the sheep is disrespectful to an
area that is Kodesh. Therefore, they extended the Lishkah to the north,
where its entrance led to non-Kodesh area (i.e. the northern side of the
Beis ha'Mokad), making the Lishkah, too, Chol.
(b) Rabeinu Chananel (in his first explanation) and the Aruch, citing Rav
Moshe ha'Darshan, suggest that "Aktzuyei Maktzei" means that the Lishkas
ha'Tela'im was "set away" from the corner of the Bei ha'Mokad, almost in the
center of the western side of the Beis ha'Moked (but a bit closer to the
south, as the Gemara concludes). Therefore, when one looked in from the
north, since it was still a distance away it looked as though it was in the
southwest corner, and vice versa.
(c) The BA'AL HA'ME'OR (in our Sugya) appears to have learned that the
Lishkas ha'Tela'im was indeed in the southwest corner of the Beis ha'Mokad,
but the southern wall of the Lishkas ha'Tela'im was not the southern wall of
the Beis ha'Mokad. Rather, its southern wall began at the corner, and
protruded north into the Beis ha'Moked at an angle as it projected towards
the east (see mini-diagram below; north is up). Therefore, coming from the
south it seemed as though the Lishkas ha'Tela'im's main area was more
towards the north and v.v.
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(c) The RAMBAM (Perush ha'Mishnayos, Midos 1:6) suggests what seems to be
an original answer to the Gemara's question. He explains that Lishkas
ha'Tela'im was in the southwestern corner of the *Beis ha'Moked*, which was
at the same time the northwest of the *Azarah*. That is, the Mishnah in
Midos which puts the Lishkas ha'Tela'im on the northwest is not referring to
a side of Beis ha'Mokad, but of the Azarah. Although this explanation is
brilliant and resolves the contradiction, nevertheless the Gemara itself
seems to suggest other explanations! (In fact, RIVA, in Tosfos 17b DH v'Ha,
asks why the Gemara did *not* offer this seemingly simple answer.)
Rabeinu Chananel in our Sugya makes the same suggestion as the Rambam, and
although there appears to be some words missing in our texts of his
commentary, it seems that he means to say one of two things:
1. Either he learned that this is the intention of "Aktzuyei Mekatzya" --
the Lishkah was "set into a corner" from two different perspectives. (See
Chazon Ish, Orach Chayim 126:16)
2. The Rambam and Rabeinu Chananel may have learned that when the Gemara
continues "u'Mistabra...," it is *rejecting* the answer of Aktzuyei
Mekatzya, and insisting that the Lishkas ha'Tela'im was indeed entirely in
the southeast of the Beis ha'Mokad. Since the Gemara does not explain
explicitly how to resolve this with the Mishnah in Tamid, that Rambam gives
his suggestion for what the Gemara must have meant.