1) HOW DOES THE MECHANISM OF A "KORAH" WORK?
QUESTION: Rav explains that the Chachamim in the Mishnah derive the maximum height at which a Korah may be placed from the height of the entrance to the Heichal, while Rebbi Yehudah derives it from the height of the entrance to the Ulam.
The Gemara (5a) teaches that the Korah at the entrance to a Mavoy permits the use of the Mavoy on Shabbos in one of two ways: either it serves as a reminder (Heker) that one may not carry from the Mavoy to the Reshus ha'Rabim, or it serves as an actual partition (Mechitzah) between the Mavoy and the Reshus ha'Rabim. According to both approaches, however, Rav's sources for the maximum height of a Korah are difficult to understand. Rav says that according to the Chachamim, we derive the maximum height of a doorway from the height of the entrance to the Heichal. Since that entranceway was 20 Amos high, we learn that a doorway that is higher than 20 Amos is not considered a doorway. The law of a Korah, though, has nothing to do with the definition of a doorway. Rather, a Korah that is too high either provides no Heker (as the Gemara suggests on 3a) or is not considered a Mechitzah, since the laws of Gud Achis do not apply to a Korah that cannot be seen (Rashi, 5a DH u'Man).
ANSWER: The RASHBA and other Rishonim explain that there is a third possible reason why a Korah enables one to carry inside a Mavoy. A Korah works by giving the opening that it covers the form of a doorway (like a Tzuras ha'Pesach, even though the Korah has no side posts upon which it rests). Accordingly, it is obvious that a Korah cannot be placed higher than the height of the tallest doorway.
2) SLAUGHTERING "SHELAMIM" WHILE THE DOORS OF THE "HEICHAL" ARE OPEN
QUESTION: Rav Yehudah teaches in the name of Shmuel that an animal that is offered as a Korban Shelamim must be slaughtered "Pesach Ohel Mo'ed," while the doors of the Heichal are open.
RASHI in Zevachim (61a, DH Iba'is Eima) says that this requirement applies only to Shelamim and not to other Korbanos. TOSFOS here and in Zevachim asserts that it applies to other Korbanos as well.
Why, according to Rashi, does the requirement to slaughter a Korban while the doors of the Heichal are open apply only to a Korban Shelamim?
ANSWER: The MESHECH CHOCHMAH (Shemos 29:11) suggests a reason why, according to Rashi, this requirement applies only to Shelamim. The IBN EZRA (Vayikra 1:5) points out that a Korban Olah must be slaughtered in the northern part of the Azarah, which corresponds to the position of the Shulchan in the Heichal. The Meshech Chochmah explains that the Ibn Ezra means that the Olah is slaughtered in the north to denote that it is Kadosh and belongs entirely to Hash-m (it belongs to "Shulchan Gavo'ah").
However, only Kodshei Kodashim are slaughtered in the northern part of the Azarah. What act is done with Kodshim Kalim to show that they, too, are Kadosh and belong to Hash-m? The Meshech Chochmah suggests that the act of slaughtering Kodshim Kalim (Shelamim) while the doors to the Heichal are open shows that the Korban is dedicated to Hash-m.
With this understanding, the Meshech Chochmah explains a verse that seems to contradict the words of Rashi. The verse (Shemos 29:11) says that the Korban Olah that was brought at the time of the dedication of the Mishkan (Shiv'as Yemei ha'Milu'im) had to be slaughtered "Pesach Ohel Mo'ed." According to Rashi, only Shelamim, and not Olos, are slaughtered while the doors of the Heichal are open!
The Meshech Chochmah answers that the Gemara in Shabbos (87b) says that the eighth day of the dedication of the Mishkan was the first day for eating Kodshim. Tosfos there cites a variant reading which says that it was the first day for "slaughtering Kodshim in the north." Accordingly, the Korbanos that were brought before the eighth day were not slaughtered in the north, even though they were Kodshei Kodshim. As a result, they were missing the symbolic indication that they were Kadosh and directed towards Hash-m. Therefore, these Korbanos in particular were slaughtered "Pesach Ohel Mo'ed"!

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3) THE MAXIMUM HEIGHT AND WIDTH OF AN ENTRANCEWAY
QUESTION: According to the Chachamim in the Mishnah (2a), the maximum height of an entranceway is 20 Amos, and the maximum width of an entranceway is 10 Amos. Rebbi Yehudah disagrees about the maximum height and maintains that an entranceway may be higher than 20 Amos. Rav says that the Chachamim derive the maximum height of an entranceway from the height of the entrance to the Heichal, which was 20 Amos high. Rebbi Yehudah derives the height of an entranceway from that of the Ulam, which was 40 Amos high.
The Gemara challenges Rav's statement and says that if the Chachamim and Rebbi Yehudah derive the measurements from the entranceways which were in the Beis ha'Mikdash, then they should maintain that an entranceway may be as wide as 20 Amos, and not just 10, since the entranceway to the Chatzer (courtyard) was 20 Amos wide (and 5 Amos high).
Why does the Gemara ask this question on both the opinion of the Chachamim and that of Rebbi Yehudah? It is not a problem according to the view of Rebbi Yehudah! Rav says that Rebbi Yehudah's opinion is derived from the height of the entrance to the Ulam (40 Amos); the Ulam itself was also 20 Amos wide! It must be that Rebbi Yehudah maintains that the maximum width of an entranceway indeed is 20 Amos!
If, on the other hand, the Gemara assumes at this point that Rebbi Yehudah agrees with the Chachamim that the maximum width of an entranceway is 10 Amos (as is implied from the following Sugya), then the Gemara should challenge Rebbi Yehudah's opinion from the 20-Amah width of the entrance to the Ulam itself, since it is from the Ulam that Rebbi Yehudah derives the maximum height of an entranceway! (REBBI AKIVA EIGER in GILYON HA'SHAS)
ANSWERS:
(a) TOSFOS in Zevachim (60a) proves, based on this question and other questions, that the logic of the first explanation cited by Rashi here (DH mi'Sefas Kela'im), which Rashi himself rejects, is correct. According to the first explanation cited by Rashi, when the Gemara questions the Chachamim and Rebbi Yehudah from the dimensions of the entrance to the Chatzer, its question regards only the height and not the width of an entranceway. The Gemara asks that the height of an entranceway should be no more than 5 Amos, since that is the height of the entrance to the Chatzer. Accordingly, the Gemara's question applies to both the Chachamim (who say that the maximum height is 20 Amos) and Rebbi Yehudah (who says that the maximum height is 40 Amos).
Rashi (DH Leilfu mi'Pesach), however, rejects this explanation, because there is no reason to derive the maximum height of an entranceway from the Chatzer (which was only 5 Amos high) when there were higher entranceways -- those of the Heichal and of the Ulam!
Tosfos resolves Rashi's difficulty by saying that the entranceways of the Heichal and Ulam might not be considered entranceways. Those two entranceways correspond to the entranceway to the Mishkan, which the Torah calls "Pesach." That opening, however, was not a real entranceway, because it had no doorposts, as the eastern side of the Mishkan was entirely open. Accordingly, it may be argued that that the entranceways in the Beis ha'Mikdash which correspond to the entranceway of the Mishkan are also not considered real entranceways, and they cannot be used to determine the dimensions of an entranceway (if we can find another source for the dimensions of an entranceway).
The Gemara answers that the curtains were not merely 5 Amos high on the side of the entranceway, but they were 20 Amos high. Therefore, the Chachamim are justified in using the entranceway of the Chatzer as a source for the maximum height of an entranceway. (This answer, however, does not suffice for Rebbi Yehudah, because he maintains that an entranceway may be higher than 20 Amos. Tosfos explains that Rebbi Yehudah relies on the first answer of the Gemara, that the entranceway of the Chatzer is not called an entranceway but rather a "gateway," and therefore Rebbi Yehudah has no choice but to learn the dimensions of an entranceway from the entrance to the Ulam.)
(b) The RITVA says that according to Rashi and the other Rishonim, the reason why the Gemara also asks its question on Rebbi Yehudah is because at this point the Gemara assumes that Rebbi Yehudah agrees that the width of an entranceway is 10 Amos. He derives only the height from the Ulam. He derives the width from the Heichal. Although the Gemara could have questioned Rebbi Yehudah at this point from the width of the entrance to the Ulam (as it asks later), it prefers to ask from the entrance to the Chatzer so that its question will apply simultaneously to both the Chachamim and Rebbi Yehudah.
4) THE HEIGHT OF THE CURTAINS AROUND THE MISHKAN
QUESTION: The Gemara concludes that when the verse says that the curtains around the Miskhan were 15 Amos, it refers to their height. According to the second explanation cited by RASHI, this was the height of all the curtains around the Mishkan and not just the height of the curtains on the eastern side. Why, then, does the verse (Shemos 27:14-15) specify that the curtains on the east were 15 Amos high, if the curtains on all sides of the Mishkan were that high?
ANSWER: Perhaps the verse says specifically that the curtains on the eastern side were 15 Amos for the following reason. The Torah clearly says that the Masach (veil) in front of the entrance to the Chatzer (which was on the east) was "20 Amos." Since the Gemara concludes that the entranceway covered by the Masach was not 20 Amos wide, but rather no more than 10 Amos wide, it must be that this verse (that says 20 Amos) refers to the height of the Masach and not to its width. Apparently, the entranceway was 20 Amos high, even though the curtains around the rest of the Mishkan were only 15 Amos high.
If the curtains on the eastern side were the same height as the curtains all around the Mishkan, then the Masach would extend above the height of the curtains by 5 Amos. We might have thought that on the eastern side, the curtains were also 20 Amos high in order to match the height of the Masach. The verse therefore specifies that even the curtains on the eastern side were only 15 Amos high. (M. KORNFELD)

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