1) THE ARGUMENT BETWEEN RAV AND SHMUEL: "SHILSHUL" OR "ZERIKAH"
QUESTION: When one domain is shared by more than one Chatzer, the law is that the use of that domain is allotted to the Chatzer that has the least difficulty in using it. Rav and Shmuel (83b) argue about a case in which the residents of one Chatzer can use a certain domain only by throwing ("Zerikah") objects onto it, and the residents of an adjacent Chatzer can use the same domain only by lowering ("Shilshul") objects down onto it. Whose usage of the domain is considered to be easier? Rav says that since both Zerikah and Shilshul are difficult ways to use the domain, the two Chatzeros have equal use of the area. Consequently, the residents of both Chatzeros are forbidden from carrying into the domain on Shabbos. Shmuel maintains that Shilshul is an easier way to use an area than Zerikah, and thus the Chatzer that uses the domain through Shilshul is entitled to the exclusive right to use it.
The Gemara (84a) questions the opinion of Rav from the Mishnah (83b) which states that the right to use a mound of dirt around a pit or a large rock which is ten Tefachim high is given to the residents of the balcony. Even though the residents of the balcony are able to use the top of the mound only by lowering things onto it, this is considered an easier form of usage than that of the residents of the Chatzer, who have to throw things onto the top of the mound. This seems to refute the opinion of Rav.
What is the Gemara's question? The Mishnah is discussing the use of the top of the mound around the pit. It is not discussing the use of the inside of the pit itself. In order to use the top of the mound, the residents of the balcony do not have to lower anything onto it, since the mound is at the same level as the floor of the balcony!
(a) The RITVA answers in the name of TOSFOS (different from the Tosfos in our Gemara) that the Mishnah cannot be referring to the mound around the pit, because an ordinary mound does not have a width of four Tefachim at the top. It cannot become forbidden, because it is like a Makom Petur and is subordinate to the domains on each side, to the Chatzer and to the balcony. The Mishnah must be referring to the inside of the pit.
(b) The RITVA gives a second answer. It must be permitted for the residents of the balcony to use the inside of the pit itself. If they would be prohibited from using the pit, they would also be prohibited from using the mound around it, because the usage of the mound is subordinate to the pit (since the primary area of use is the pit). It must be that they are permitted to use the pit, even though they must lower things into it.
(c) The GA'ON YAKOV answers that the Gemara understands that when the Mishnah mentions "the mound around a pit," it must be referring to the inside of the pit. If the Mishnah is referring only to the actual mound around the pit, then the Mishnah would not have to mention both that case and the case of a large rock, because the case of the mound around the pit would be the same as the case of a large rock.
2) A LEDGE TEN TEFACHIM HIGH ON THE WALL BETWEEN A CHATZER AND AN ALIYAH
QUESTIONS: The Beraisa says that when a wall separates a Chatzer from an Aliyah (a second story), the residents of the Chatzer may use the bottom ten Tefachim of the wall, and the residents of the Aliyah may use the top ten Tefachim. The Beraisa explains that this Halachah applies when there is a ledge that protrudes from the wall. When the top of the ledge is within ten Tefachim of the bottom of the wall, the residents of the Chatzer may use it. When the top of the ledge is within ten Tefachim of the top of the wall, the residents of the Aliyah may use it. This implies that when the top of the ledge is exactly between the bottom ten and top ten Tefachim of the wall, both the Chatzer and the Aliyah are forbidden to use it.
This Beraisa seems to contradict the opinion of Shmuel, who says that when one domain (the Aliyah) can use the ledge through Shilshul (lowering objects down onto it), and the other domain (the Chatzer) can use it only through Zerikah (throwing objects onto it), the Aliyah has the exclusive right to use the ledge. The Beraisa, however, implies that the ledge may not be used by either domain, as Rav says.
The Gemara answers that the Beraisa is referring to a wall that is 19 Tefachim high, where there is no space between the top ten Tefachim and the lower ten Tefachim. Accordingly, we cannot infer from the Beraisa anything about a case where one domain can use the ledge through Shilshul and the other through Zerikah.
(a) Suppose the wall is 19 Tefachim high. If the ledge is 9 1/2 Tefachim from the ground, it is still within the Aliyah's ten Tefachim. In such a case, both the Aliyah and the Chatzer are within ten Tefachim of the ledge, and thus the ledge should be forbidden to be used because it is shared by two domains. Why, then, does the end of the Beraisa state, "If the ledge is below ten Tefachim, it goes to the Chatzer"? The ledge should have to be below nine Tefachim for the Chatzer to be permitted to use it!
(b) Similarly, why does the beginning of the Beraisa say, "The residents of the Chatzer may use [the ledge when it is within] the lower ten Tefachim, and the residents of the Aliyah may use [the ledge when it is within] the upper ten Tefachim"? This is not accurate -- they may each use the ledge only if it is within nine Tefachim, because the tenth is shared by both (since it is within ten from above and within ten from below)!
(a) The MAHARSHA answers that when the Beraisa says the Chatzer may use the ledge when it is below ten Tefachim, it does not refer to the ten Tefachim at the bottom of the wall. Rather, it refers to when the ledge is below the ten Tefachim immediately under the Aliyah. None of this area is a shared area. In contrast, when the Beraisa says that the Aliyah may use the ledge when it is above ten Tefachim, it means above ten Tefachim from the ground If the ledge is located between the ninth and tenth Tefach from the ground, it may not be used by the residents of the Chatzer or the residents of the Aliyah.
This, however, does not answer the second question, because the beginning of the Beraisa states explicitly that the residents of the Chatzer may use the "lower ten Tefachim."
(b) The RASHASH answers the second question. When the first part of the Beraisa says that the residents of the Chatzer use the lower ten Tefachim, it does not mean that they are permitted to use the lower ten Tefachim on Shabbos. Rather, it means merely that they tend to use the lower ten Tefachim during the week. Similarly, the residents of the Aliyah tend to use the upper ten Tefachim. The Beraisa is not presenting a Halachah, but it is merely introducing the case. Because they both tend to use the tenth Tefach during the week, both are indeed prohibited from using a ledge that is in the tenth Tefach on Shabbos without an Eruv.
3) A ROOF USED BY RESHUS HA'RABIM
QUESTION: The Gemara teaches that two partially overlapping surfaces at different heights are considered the same surface if they are within ten Tefachim of height of each other. The Gemara demonstrates this from a statement of Rav Nachman in the name of Shmuel regarding a case of a roof next to Reshus ha'Rabim. Shmuel said, "A roof next to Reshus ha'Rabim requires a permanent ladder to permit it [to be used by those in the Chatzer]."
The case Shmuel discusses is not clear. What are the two surfaces that are within ten Tefachim of each other in this case? In addition, why is it that the people in Reshus ha'Rabim prohibit the residents of the Chatzer from using the roof? Why does leaning a ladder against the roof in a permanent manner permit the residents of the Chatzer to use the roof?
RASHI explains that the Gemara is discussing a building at the edge of a Chatzer. The back of the building is adjacent to Reshus ha'Rabim. The building is surrounded by a balcony which has a fence around it and an opening of less than ten Amos wide that faces Reshus ha'Rabim. Rashi explains that the roof (above the balcony) is within ten Tefachim of the balcony, and the balcony (above Reshus ha'Rabim) is within ten Tefachim of the Reshus ha'Rabim. The Gemara attempts to demonstrate that the people in Reshus ha'Rabim -- by virtue of their presence within ten Tefachim of the balcony -- are considered as though they are on the balcony. Therefore, they may carry from Reshus ha'Rabim to the roof, which is within ten Tefachim of the balcony. Even though there are more than ten Tefachim between the Reshus ha'Rabim and the roof, the people in Reshus ha'Rabim are considered to be within ten Tefachim of the roof. Since they have use of the roof, the roof is prohibited to the residents of the Chatzer.
Why does a permanent ladder permit the residents of the Chatzer to use the roof? If they erect a ladder from the balcony to the roof on the side facing the Chatzer, then those who live on the second story (where the balcony is) are able to reach the roof and use it. This is a way of establishing a claim, so to speak, to the right to use the roof, and a way of showing that they intend to use it, which should prohibit the people in Reshus ha'Rabim from using it. However, a temporary ladder does not show that they are claiming the roof as theirs, and therefore they need a permanent ladder. A permanent ladder shows that they want to use the roof on a regular basis, and thus it becomes prohibited for the people in Reshus ha'Rabim to use the roof, because they would be trespassing on private property.
The Gemara makes no mention of the balcony that Rashi includes in the case. Indeed, Rashi mentions that some understand that there is only a roof and a Reshus ha'Rabim next to it, and they are within ten Tefachim of each other (this is also how Rabeinu Tam in Tosfos learns). Rashi argues that this cannot be the case, because if the roof is within ten Tefachim of Reshus ha'Rabim, then it is a Karmelis, and no matter how many ladders are placed there, it remains forbidden to carry from the Chatzer (a Reshus ha'Yachid) to the roof (a Karmelis). Rather, it must be that there is a balcony (which the Gemara does not mention) between the roof and the ground. The roof itself is more than ten Tefachim from the ground and thus it is not a Karmelis.
Rashi explains that the balcony does not become a Karmelis because it has a fence around it (with a small opening). Why, then, does Rashi insist that if there had been no balcony and the roof itself was within ten Tefachim of the ground, that roof would have been a Karmelis? Rashi should have answered that there is a fence around the roof, making it a Reshus ha'Yachid and not a Karmelis! (NACHAL ARAVIM; Rabeinu Tam indeed suggests that this is the case in the Gemara.)
(a) Apparently, if the roof would have a fence, the fence itself would prevent the people in Reshus ha'Rabim from using it, and it would establish for the residents of the Chatzer the exclusive right to the use of the roof. A fence around the roof would serve the same function as a permanent ladder. Only when a roof has no fence may the people in Reshus ha'Rabim use it. A balcony is different; even though it has a fence, the fence does not establish a claim to the roof for the residents of the Chatzer (but only a claim to the balcony). Even though the people in Reshus ha'Rabim do not have use of the balcony due to the fence, they are considered to be within ten Tefachim of the roof simply because they are, according to Halachah, in the same Reshus as the balcony (i.e., in a Reshus which is within ten Tefachim of the balcony). Since the balcony is in the same area as Reshus ha'Rabim, the people of Reshus ha'Rabim are considered to be within ten Tefachim of the roof.
(b) The NACHAL ARAVIM answers that Rashi indeed could have said that the Gemara is discussing a roof without a balcony, and that the roof has a fence around it (which removes its status of a Karmelis). However, Rashi maintains that it is improbable that the roof in this case has a fence around it, because Shmuel did not mention anything about a fence. (Even though Rashi himself says that the balcony has a fence around it, and Shmuel made no mention of a balcony or a fence, Rashi is explaining the Gemara's initial assumption (Havah Amina). Therefore, the Gemara may suggest that as a forced interpretation. In the Gemara's conclusion, however, Rashi prefers not to say that the roof has a fence around it, since Shmuel did not mention a fence.)