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===Angle of the Slope===
===Angle of the Slope===
# A slope that that has a height of 10 tefachim over a distance of 4 amot or less<ref>Sfat Emet (Shababt 100a s.v. amar rav)</ref> is considered a wall for enclosing a reshut hayachid.<ref>Gemara Shabbat 100a, Rambam Shabbat 14:16, Shulchan Aruch and Rama O.C. 363:36, Shulchan Aruch O.C. 362:2</ref> According to majority of poskim, this distance is measured along the slope and not the floor (Picture #1), however, a minority of poskim hold it is measured along the ground (Picture #2).<ref>Rabbenu Chananel (Shabbat 100b) and Ritva (Shabbat 100a s.v. tel, Eruvin 19b s.v. tel) hold that 4 amot is measured along the slope, while Tosfot Zevachim (63a s.v kol) holds that 4 amot is measured along the ground. Goan Yakov (Eruvin 19b), Mishna Brurah 345:5, 363:154, Aruch Hashulchan 345:28, Maharalbach 19, and Netivot Shabbat 16:6 hold like Rabbenu Chananel. Mahalbach explains that this is also the view of Rashi Eruvin 19b and Rambam Shabbat 14:16. Markevet Hamishna explains Rambam like Tosfot. Sfat Emet Shabbat 100a says Rashi agrees with Rabbenu Chananel. (There Tosfot write that a slope of a triangle with height 9 and floor 20 is steeper than a tel hamelaket. According to Rabbenu Chananel it isn’t true.) if 4 amot is measured on the floor then the angle of the slope is arctan(10/24)=22.6 degrees. If 4 amot is measured on the slope then the angle of the slope is arcsin(10/24)=24.6 degrees.</ref> A tel hamelaket has the halacha of gud asik.<ref>Rashi Eruvin 15a s.v. gevoha, Machaneh Yisrael (12:16:5 p.293), Netivot Shabbat ch. 16 fnt. 19. See Rav Chaim Halevi on Rambam Sukkah 11:4 who suggests that Rambam doesn't hold of gud asik but, nonetheless, the top of the tel hamelaket is a reshut hayachid that extends upward. Chazon Ish 108:9 implies that there is no gud asik for the slope of the tel hamelaket.</ref>
# A slope that that has a height of 10 tefachim over a distance of 4 amot or less<ref>Sfat Emet (Shababt 100a s.v. amar rav)</ref> is considered a wall for enclosing a reshut hayachid.<ref>Gemara Shabbat 100a, Rambam Shabbat 14:16, Shulchan Aruch and Rama O.C. 363:36, Shulchan Aruch O.C. 362:2</ref> According to majority of poskim, this distance is measured along the slope and not the floor (Picture #1), however, a minority of poskim hold it is measured along the ground (Picture #2).<ref>Rabbenu Chananel (Shabbat 100b), Ritva (Shabbat 100a s.v. tel, Eruvin 19b s.v. tel), and Riaz (Eruvin 2:1:7) hold that 4 amot is measured along the slope, while Tosfot Zevachim (63a s.v kol) holds that 4 amot is measured along the ground. Goan Yakov (Eruvin 19b), Mishna Brurah 345:5, 363:154, Aruch Hashulchan 345:28, Maharalbach 19, and Netivot Shabbat 16:6 hold like Rabbenu Chananel. Mahalbach explains that this is also the view of Rashi Eruvin 19b and Rambam Shabbat 14:16. Markevet Hamishna explains Rambam like Tosfot. Sfat Emet Shabbat 100a says Rashi agrees with Rabbenu Chananel. (There Tosfot write that a slope of a triangle with height 9 and floor 20 is steeper than a tel hamelaket. According to Rabbenu Chananel it isn’t true.) if 4 amot is measured on the floor then the angle of the slope is arctan(10/24)=22.6 degrees. If 4 amot is measured on the slope then the angle of the slope is arcsin(10/24)=24.6 degrees.</ref> A tel hamelaket has the halacha of gud asik.<ref>Rashi Eruvin 15a s.v. gevoha, Machaneh Yisrael (12:16:5 p.293), Netivot Shabbat ch. 16 fnt. 19. See Rav Chaim Halevi on Rambam Sukkah 11:4 who suggests that Rambam doesn't hold of gud asik but, nonetheless, the top of the tel hamelaket is a reshut hayachid that extends upward. Chazon Ish 108:9 implies that there is no gud asik for the slope of the tel hamelaket.</ref>
# A slope that is more gradual than 10 tefachim within 4 amot, such as 10 tefachim over 5 amot, is not considered a wall.<ref>Rashi Shabbat 100a s.v. tel writes that if the slope is more gradual than 10 tefachim within 4 amot it is like the ground of the reshut harabbim since people can walk over it easily. Taz 363:28 and Mishna Brurah 363:154 quote Rashi. Chazon Ish (65:70 s.v. achrei) suggests that an area that is raised up or lower 10 tefachim than the area next to it, it could be a reshut hayachid, since it is set off from the reshut harabbim even though the slope is more gradual than 10 amot within 4 amot. This is true on condition that people don't walk over the walls. For example, if there is a house with walls that are sloped more gradually than 10 amot within 4 amot, it is a reshut hayachid inside since people don't walk over the walls. His proof is Sukkah 19a. Netivot Shabbat ch. 6 fnt. 17 notes that the implication of the poskim is unlike this Chazon Ish.</ref>
# A slope that is more gradual than 10 tefachim within 4 amot, such as 10 tefachim over 5 amot, is not considered a wall.<ref>Rashi Shabbat 100a s.v. tel writes that if the slope is more gradual than 10 tefachim within 4 amot it is like the ground of the reshut harabbim since people can walk over it easily. Taz 363:28 and Mishna Brurah 363:154 quote Rashi. Chazon Ish (65:70 s.v. achrei) suggests that an area that is raised up or lower 10 tefachim than the area next to it, it could be a reshut hayachid, since it is set off from the reshut harabbim even though the slope is more gradual than 10 amot within 4 amot. This is true on condition that people don't walk over the walls. For example, if there is a house with walls that are sloped more gradually than 10 amot within 4 amot, it is a reshut hayachid inside since people don't walk over the walls. His proof is Sukkah 19a. Netivot Shabbat ch. 6 fnt. 17 notes that the implication of the poskim is unlike this Chazon Ish.</ref>
# The slope is considered a wall where it reaches 10 tefachim within 4 amot. That is the top of the slope is where it is considered to be a the wall and not the bottom of the slope.<ref>Rashi Shabbat 100a s.v. tel and s.v. otto. Machaneh Yisrael (12:18 p. 294) writes that only the top of the slope where it reaches 10 tefachim within 4 amot is considered a wall and not the bottom of the slope.</ref>
# The slope is considered a wall where it reaches 10 tefachim within 4 amot. That is the top of the slope is where it is considered to be a the wall and not the bottom of the slope.<ref>Rashi Shabbat 100a s.v. tel and s.v. otto. Machaneh Yisrael (12:18 p. 294) writes that only the top of the slope where it reaches 10 tefachim within 4 amot is considered a wall and not the bottom of the slope.</ref>
#Once the slope is 10 tefachim high within 4 amot, the area that slopes above it is considered within the walls of a reshut hayachid.<ref>Maharshal (Shabbat 100a s.v. bdibur hamatchil tel) explains that Rashi holds that even the slope is also considered a reshut hayachid once the slope reaches 10 tefachim high within 4 amot of distance.</ref> Some argue that it isn't a reshut hayachid until the area flattens out on top.<ref>Chazon Ish 108:9. Tosfot Shabbat 5b s.v. kotel writes that a slanted wall which is less than 10 tefachim from the ground is considered like a reshut harabbim only if people place items on top of it. Tosfot implies that people didn't use the slanted wall, it would be considered a karmelit according to its dimensions. Ramban disagrees and argues that a slanted  wall is like a straight wall and the side of it is considered airspace of the reshut harabbim. Rashba defends Tosfot by saying that the side of a wall is the airspace of a reshut harabbim, but a slanted wall is considered a new domain since there is a place upon it to place items. Chazon Ish applies this discussion to a slope of a tel hamelaket above 10 tefachim. According to Ramban, since it is like a wall, the surface is considered the airspace of the domain below. In practice it would be a makom patur since it is 10 tefachim above a reshut harabbim. Even though according to Tosfot it seems that the slope is considered a new domain and should be a reshut hayachid, Chazon Ish explains that isn't the case. Tosfot fundamentally agrees with Ramban, though he considers the sloped wall to be a new domain since no one can walk below it and can't be called airspace. However, above ten tefachim where walking below it is irrelevant Tosfot agrees with Ramban. Machaneh Yisrael (12:16:5 p. 293) rejects Chazon Ish's conclusion because it is against the Rashba and also Ritva Eruvin 90a. Machaneh Yisrael holds like Maharshal. Netivot Shabbat ch. 16 fnt. 19 quotes the dispute between Maharshal and Chazon Ish.</ref>
#Once the slope is 10 tefachim high within 4 amot, the area that slopes above it is considered within the walls of a reshut hayachid.<ref>Maharshal (Shabbat 100a s.v. bdibur hamatchil tel) explains that Rashi holds that even the slope is also considered a reshut hayachid once the slope reaches 10 tefachim high within 4 amot of distance.</ref> Some argue that it isn't a reshut hayachid until the area flattens out on top.<ref>Chazon Ish 108:9. Tosfot Shabbat 5b s.v. kotel writes that a slanted wall which is less than 10 tefachim from the ground is considered like a reshut harabbim only if people place items on top of it. Tosfot implies that people didn't use the slanted wall, it would be considered a karmelit according to its dimensions. Ramban disagrees and argues that a slanted  wall is like a straight wall and the side of it is considered airspace of the reshut harabbim. Rashba defends Tosfot by saying that the side of a wall is the airspace of a reshut harabbim, but a slanted wall is considered a new domain since there is a place upon it to place items. Chazon Ish applies this discussion to a slope of a tel hamelaket above 10 tefachim. According to Ramban, since it is like a wall, the surface is considered the airspace of the domain below. In practice it would be a makom patur since it is 10 tefachim above a reshut harabbim. Even though according to Tosfot it seems that the slope is considered a new domain and should be a reshut hayachid, Chazon Ish explains that isn't the case. Tosfot fundamentally agrees with Ramban, though he considers the sloped wall to be a new domain since no one can walk below it and can't be called airspace. However, above ten tefachim where walking below it is irrelevant Tosfot agrees with Ramban. Machaneh Yisrael (12:16:5 p. 293) rejects Chazon Ish's conclusion because it is against the Rashba and also Ritva Eruvin 90a. Machaneh Yisrael holds like Maharshal. Netivot Shabbat ch. 16 fnt. 19 quotes the dispute between Maharshal and Chazon Ish.</ref>
===If Slope Becomes Gradual in Middle===
===If Slope Becomes Gradual in Middle===
# If the slope becomes more gradual in the middle but altogether over 4 amot it reaches a height of 10 tefachim (Picture #3), many poskim hold it is considered a wall. The main point is that as a whole the area of 4 amot has a slope that rises 10 tefachim but it is irrelevant what the slope is at any point.<ref>Tosefet Shabbat 345:2, Sfat Emet (Shabbat 100a s.v. amar rav). Mishna Brurah (Biur Halacha 358:2 s.v. v'im) seems to also be other this opinion as he compares two vertical walls split by some horizontal distance to be a wall if altogether it is 10 tefachim tall over 4 amot. </ref> Other poskim hold that this would not constitute a wall. Any part of the slope which is more gradual than 24.6 degrees is not considered a wall at all is a break in the wall. If the break is larger than 4 tefachim it breaks up the two parts of the slope completely.<ref>Chazon Ish 65:62 and 111:4 writes that if at any point if the slope it becomes more gradual than 24.6 degrees that part is not considered part of the slope and would break it up if it is wider than 3 tefachim. That is true even if altogether the slope is 10 tefachim tall within 4 amot. However, in 65:70 he prefers the logic that it would be a wall unless it is broken up with an area of 4 tefachim. In 111:4 he also uses the width of 4 tefachim. Netivot Shabbat 16:8 codifies the Chazon Ish, though in footnote he notes Tosefet Shabbat and Biur Halacha's view.</ref>
# If the slope becomes more gradual in the middle but altogether over 4 amot it reaches a height of 10 tefachim (Picture #3), many poskim hold it is considered a wall. The main point is that as a whole the area of 4 amot has a slope that rises 10 tefachim but it is irrelevant what the slope is at any point.<ref>Tosefet Shabbat 345:2, Sfat Emet (Shabbat 100a s.v. amar rav). Mishna Brurah (Biur Halacha 358:2 s.v. v'im) seems to also be other this opinion as he compares two vertical walls split by some horizontal distance to be a wall if altogether it is 10 tefachim tall over 4 amot. </ref> Other poskim hold that this would not constitute a wall. Any part of the slope which is more gradual than 24.6 degrees is not considered a wall at all is a break in the wall. If the break is larger than 4 tefachim it breaks up the two parts of the slope completely.<ref>Chazon Ish 65:62 and 111:4 writes that if at any point if the slope it becomes more gradual than 24.6 degrees that part is not considered part of the slope and would break it up if it is wider than 3 tefachim. That is true even if altogether the slope is 10 tefachim tall within 4 amot. However, in 65:70 he prefers the logic that it would be a wall unless it is broken up with an area of 4 tefachim. In 111:4 he also uses the width of 4 tefachim. Netivot Shabbat 16:8 codifies the Chazon Ish, though in footnote he notes Tosefet Shabbat and Biur Halacha's view.</ref>
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