1)

(a)The pit will not be permitted by means of a ledge which is within four Tefachim of the windows - because then it is a pit which is half in the Reshus of the one and half in the Reshus of the other, about which the Mishnah states (later in this Perek) that it is forbidden to both courtyards, unless they make an Eruv or arrange a Mechitzah Teluyah.

(b)We are talking about courtyards which have no entrances, and their only use is via the windows (otherwise we will be left with the problem mentioned in a).

(c)Really not even a ledge is necessary in this case. It is no more than a Heker, to remind them generally not to carry in another Reshus without the required Tikun.

2)

(a)According to Rav Yehudah, not even a ledge is necessary - all that is needed is a cane (or reed) projected from the window, to enable them to carry.

3)

(a)Rav Yehudah was a Talmid of Rav. Then, after Rav's death, he went to learn by Shmuel. Consequently, we assume, that whatever he quotes, he heard either from one, or from the other.

(b)He cannot possibly have heard this particular Din from Rav - because, according to Rav, using the air (i.e. by throwing from a distance) never forbids the other users to use it on Shabbos.

(c)From Shmuel's Din of 'Gag ha'Samuch li'Reshus ha'Rabim, Tzarich Sulam Kavu'a Lehatiro' - we see that, although the passers-by only use the roof by throwing on to it, it nevertheless requires some sort of Tikun (not like Rav).

(d)The Gemara rejects this proof - using the same argument as it did to disprove Abaye's contention on the previous Amud: by pointing out that the passers-by in the street use it for their hats (in which case even Rav will agree that a Tikun is necessary).

4)

(a)Rav Yehudah learns his Din (of permitting even a cane) - from the very statement of Shmuel on which he himself commented earlier (Bor she'Bein Shtei Chatzeros ... Zeh Motzi Ziz u'Memale' etc.), only Abaye had Rav Yehudah's statement as an independent one (not pertaining to the statement of Shmuel).

5)

(a)In connection with the Mishnah of two ledges above water, when the one owner made walls and the other did not, in which case both parties are forbidden to draw water from the hole in the ledge unless they make an Eruv or arrange a Mechitzah Teluyah - Rav comments 'Lo Shanu Ela bi'Semuchah, Aval b'Mufleges Arba'ah, Elyonah Muteres' etc., from which it would appear that, whenever the one can only use the Reshus in question via the air, he does not forbid the other owner to use it.

(b)There is no proof from there, concludes the Gemara - because, since the one can use it through Shilshul, and the other only through Zerikah and Shilshul, it is more like 'la'Zeh bi'Zerikah, vela'Zeh be'Pesach' (which even according to Rav, goes to the latter.

(c)Rav says that if there are two houses that are joined by a series of three ruins (consisting of three rooms with broken walls) - each house may throw from the window to the ruin next to it (but not to the middle one).

(d)Neither house is permitted to throw from their window to the far ruin (since the far house is able to use it easily).

6)

(a)Rav permits the pit in between two Chatzeros - because it can only be used via the air (i.e. throwing), whereas the middle room in our case is forbidden, since as we shall see in the next answer, that particular ruin is used by both houses, either by throwing or by lowering (which Rav agrees will forbid).

(b)The Gemara concludes that the middle room is not in line with the other two, but at the side (and is therefore forbidden because there are other windows opening directly into it from both houses, making it a case of 'la'Zeh be'Shilshul u'bi'Zerikah, ve'la'Zeh be'Shilshul u'bi'Zerikah') - because otherwise, if it would be in line with the others, it would be a matter of 'la'Zeh bi'Zerikah, ve'la'Zeh bi'Zerikah', in which case, both should be permitted, if Rav holds that usage through the air only on the part of one does not forbid the other one to use that reshus.

7)

(a)Shmuel requires a ledge in the case of the pit in between two Chatzeros (even though they only use it via the air) - because we are speaking about Reshuyos de'Rabbanan (meaning that both are a Reshus ha'Yachid, and the Isur is only de'Rabbanan), which requires strengthening, whereas Rav Dimi quoting Rebbi Yochanan, permits both the B'nei Reshus ha'Rabim and the B'nei Reshus ha'Yachid to use a common Makom Petur without any Tikun, because they are Reshuyos d'Oraysa (i.e. carrying from one to the other is an Isur d'Oraysa), and whatever is d'Oraysa, does not need strengthening.

(b)If someone owns two houses on opposite sides of the street, Shmuel permits throwing from one to the other without a Tikun - because, whenever both are Reshuyos d'Oraysa, he is lenient, as we just explained.

(c)Rav is strict there (even though he is lenient here) - because we are speaking when the two houses (i.e. their windows or roofs) are on different levels, and there is reason to be afraid that his throw misses its mark, the object falls in the street, and he will go and fetch it.

8)

(a)One may place one's Eruv - in a Beis-Sha'ar of a Chatzer shel Yachid.

(b)One may place a Shituf Mavo'os in a Beis-Sha'ar or in other locations in which Eruvei Chatzeros cannot be placed.

(c)A Shituf Mavo'os must be placed where it is well-guarded. Consequently, it cannot be placed in the open in the Mavoy.

9)

(a)If the residents were sitting and eating when Shabbos comes in, the bread on the table may automatically be used for an Eruv - if the residents were sitting and eating in one of the houses of the Chatzer; and it may be used as a Shituf, if they were eating in the courtyard.

10)

(a)Someone who lives in one of the storehouses in the Chatzer, will forbid the other residents from carrying, if he does not participate in the Eruv.

(b)When Rebbi Yehudah says 'Im Yesh Sham Tefisas Yad shel Ba'al ha'Bayis, Eino Oser' - he means that if the owner of the Chatzer retains the right to place his things in one of the storehouses, then the person whom he authorized to live there, will not prevent the owner from carrying there (see Bartenura).

(c)Rebbi Yehudah's principle is restricted to storing something that is Muktzeh, but not to things that are not Muktzeh, and which the owner might moved on Shabbos.

11)

(a)When Rebbi (after referring to Buni'as ben Buni'as as someone who is worth a hundred Manah) said about a second man 'Clear the way for someone who is worth two hundred Manah' - Rebbi Yishmael b'Rebbi Yossi point out to him that Buni'as ben Buni'as was far wealthier than he thought, and that he owned 'a thousand ships at sea, and a thousand cities on dry land'.

(b)Rebbi response to this - was one of surprise; he should tell Buni'as' father that in the future, when sending his son before him, he should send him in clothes that befitted his status.

(c)Rebbi and Rebbi Akiva used to honor the rich - because of the Pasuk in Tehilim "Yeshev Olam" etc. - It is those who perform Chesed (the rich) providing the poor with their sustenance, that ensure the world's continuity.