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1)

(a) Abaye holds, that someone who throws a bee-hive that is ten Tefachim tall and six Tefachim in diameter, is Patur, because he has thrown a Reshus, and not an object. If the object is less than six Tefachim in diameter, he has thrown an object, for which he is Chayav.

(b) A square object must be four by four Tefachim in order to become a Reshus. Consequently, for throwing any object less than that, one will be Chayav.
Now for a circle to contain a square of of four by four Tefachim, it needs a diameter of five and three fifths Tefachim, which means that anything with a larger diameter than that, will be termed a Reshus, for which one will be Patur.
Consequently, when Abaye is Mechayev for throwing a Kaveres with a diameter of between five and three fifths and six Tefachim, he must mean Chayav (meaning forbidden) mi'de'Rabbanan, for which he will not be Chayav Chatas.

(c) Rava maintains that, even if the Kaveres is less than six Tefachim in diameter, he will be Patur, because some of the reeds are bound to protrude upwards above ten Tefachim (but if the Kaveres was less than ten Tefachim, he would always be Chayav.

(a) If the Kaveres landed upside down, then he would be Patur even if it had a diameter of less than six Tefachim - provided it was at least seven and a half Tefachim, because, since the Kaveres lands with the bottom of its walls facing the ground, the moment it reaches within three Tefachim of the ground, the principle of 'Levud' would apply. This means that we consider the walls as if they extended to the ground. And at that moment, the top of the Keveres is more than ten Tefachim from the ground. Consequently, he will be Patur.

(b) It does not need to be seven and a half Tefachim tall; it will suffice if it is a fraction more than seven Tefachim and a Mashehu.

(c) Rav Ashi is Mechayev in the latter case, because, in his opinion, the principle of 'Levud' only applies to walls whose chief purpose is to be joined to the ground - and the walls of a Kaveres are not meant to be joined to the ground, only to protect the honey that it contains.

(a) A board of between three and nine Amos in the Reshus ha'Rabim is considered a Karmelis, since it cannot be used easily by the public who use the street. Therefore, if someone throws onto it, he will be Patur.

(b) If however, the board is nine Tefachim high (specifically nine, according to Rashi), then (like a board of less than three Tefachim, which people walk on) it is considered part of the Reshus ha'Rabim, because people use it easily, to adjust their loads on it.

(c) Rava maintains that a hole of nine Tefachim is different, because it is not easily used and in his opinion, 'Tashmish Al Yedei ha'Dechak, Lo Shemei Tashmish'.

(d) 've'Chen be'Guma' in the Beraisa, refers specifically to the Reisha, which gaves a box of ten Tefachim tall and four by four Tefachim by four which is standing in the Reshus ha'Rabim, the Din of a Reshus ha'Yachid.

4)

(a) 'le'Ma'alah mi'Yud' regarding the pit in the Reshus ha'Rabim, refers not to above ten Tefachim in a pit of *more* than ten Tefachim (since in a pit of ten Tefachim, there is no difference between above ten Tefachim and below ten Tefachim), but to a pit of *less* than ten Tefachim. His Eiruv is an Eiruv because one has fulfilled the requirement of himself (who is standing in a Reshus ha'Rabim) and the Eiruv, being in the same Reshus.

(b) This clashes with Rava, who holds that a pit of nine Tefachim has the Din of a Karmelis, because 'Tashmish Al Yedei ha'Dechak, Lo Shmei Tashmish'?

(c) He and his Eiruv are in a Karmelis means that we are not speaking about a pit in a Reshus ha'Rabim, but a pit in a Bik'ah, which is a Karmelis. Consequently, both he and the Eiruv are in a Karmelis. The reason that the Beraisa refers to it as a Reshus ha'Rabim, is because it is not in a Reshus ha'Yachid (because if it would be, there would be no difference between a pit of more than ten Tefachim and one of less).

(d) Rebbi maintains that the Rabbanan's decrees do not apply to Bein ha'Shamashos (between Sheki'ah and nightfall). Consequently, in view of the fact that Eiruvei Techumin come into effect at Bein Hashemashos, the Beraisa can even speak when the pit is in a Reshus ha'Rabim, and when nine Tefachim in a pit is a Karmelis (like Rava); nevertheless, his Eiruv will be valid, because to carry from a Karmelis to a Reshus ha'Rabim is only Asur mi'de'Rabbanan, and Isurim de'Rabbanan do not apply then.

(a) One 'Rekek Mayim' applies to a pool (a large puddle) of water in the summer and the other, to the winter. We might have thought that the pool is counted as part of the Reshus ha'Rabim in the summer, because people will enter it in order to cool down. Or that it is only in the winter that it is considered part of the Reshus ha'Rabim, because people will enter it in order to clean themselves from the mud that abounds then.

(b) By repeating 'Mehaleches Bo', the Beraisa is stressing that it is only 'Hiluch Al Yedei ha'Dechak' that is considered Hiluch, but not 'Tashmish Al Yedei ha'Dechak' - like Rava contends.

7)

(a) Someone who stands on a threshold which is either a Reshus ha'Rabim or a Reshus ha'Yachid, and hands something to - or receives from - a person in the opposite Reshus, he will be Chayav. If the threshold is a Karmelis, then it is Asur mi'de'Rabbanan to do so.
The Beraisa which permits someone to do just that, must be speaking about a threshold which is a Makom Petur.

(b) The threshold of a Reshus ha'Rabim is for example, a threshold which has no roof, which is within three Tefachim of the ground, and which is situated by the opening of a Mavuy outside its Lechi (the vertical plank which serves as an Eiruv).

(c) A threshold which is a Reshus ha'Yachid is the equivalent case, but when the threshold either has a roof, or is situated inside the Lechi, or if it is more than ten Tefachim high and four by four Tefachim. Whereas the threshold will be a Karmelis if it is between three and ten Tefachim high.

(d) Rava is Mechayev someone who carries in the Reshus ha'Rabim above ten Tefachim, because he did not make a Hanachah in the Makom Petur. Whereas in the case in the Beraisa, where he made a Hanachah (in the Mekom Petur where he is standing, when he took the object from the one person to give to the other), even Rava will agree that he is Patur - although mi'de'Rabbanan, it is Asur to do so.