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1)

(a) If we establish the Mishnah in 'Kol Gagos' like Rebbi (who requires two boards for a Chatzer), like Rebbi Zeira ('be'Nichnasin Koslei Ketanah li'Gedolah'), and like Ravina ('be'Muflagin mi'Kosel Zeh bi'Shenayim, u'mi'Kosel Zeh be'Arba'ah') and not like Rebbi Yossi (who requires a Lechi of at least *three* Tefachim) - then why did the Beraisa find it necessary to say 'Ketanah be'Eser, Gedolah be'Achas-Esrei'? To permit the large Chatzer, ten Amos and two Tefachim (see Tosfos DH 'u'Sh'nei') will suffice, whereas to forbid the small Chatzer, any amount over and above three Tefachim on either side will forbid it, so why establish the case when the large Chatzer is just one Amah in excess of the small one, conveying the possibility that there are three Tefachim on either side?

(b) It would be better to establish Rebbi and the Beraisa like Rebbi Yossi (and not like Rebbi Zeira and Ravina) - because then we will need the large Chatzer to be eleven Amos (one Amah more than the small Chatzer), in order to have two boards (like Rebbi), each one of three Tefachim (like Rebbi Yossi).

(c) Once we establish the Mishnah in this way - we have clear proof that 'Nir'eh mi'Bachutz ve'Shaveh mi'Bifenim Eino Nidon Mishum Lechi' (Otherwise, why is the small Chatzer forbidden?).

(a) Rav Huna is quoted as saying that a Lechi less than four Amos long, which continues with the wall of the Mavuy (but is narrower than it) - has the Din of a Lechi, but a Lechi of four Amos is considered part of the Mavoy, and does *not*. Consequently, one may only carry up to its most innermost point.

(b) Rav Yosef learnt the following three things from Rav Huna's statement -

1.. that carrying beyond the innermost point of the Lechi is forbidden;
2. that the minimum length of a Mavoy is four Amos (and not four Tefachim);
3. that 'Nir'eh mi'Bachutz, ve'Shaveh mi'Bifenim, Nidon Mishum Lechi'.

(c) When Rav Yosef ruled that 'Nir'eh mi'Bachutz, ve'Shaveh mi'Bifenim Nidon Mishum Lechi', he was not worried about the Mishnah in Kol Gagos and the Beraisa quoted above - because he followed the Beraisa of Rebbi Chiya (on the previous Amud), which holds like that.

(a) 'Pasei Bira'os' - are four posts, each one of one Amah by one Amah placed in the Reshus ha'Rabim thirteen and a third Amos apart (according to Rebbi Yehudah).y flank a water pit of at least ten Tefachim deep, and permit drawing water from the pit (a Reshus ha'Yachid) and drinking it, in what had previously been a Reshus ha'Rabim.

(b) The Gemara thought to make a Kal va'Chomer from Pasei Bira'os - if Pasei Bira'os, which is *not* invalid despite the length of the breaches exceeding that of the posts - yet it *is* invalidated if its length exceeds thirteen and a third Amos; then a Mavoy, which is invalid when the length of its breaches exceeds that of its wall, should certainly be invalid (even according to Rebbi Yehudah) when its entrance exceeds thirteen and a third Amos.

(c) Maybe, argues the Gemara, it is *because* Chazal permit Pasei Bira'os even when the breach exceeds the length of the posts - that they did not want to add another leniency, and to permit one that is more than thirteen and a third Amos; whereas a Mavoy, where they are *strict* with regard to where the length of the breach exceeds that of the wall, they may well be lenient (according to Rebbi Yehudah) and permit an entrance that is even more than thirteen and a third Amos long. Alternatively, we might say that it is by Pasei Bira'os, where Chazal are lenient with regard to where the breach exceeds the posts, that they are also lenient with regard to the Shiur of thirteen and a third; whereas by Mavoy, where they are strict with regard to the former, we cannot assume that they will be lenient with regard to the latter, perhaps there the maximum Shiur (according to Rebbi Yehudah), will be anything between ten and thirteen and a third Amos).

(a) A vertical pole in the middle of an entrance that is twenty Amos wide cannot permit carrying in the Mavoy (in spite of Levi's Beraisa) - because the space on either side of the pole will negate the pole (which is why Levi rules not like that Beraisa).

(b) Levi therefore, gives two ways of rectifying it - either by placing a board of ten Tefachim tall and four Amos long in between its two opposite walls and parallel to them (In this way, one now has two Mavoyos, each with its own entrance of ten Amos); or, if the entrance is fifteen Amos wide, he takes a board of three Amos, and places it adjacent to the wall, but at a distance of two Amos (He does the same on the opposite side, if the entrance is twenty Amos wide). In this way, he has effectively blocked the first two Amos (because of Omed Merubeh al ha'Parutz), and is now left with an opeming of only ten Amos.

5)

(a) Arranging a plank of one and a half Amos adjacent to one of the walls, and a second plank of one and a half Amos next to it, but at a distance of two and a half Amos, may have been effective - due to the fact that we would combine the two planks to negate the two and a half Amos in between them, creating a wall of five and a half Amos, and leaving an opening of less than ten.

(b) It may well be that 'Omed Merubeh al ha'Parutz is effective even if the Omed is in two places (and we have to combine them) - Here it will nevertheless be ineffective, because the space on either side of the second plank (each of which is in excess of the plank) combine to negate it.

(c) The Gemara does not suggest placing a plank of one Amah adjacent to the wall, a second plank at an interval of an Amah and a third plank at an interval of an Amah - not necessarily because 'Parutz ke'Omed Asur', but because the Amah space next to the plank combines with the space on the other side of the third plank (which is in excess of the plank) to negate it (even though the Amah space is not in excess of the Amah plank).

(a) The Gemara did not suggest placing a plank one and a half Amos wide, one Amah away from the wall, and another plank one and a half Amos wide, one Amah away from the first plank ...

1. ... because Chazal did not want to trouble him to do this.
2. space on either side will not combine here to negate the plank in the middle - because neither space exceeds the width of the plank.

(b) We are not worried that, in the case of Rav Yehudah (where one placed a three Amah board at a distance of two Amos), people may stop using the original entrance, and start using the small two Amah entrance at the side - because people do not usually exchange a large entrance for a smaller one.

(c) Our case is not comparable to that of Rebbi Ami and Rebbi Asi - they *did* invalidate a Mavoy whose side wall had a breach of three Tefachim at the point where it was adjacent to the entrance - because *there*, the breach enabled people to take a short cut, in which case, people *do* tend to avail themselves of the smaller one.

(a) 'Or ha'Asla ve'Chalal She'lo, Mitztarfin be'Tefach' - means that the leather of the seat of (a sort of portable toilet) combines with the hole in the middle to make up a Tefach. This means that it has the Din of an Ohel (in spite of the hole), to transmit Tum'as Mes to whatever is underneath it.

(b) No! They are not arguing over the Shiur of a Tefach: Ravin, who gives the Shiur as one and a half finger-breadths on either side, and one finger- breadth in the middle for the hole - is speaking about *thumb*-breadths; whereas Rav Dimi, who gives the Shiur as two finger-breadths of leather seating on either side, and a hole of two Tefachim in the middle - speaks about finger-breadths that are gauged by the little *finger* (the Amah is the same, but the fingers are not).

(c) Abaye explains that, according to Rav Dimi (who says two Tefachim on either side and two Tefachim in the middle), the Omed on either side will combine to negate the Parutz in the middle, according to Ravin, they do not - unless they each side exceeds the Parutz (which explains why he gives the Shiur as one and a half Tefachim on either side, and a Tefach in the middle, and not one and a third Tefachim on either side and one and a third in the middle).

(d) If Abaye was right, argued Rav Dimi, then he (Rav Dimi) ought to have given the Shiur as one and two thirds Tefachim on either side, and two and a third in the middle. Since he gave the Shiur as *two Tefachim* on either side and *two* in the middle, he clearly holds 'Parutz La'av ke'Omed'; whereas Ravin holds 'Parutz ke'Omed', which is why he needs to explain that the Shiur on each of the two sides exceeded the Shiur of the hole in the middle (in order to negate the hole).