1)

(a)We have already learned that at the side of the Sukah, four Amos of Pasul Sechach invalidates the Sukah. Only three Tefachim of space is needed at the side to invalidate it.

(b)bearing in mind this Halachah, Dofen Akumah cannot mean - that we consider the wall as if a. it was bent and b. that it extended underneath the Sechach Pasul up to the Sechach Kasher (because, if it did, then the Sukah should be Kasher even if there was up to four Amos of space at the side, no less than if it was Sechach Pasul).

(c)The Tana gives three examples of Dofen Akumah. Despite having stated ...

1. ... the case of the broken ceiling of a house, he nevertheless found it necessary to add that of the covered stoep or passageway surrounding a courtyard - since (unlike like the walls of the house in the previous case) the walls of the houses surrounding the courtyard were not made for the courtyard (in which case 'Dofen Akumah' might not have applied).

2. ... the previous two cases, he still found it necessary to add the case of the Sukah with Pasul Sechach around the side - because we might otherwise have thought that we only say 'Dofen Akumah' by materials that are at least fit for Sechach and are only Pasul because of 'Ta'aseh v'Lo min he'Asuy'. Now we see that it applies in all cases (even if the material of which the wall was made is not eligible to be used as Sechach).

2)

(a)According to the Rabanan d'Bei Rav, four Tefachim of Pasul Sechach will invalidate the Sukah in the middle of the Sukah. Rabah queried them from our Mishnah - which validated a Sukah with up to four Amos of Pasul Sechach.

(b)They answered by citing Rav and Shmuel - who confined the Mishnah to Sechach Pasul at the side of the Sukah, which is Kasher because of 'Dofen Akumah' ...

(c)... whereas they were referring to Sechach Pasul in the middle of the Sukah, where four Tefachim invalidates ...

(d)... because it is a Makom Chashuv (and therefore constitutes a Chatzitzah). Note, that Rabah does not hold of the principle of Dofen Akumah.

3)

(a)Rabah attempted to disprove the Rabanan d'Bei Rav from the case of a Sukah with less than four Tefachim of Pasul Sechach next to less than three of space, which is Kasher. If filling in that space with Pasul Sechach (which is more lenient than space, since the Shi'ur of the former is four Tefachim, whereas that of the later is three) he argues, will invalidate the Sukah, then why should the space (which is stricter than Sechach Pasul) not likewise invalidate it (even if one did not fill it in with Pasul Sechach)?

(b)They retorted that, in that case, Rabah should ask himself the same question (seeing as according to him too, the Shi'ur of air is even more stringent vis-a-vis Sechach Pasul - than it is according to them) in a case where there was Sechach of less than four Amos, plus air less than three, which one subsequently filled in with Pasul Sechach.

4)

(a)According to his opinion, Rabah answers, four Amos is the fixed Shi'ur of Pasul Sechach that disqualifies a Sukah - irrespective of whether it is at the side or in the middle. Consequently, since its Shi'ur is not equivalent to that of space, they cannot combine to disqualify the Sukah (which explains why two and half Tefachim of space cannot complete the deficiency of two and a half Tefachim in four Amos of Sechach Pasul, whilst the same amount of Sechach Pasul can). Whereas according to Rabanan d'Bei Rav, in whose opinion the four Tefachim of Sechach Pasul in the middle of the Sukah is not a Shi'ur, but a S'vara (as we explained), the reason that four Tefachim of Pasul Sechach invalidates the Sukah is because there is a significant area of four Tefachim without Kasher Sechach. That being the case, what is the difference whether that area is filled with Pasul Sechach or with space? Hence Rabah's original Kashya: If Pasul Sechach invalidates the Sukah, Kal va'Chomer space!?

(b)Abaye queries Rabah from a small Sukah, the Shi'urim are the same, since three Tefachim of either space or of Pasul Sechach, will render the Sukah Pasul (in which case, they ought to combine even by a large Sukah)!?

(c)Rabah rejects Abaye's query however - on that the reason that three Tefachim of Pasul Sechach invalidates a small Sukah is not because of the Shi'ur of Pasul Sechach, but because the Sukah is too small.

5)

(a)The Mishnah in Kelim gives the Shi'ur Tum'ah of cloth as three by three Tefachim; of sackcloth, four by four; of leather, five by five; and of a mat made of platted reeds, six by six. The Tana is referring to - Tum'as Mishkav or Midras (e.g. if one designated it for a Zav to lie on).

6)

(a)This is based on a statement of Rebbi Shimon in a Beraisa, who declares any of them Tamei Mishkav, if one makes a patch of a square Tefach to sit on (Tum'as Moshav).

(b)Resh Lakish Amar Rebbi Yanai establishes this - where any one of them is sewn as a patch into the saddle-cloth of a donkey.

(c)When the Tana in Kelim says 'ha'Mekatze'a mi'Kulan Tefach al Tefach', he might also mean - that one makes a patch out of any combination of these materials.

7)

(a)The statement of Rabah, citing the Rabanan d'Bei Rav, currently under discussion, was learned in Sura. The Neherdeans cited a second Lashon in the name of Rav Yehudah - who cited Shmuel.

(b)Shmuel learns like the Rabanan d'Bei Rav, who invalidate a plank of four Tefachim in the middle of the Sukah and four Amos at the side - whereas Rav, in this Lashon, gives both Shi'urim as four Amos.

(c)Shmuel reconciles the Mishnah, which validates a plank of four Tefachim, with his own opinion - by establishing it at the side of the Sukah.

8)

(a)In the Beraisa that we quoted earlier in the Perek, the Tana Kama rules that two sheets combine - to make up four Amos, to render the Sukah Pasul because of Sechach Pasul, but not two planks.

(b)The two planks combine however - since the author of the Beraisa is Rebbi Yehudah, who does not hold of Gezeiras Tikrah.

(c)Rebbi Meir maintains - that two planks combine, just like two sheets.

(d)Assuming that the Beraisa is speaking about the middle of the Sukah, according to the second Lashon, Rav will explain - that Rebbi Meir is speaking about the two planks to combine to make up four Amos.

9)

(a)According to the first Lashon of Rav, the problem is what Rebbi means when he says that two planks combine in the middle of the Sukah, 'Mah Nafshach' ... if each one is four Tefachim, then they do not need to combine in order to be Pasul; whereas if it is less, then they are mere posts, so why do they combine to invalidate the Sukah?

(b)This not a problem according to Shmuel - in whose opinion Rebbi Meir and Rebbi Yehudah's Machlokes is by boards that are between three and four Tefachim (in which case, the second part of the 'Mah Nafshach' is not a problem).

(c)Rav resolves the problem - by establishing the Beraisa with regard to four Amos (not in the middle of the Sukah, but) at the side.

(d)In the Beraisa that we cited earlier, Rebbi Meir invalidates a Sukah comprising planks of less than four Tefachim - Rebbi Yehudah declares it Kasher.

10)

(a)Rebbi Meir concedes that the Sukah is Kasher - if the space between one plank and the next (which one fills with Kasher Sechach) is the same width as the plank (even if the planks are four Tefachim wide).

(b)This poses a problem on Rav's second Lashon - where he invalidates planks of four Tefachim in the middle of the Sukah.

(c)We answer this Kashya - by establishing the Beraisa by a Sukah that is exactly eight Amos (forty-eight Tefachim) where a plank of four Tefachim is placed on either side of the Sukah first (and then a space, a plank and a space, and so on. This results in a space of eight Tefachim in the middle, which one fills in with Sechach), leaving us with a Sukah with 'bent walls' of less than four Amos, and more than seven by seven Tefachim in the middle, which is Kasher.