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1) MISHNAH: DOFEN AKUMAH

(a) An open space of three Tefachim between the wall and the S'chach invalidates the S'chach.
(b) A skylight in a room is invalid if it four Amos away from the wall.
(c) A courtyard (three adjoining homes with a covered porch in front of each) will be invalid if the ceiling of the porch is four Amos.
(d) Similarly invalid is S'chach which is surrounded with four Amos of invalid S'chach.

(a) Question: Why did we need three illustrations of Dofen Akumah?
(b) Answer: Each case has a potential leniency which might cause us to limit the application of Dofen Akumah.

1. The case of the skylight might be lenient in that the walls were constructed to enclose a dwelling (unlike the walls of the homes in the courtyard which were not made to enclose a dwelling).
2. The Sukah with S'chach Pasul around the side might be lenient since those surrounding materials are fit for S'chach (their Pesul is owing to Ta'aseh ve'Lo min he'Asui).
3. We thus are taught that Dofen Akumah applies in all cases, even if the material of which the wall was made is not fit to be used as S'chach at all.

(c) (Rabah, reporting the view of Rabanan d'vei Rav) A three- Tefach break in the S'chach will invalidate the Sukah and four Tefachim of S'chach Pasul will interrupt the Sukah.
(d) Question (Rabah): But our Mishnah allows S'chach Pasul up to four Amos (while three Tefachim is only an open space)!?
(e) Answer (the Rabanan citing Rav and Shmuel): The Mishnah speaks of the distance to the *side* of the Sukah (Dofen Akumah).
(f) Question (Rabah): But what of the case of a Sukah with less than four Tefachim of S'chach Pasul next to less than three Tefachim of space.

1. Surely it should be Kosher.
2. If filling in that space with S'chach Pasul (which is more lenient than space, since the Shiur of S'chach Pasul is four Tefachim, while that of space is three) will invalidate the Sukah, then why should the *space* (which is stricter than S'chach Pasul) not likewise invalidate it?

(g) Answer (Rabanan): With that reasoning, you (Rabah) should ask yourself the same question (since according to you too, the Shiur of air is even more stringent vis-a-vis S'chach Pasul than it is according to us)!

(h) Question (Rabah): According to my opinion, four Amos is the fixed Shiur of S'chach Pasul that disqualifies a Sukah while the Shiur of space (three Tefachim) is unrelated to the Shiur of S'chach Pasul and they do not combine to disqualify the Sukah.

1. According to you, however, in whose opinion the four Tefachim of S'chach Pasul in the middle of the Sukah is not a given Shiur, but a Sevara (based on four Tefachim as a Makom Chashuv, ie. there is a significant area of four Tefachim without Kosher S'chach) then what is the difference if those four Tefachim are S'chach Pasul or space?
2. Hence Rabah's original question returns, if S'chach Pasul invalidates the Sukah, the certainly space should?

(i) Answer (Abaye): The case of a minimum Sukah, where the Shiurim are the same (since three Tefachim of either space or of S'chach Pasul will invalidate the Sukah) then space and S'chach Pasul should combine even by a larger Sukah?
(j) Question (Rabah): The invalidation of a minimum Sukah is not the result of the Shiur of S'chach Pasul or of space, but because there is lacking a Shiur Sukah!

(a) Question: Rabah's premise, that when Shiurim are distinct (such as four Amos for S'chach Pasul and three Tefachim for space) they do not combine, seems counter to the Mishnah in Keilim!?

1. The Shiur Tumah for cloth is three by three Tefachim; for sackcloth, four by four; for leather, five by five; and for reed mat, six by six.
2. Each of these will combine with the next in line (if sewn together) to become subject to the more lenient Shiur of Tumah (e.g. cloth with sackcloth combine to be subject to a Shiur of four Tefachim; sackcloth with leather combine to a Shiur of five; and leather and platted reeds to a Shiur of six Tefachim.

(b) Answer: They combine to become Tameh because sometimes they all have the same Shiur; whereas S'chach Pasul and space never have the same Shiur.

1. All of the above materials have the same Shiur (of one Tefach) when they are sewn as a patch into the saddle-cloth of a donkey.
2. Question: Of what use is a cloth of one Tefach!?
3. Answer (Resh Lakish citing R. Yanai): It can serve as a patch on the donkey.

(a) (R. Yehudah citing Shmuel) S'chach Pasul invalidates beyond four Amos, when its area four by four Tefachim.
(b) (Rav) The Pesul of S'chach Pasul is always four Amos (the position of Rabah in the Sura version).
(c) Question: What of the Mishnah, which allows a plank of four Tefachim!?

1. This is understandable according to Rav, since S'chach Pasul always invalidates with four Amos.
2. But for Shmuel, this should be S'chach Pasul!?

(d) Answer: That plank was at the side of the Sukah, within four Amos of the wall.
(e) Question (on Rav): What of the first version of the Beraisa discussed on 14a (that the Shiur for planks is four Tefachim)?

1. R. Meir holds that two planks combine (like cloths).
2. According to the first Lashon there, Rav holds that in the middle of the Sukah, four *Tefachim* invalidate the Sukah, then of what case is the Beraisa speaking?

i. If each plank is *four* Tefachim wide, then why should it be necessary to combine two planks?
ii. If they are *less* than four Tefachim then for Rav (who establishes the Machlokes between R. Meir and R. Yehudah in the Mishnah on 14a by planks of four Tefachim) anything *less than four* Tefachim is S'chach Kosher, no matter how many combine to form the S'chach!?

(f) Answer (Rav): The Beraisa speaks by planks of four Tefachim, that are placed at the side of the Sukah which will invalidate it if they total four Amos.