while the perimeter of a square circumscribed by a circle is smaller than the circumference of that circle by half, i.e., if one adds half the perimeter of the square to the perimeter of the square, that is equal to the circumference of its circumscribing circle. Therefore, a circle with a circumference of twenty-four cubits would circumscribe a square with a perimeter of sixteen cubits, as prescribed by Rabbi Yoḥanan. The Gemara notes: And that is not the case, as we see that the circumference of the circumscribing circle is not that much. The actual circumference is closer to seventeen cubits. רִיבּוּעָא דְּנָפֵיק מִגּוֹ עִיגּוּלָא — פַּלְגָא. וְלָא הִיא, דְּהָא קָחָזֵינַן דְּלָא הָוֵי כּוּלֵּי הַאי.
§ Rabbi Levi said in the name of Rabbi Meir: With regard to two craftsmen’s booths, one within the other, as potters would build two booths, an inner one used as living quarters and an outer one for plying their craft and selling their wares, the inner one is not fit for fulfillment of the mitzva of sukka, since the potter resides there year-round and it is not evident during the Festival that he is residing there for the sake of the mitzva of sukka. And since it a permanent residence, it is also obligated in the mitzva of mezuza. And the outer booth is fit for fulfillment of the mitzva of sukka, since he does not reside there year-round, and when he resides there during the Festival it is evident that he is doing so for the sake of the mitzva. Since it is not designated as a year-round residence, but rather serves as an entrance to his residence and a passage for merchants and merchandise, it is not considered a residence and is not obligated in the mitzva of mezuza. אָמַר רַבִּי לֵוִי מִשּׁוּם רַבִּי מֵאִיר: שְׁתֵּי סוּכּוֹת שֶׁל יוֹצְרִים זוֹ לִפְנִים מִזּוֹ — הַפְּנִימִית אֵינָהּ סוּכָּה, וְחַיֶּיבֶת בִּמְזוּזָה. וְהַחִיצוֹנָה סוּכָּה, וּפְטוּרָה מִן הַמְּזוּזָה.
The Gemara asks: Why is the outer booth exempt from the mitzva of mezuza? Let the outer booth be considered like a gatehouse of the inner booth and therefore be obligated in the mitzva of mezuza. The Gemara answers: It is exempt because even the inner booth is not a permanent residence. It requires a mezuza because the potter resides there year-round; however, that alone does not render it a full-fledged residence that would obligate one to affix a mezuza to the outer booth as its gatehouse. וְאַמַּאי? תִּהְוֵי חִיצוֹנָה כְּבֵית שַׁעַר הַפְּנִימִית, וְתִתְחַיֵּיב בִּמְזוּזָה! מִשּׁוּם דְּלָא קְבִיעַ.
The Sages taught: The booths represented by the mnemonic: Gimmel, nun, beit, kaf, which stands for a booth of gentiles [goyim], a booth of women [nashim], a booth of domesticated animals [behema], a booth of Samaritans [Kutim], a booth of any sort, each is fit for use as a sukka, provided it is roofed in the standard sense. None of them is disqualified due to the one who constructed it or the purpose for which it was constructed. תָּנוּ רַבָּנַן: גַּנְבַּ״‎ךְ: סוּכַּת גּוֹיִם, סוּכַּת נָשִׁים, סוּכַּת בְּהֵמָה, סוּכַּת כּוּתִים סוּכָּה מִכׇּל מָקוֹם — כְּשֵׁרָה, וּבִלְבַד שֶׁתְּהֵא מְסוּכֶּכֶת כְּהִלְכָתָהּ.
The Gemara asks: What is the meaning of the term: In the standard sense? Rav Ḥisda said that it means: And provided that one established the booth to provide shade of a sukka from its roofing, it may be used to fulfill the mitzva of sukka. מַאי ״כְּהִלְכָתָהּ״? אָמַר רַב חִסְדָּא: וְהוּא שֶׁעֲשָׂאָהּ לְצֵל סוּכָּה.

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The Gemara asks: What does the phrase: A booth of any sort, come to include? What other booths are included in this generalization? The Gemara answers: It comes to include the booths listed in another baraita with the mnemonic: Reish, kuf, beit, shin, as the Sages taught: The booth known by the mnemonic reish, kuf, beit, shin, which stands for the booth of shepherds [ro’im], the booth of fig driers [kayyatzim], the booth of guards of fields [burganin], the booth of the guards of produce [shomerei peirot], a booth of any sort, each is fit, provided it is roofed in the standard sense. ״מִכׇּל מָקוֹם״ לְאֵתוֹיֵי מַאי? לְאֵתוֹיֵי: סוּכַּת רַקְבַּ״‎שׁ. דְּתָנוּ רַבָּנַן: סוּכַּת רַקְבַּ״‎שׁ: סוּכַּת רוֹעִים, סוּכַּת קַיָּיצִים סוּכַּת בּוּרְגָּנִין סוּכַּת שׁוֹמְרֵי פֵירוֹת, סוּכָּה מִכׇּל מָקוֹם — כְּשֵׁרָה, וּבִלְבַד שֶׁתְּהֵא מְסוּכֶּכֶת כְּהִלְכָתָהּ.
The Gemara asks again: What is the meaning of the term: In the standard sense? Rav Ḥisda said that it means: And provided that one established the booth to provide shade of a sukka, it may be used to fulfill the mitzva of sukka. מַאי ״כְּהִלְכָתָהּ״? אָמַר רַב חִסְדָּא: וְהוּא שֶׁעֲשָׂאָהּ לְצֵל סוּכָּה.
The Gemara asks: What does the phrase: A booth of any sort, come to include? The Gemara answers: It comes to include the booths listed in the first baraita cited above with the mnemonic gimmel, nun, beit, kaf. ״מִכׇּל מָקוֹם״ לְאֵתוֹיֵי מַאי? לְאֵתוֹיֵי: סוּכַּת גַּנְבַּ״‎ךְ.
The Gemara explains: This tanna who taught and detailed the halakhot of booths of gimmel, nun, beit, kaf did so because the fitness of the booths of gimmel, nun, beit, kaf for use in fulfilling the mitzva of sukka is powerful and more obvious to him because they are permanent structures, even though their builders are not obligated in the mitzva. And he taught: Booths of any sort, to include the booths of reish, kuf, beit, shin, which, although they are seasonal and not permanent structures, may still be used to fulfill the mitzva of sukka. הַאי תַּנָּא דְּגַנְבַּ״‎ךְ, אַלִּימָא לֵיהּ גַּנְבַּ״‎ךְ מִשּׁוּם דִּקְבִיעִי, וְקָא תָּנֵא ״מִכׇּל מָקוֹם״ לְאֵתוֹיֵי רַקְבַּ״‎שׁ, דְּלָא קְבִיעִי.
And that other tanna who taught and detailed the halakhot of booths of reish, kuf, beit, shin did so because the fitness of the booths of reish, kuf, beit, shin for use in fulfilling the mitzva of sukka is powerful and more obvious to him because those who constructed the booths are obligated in the mitzva of sukka. And he taught: Booths of any sort, to include the booths of gimmel, nun, beit, kaf, which, although those who constructed them are not obligated in the mitzva, may still be used to fulfill the mitzva of sukka. וְהַאי תַּנָּא דְּרַקְבַּ״‎שׁ, אַלִּימָא לֵיהּ רַקְבַּ״‎שׁ, דִּבְנֵי חִיּוּבָא נִינְהוּ, וְתָנֵא ״מִכׇּל מָקוֹם״ לְאֵתוֹיֵי גַּנְבַּ״‎ךְ, דְּלָאו בְּנֵי חִיּוּבָא נִינְהוּ.