פָּחוֹת מֵאַרְבָּעָה – אֵין צָרִיךְ לְהָבִיא קוֹרָה אַחֶרֶת, אַרְבָּעָה – צָרִיךְ לְהָבִיא קוֹרָה אַחֶרֶת.

If there is a gap of less than four handbreadths, one need not bring another cross beam. However, if there is a gap of four handbreadths, one must bring another cross beam.

וְכֵן שְׁתֵּי קוֹרוֹת הַמַּתְאִימוֹת, לֹא בָּזוֹ כְּדֵי לְקַבֵּל אָרִיחַ, וְלֹא בָּזוֹ כְּדֵי לְקַבֵּל אָרִיחַ, אִם מְקַבְּלוֹת אָרִיחַ לְרָחְבּוֹ טֶפַח – אֵין צָרִיךְ לְהָבִיא קוֹרָה אַחֶרֶת, וְאִם לָאו – צָרִיךְ לְהָבִיא קוֹרָה אַחֶרֶת.

And similarly, if two parallel, extremely narrow cross beams are placed alongside each other, even though there is not sufficient width in this beam in order to receive and support a small brick, and there is not sufficient width in that beam in order to receive and support a small brick, if the two beams together can receive a small brick along its handbreadth width, one need not bring another cross beam to render the alleyway fit for one to carry within it. But if not, one is required to bring another cross beam.

רַבָּן שִׁמְעוֹן בֶּן גַּמְלִיאֵל אוֹמֵר: אִם מְקַבְּלוֹת אָרִיחַ לְאָרְכּוֹ שְׁלֹשָׁה טְפָחִים – אֵין צָרִיךְ לְהָבִיא קוֹרָה אַחֶרֶת, וְאִם לָאו – צָרִיךְ לְהָבִיא קוֹרָה אַחֶרֶת.

Rabban Shimon ben Gamliel says: If the two cross beams can receive a small brick along its length, which is three handbreadths, one need not bring another cross beam, but if not, one must bring another cross beam.

הָיוּ אַחַת לְמַעְלָה וְאַחַת לְמַטָּה, רַבִּי יוֹסֵי בְּרַבִּי יְהוּדָה אוֹמֵר: רוֹאִין הָעֶלְיוֹנָה כְּאִילּוּ הִיא לְמַטָּה וְאֶת הַתַּחְתּוֹנָה כְּאִילּוּ הִיא לְמַעְלָה, וּבִלְבַד שֶׁלֹּא תְּהֵא עֶלְיוֹנָה לְמַעְלָה מֵעֶשְׂרִים אַמָּה וְהַתַּחְתּוֹנָה לְמַטָּה מֵעֲשָׂרָה. הָא זֶה וָזֶה בְּתוֹךְ עֶשְׂרִים – אָמְרִינַן חֲבוֹט רְמִי, אַף עַל גַּב דְּלֵית בֵּיהּ טֶפַח!

Rabbi Yosei, son of Rabbi Yehuda, says: If these two narrow cross beams are placed at different heights, one above and one below, one considers the upper one as though it were below, and the lower one as though it were above, i.e., close together. If the two together are capable of supporting a small brick, they render the alleyway fit for one to carry within it, although they are not actually close to each other, provided that the upper cross beam is not above twenty cubits off the ground and the lower one is not below ten handbreadths off the ground, between which a cross beam renders an alleyway fit for one to carry within it. By inference, if both this beam and that beam are within twenty cubits, we say that the principle: Lower and cast the upper beam down even though there is not the width of a handbreadth in the upper beam. This is difficult according to Rava’s opinion, as he holds that the principle: Lower and cast, does not apply when the width of the upper crossbeam is less than a handbreadth.

אָמַר לֵיהּ, תְּרֵיץ וְאֵימָא הָכִי: וּבִלְבַד שֶׁלֹּא תְּהֵא עֶלְיוֹנָה לְמַעְלָה מֵעֶשְׂרִים אֶלָּא בְּתוֹךְ עֶשְׂרִים, וְהַתַּחְתּוֹנָה סְמוּכָה לָהּ בְּפָחוֹת מִשְּׁלֹשָׁה. אִי נַמִי: בִּלְבַד שֶׁלֹּא תְּהֵא תַּחְתּוֹנָה לְמַטָּה מֵעֲשָׂרָה אֶלָּא לְמַעְלָה מֵעֲשָׂרָה, וְעֶלְיוֹנָה סְמוּכָה לָהּ בְּפָחוֹת מִשְּׁלֹשָׁה. אֲבָל שְׁלֹשָׁה, כֵּיוָן דְּלֵית בֵּיהּ טֶפַח – לָא אָמְרִינַן חֲבוֹט רְמִי.

Rav Kahana said to him: Interpret the baraita and say as follows: Provided that the upper beam is not above twenty cubits but rather within twenty cubits and the lower one is adjacent to it, less than three handbreadths from it, as in that case they are joined due to the principle of lavud and not the principle of lower and cast. Alternatively, interpret the baraita as follows: Provided that the lower beam is not below ten handbreadths but rather above ten handbreadths and the upper beam is adjacent to it, less than three handbreadths from it. However, if the distance between the beams is three handbreadths, since there is not the width of one handbreadth in the beam, we do not say: Lower and cast the upper beam, and each beam is considered on its own.

״וְשֶׁצִּילָּתָהּ מְרוּבָּה מֵחַמָּתָהּ כְּשֵׁרָה״. הָא כִּי הֲדָדֵי – פְּסוּלָה, וְהָא תְּנַן בְּאִידָךְ פִּירְקִין: וְשֶׁחַמָּתָהּ מְרוּבָּה מִצִּילָּתָהּ – פְּסוּלָה, הָא כִּי הֲדָדֵי כְּשֵׁרָה!

§ The mishna continues: A sukka whose shade exceeds its sunlight is fit. From the formulation of the mishna, it can be inferred that if its shade and sunlight are equal, the sukka is unfit. The Gemara asks: But didn’t we learn in a mishna in another chapter in this tractate: A sukka whose sunlight exceeds its shade is unfit. From the formulation of that mishna it can be inferred that if its sunlight and shade are equal, the sukka is fit. The inferences of the two mishnayot are contradictory.

לָא קַשְׁיָא: כָּאן – מִלְּמַעְלָה, כָּאן – מִלְּמַטָּה. אָמַר רַב פַּפָּא: הַיְינוּ דְּאָמְרִי אֱינָשֵׁי: כְּזוּזָא מִלְּעֵיל כְּאִיסְתְּרָא מִלְּתַחַת:

The Gemara answers: This is not difficult. Here, where the inference was that when the sunlight and shade are equal the sukka is unfit, it is referring to the ratio of shade to sunlight from above, in the sukka roofing itself; and there, where the inference was that when the sunlight and shade are equal the sukka is fit, it is referring to the ratio of shade to sunlight from below, on the sukka floor. The two inferences are not contradictory, as the lower in the sukka one observes the light, the more diffused it is. Therefore, if the shade and the sunlight are equal on the floor of the sukka , clearly, the roofing is sufficiently dense and exceeds the gaps. Rav Pappa said: That is the meaning of the folk saying with regard to light: Like a zuz coin above, like an istera coin below.

״מְעוּבֶּה כְּמִין בַּיִת״. תָּנוּ רַבָּנַן: הַמְעוּבָּה כְּמִין בַּיִת, אַף עַל פִּי שֶׁאֵין הַכּוֹכָבִים נִרְאִין מִתּוֹכָהּ – כְּשֵׁרָה. אֵין כּוֹכָבֵי חַמָּה נִרְאִין מִתּוֹכָהּ, בֵּית שַׁמַּאי פּוֹסְלִין, וּבֵית הִלֵל מַכְשִׁירִין.

The mishna continues: A sukka whose roofing is thick like a type of house is fit. The Sages taught in a baraita : With regard to a sukka whose roofing is thick like a type of house, although it is so dense that the stars are not visible from within it, the sukka is fit. However, if it is so thick that the rays of the sun are also not visible from within it, Beit Shammai deem the sukka unfit and Beit Hillel deem it fit.

מתני׳ הָעוֹשֶׂה סוּכָּתוֹ בְּרֹאשׁ הָעֲגָלָה אוֹ בְּרֹאשׁ הַסְּפִינָה – כְּשֵׁרָה, וְעוֹלִין לָהּ בְּיוֹם טוֹב. בְּרֹאשׁ הָאִילָן אוֹ עַל גַּבֵּי גָּמָל – כְּשֵׁרָה, וְאֵין עוֹלִין לָהּ בְּיוֹם טוֹב.

In the case of one who establishes his sukka at the top of the wagon or at the top of the ship, although it is portable it is fit, as it is sufficient for a sukka to be a temporary residence. And one may ascend and enter it even on the first Festival day. In the case of one who establishes his sukka at the top of a tree or atop a camel, the sukka is fit, but one may not ascend and enter it on the first Festival day because the Sages prohibit climbing or using trees or animals on the Festival.

שְׁתַּיִם בָּאִילָן וְאַחַת בִּידֵי אָדָם, אוֹ שְׁתַּיִם בִּידֵי אָדָם וְאַחַת בָּאִילָן – כְּשֵׁרָה, וְאֵין עוֹלִין לָהּ בְּיוֹם טוֹב. שָׁלֹשׁ בִּידֵי אָדָם וְאַחַת בָּאִילָן – כְּשֵׁרָה, וְעוֹלִין לָהּ בְּיוֹם טוֹב.

If two of the walls of the sukka are in the tree and one is established on the ground by a person, or if two are established on the ground by a person and one is in the tree, the sukka is fit, but one may not ascend and enter it on the first Festival day because it is prohibited to use the tree. However, if three of the walls are established on the ground by a person and one is in the tree, then since it contains the minimum number of walls required, it is fit, and one may enter it on the first Festival day.