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הֶכְשֵׁר מָבוֹי, בֵּית שַׁמַּאי אוֹמְרִים, לֶחִי וְקוֹרָה, וּבֵית הִלֵּל אוֹמְרִים, לֶחִי אוֹ קוֹרָה. רַבִּי אֱלִיעֶזֶר אוֹמֵר, לְחָיַיִן. מִשּׁוּם רַבִּי יִשְׁמָעֵאל אָמַר תַּלְמִיד אֶחָד לִפְנֵי רַבִּי עֲקִיבָא, לֹא נֶחְלְקוּ בֵּית שַׁמַּאי וּבֵית הִלֵּל עַל מָבוֹי שֶׁהוּא פָחוֹת מֵאַרְבַּע אַמּוֹת, שֶׁהוּא אוֹ בְלֶחִי אוֹ בְקוֹרָה. עַל מַה נֶּחְלְקוּ, עַל רָחָב מֵאַרְבַּע אַמּוֹת וְעַד עֶשֶׂר, שֶׁבֵּית שַׁמַּאי אוֹמְרִים, לֶחִי וְקוֹרָה, וּבֵית הִלֵּל אוֹמְרִים, אוֹ לֶחִי אוֹ קוֹרָה. אָמַר רַבִּי עֲקִיבָא, עַל זֶה וְעַל זֶה נֶחֱלָקוּ:

Что требуется для мавуи [чтобы его можно было пронести через шитуф (партнерство)] —Бет Шаммай говорит: Лечи и Коре. [Требуются оба, Бет Гилель считает, что по закону Торы требуется четыре полных раздела, а галаха леМошех миСинай («закон Моисею на Синае») разрешает лечи и кора как четвертый.] И Бет Гилель говорит: либо лечи, либо кора [Закон Торы, требующий трех полных перегородок и не более, и галаху леМошех миСинай, добавляющую четвертую через лечи любого размера или через коре как знак разделения. «Мавуи» - это мавуи, закрытые с трех сторон и открытые для общественного пользования с четвертой, длина которых больше ширины. Ибо, если длина и ширина были бы равны, это было бы как прорванный болтун (двор), открывающийся в общественное достояние, требующий доску (pas) несколько длиннее, чем четыре локтя, или две доски любого размера. Аналогично, чатер, взломанный в открытом доступе, считается мавуи и допускается с лечи или кореем. А мавуи, разрешенные через лечи, отличаются от мавуи, разрешенной через коре. Для мавуи, разрешенного через лечи, считается наличие четырех разделов, и тот, кто бросает в него что-либо из общественного достояния, несет ответственность, в то время как мавуи, разрешенное через коре, даже если ему разрешено переносить его через шитуф, не является абсолютным частный домен, и тот, кто выбрасывает что-то в него из общественного достояния, не несет ответственности, поскольку принято считать, что коре служит знаком (отличающим мавуи от общественного достояния), а лечи - разделом.] Р. Элиэзер говорит: два лечи. [Он держит с Бет Шаммай и требует лечи с обеих сторон. Галаха не соответствует Р. Элиэзеру.] На имя Р. Ишмаэля было сказано, что определенный ученик [Р. Меир] сказал в присутствии Р. Акивы: Бет Шаммай и Бет Гилель не различаются в отношении мавуи [ширина] которого составляет менее четырех локтей, [оба соглашаются], что либо лечи, либо корех [достаточно] , Где они отличаются? Где это от четырех до десяти локтей, Бет Шаммай требует Лечи и Коре, и Бет Гилель, Лечи или Коре. Р. Акива сказал: они различаются по отношению к обоим. [И первая танна также утверждает, что не проводится никакого различия между широким и узким. Талмуд объясняет, что они (первая танна и Р. Акива) отличаются по мавуи шириной менее четырех тефахимов, один из которых считает, что не требуется ни лечи, ни кора, а другой - что требуется лечи или корех. И из их заявлений не ясно, кто этого требует, а кто нет.]

Bartenura on Mishnah Eruvin

הכשר מבוי – its preparation and designation of the alley to carry within it through a combination of alleys.
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English Explanation of Mishnah Eruvin

Introduction In this mishnah Bet Shammai and Bet Hillel debate how one validates an alley such that it is permitted to carry within it.
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Bartenura on Mishnah Eruvin

ב"ש אומרים לחי וקורה – both of them (i.e., a stake and a beam) are necessary and that they hold from the Torah that we require four complete partitions and it was brought as a traditional interpretation of a written law [dating back to Moses as delivered from Sinai) and the particular application is a square-block of a stake and a crossbeam.
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English Explanation of Mishnah Eruvin

There are two levels of debates in this mishnah. There is a debate between Bet Shammai, Bet Hillel and R. Eliezer about how one validates an alley. The second debate is between Rabbi Ishmael, as presented by one of his students, and Rabbi Akiva over what was the actual dispute between Bet Hillel and Bet Shammai.
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Bartenura on Mishnah Eruvin

ובה"א או לחי או קור – for from the Torah three [complete] partitions are required and further nothing else and it was brought as a traditional interpretation of a written law [dating back to Moses as delivered from Sinai] either a stake of some small size or a beam to be recognized as a partition. And the alley that we are speaking of here is a closed alley from three directions and the fourth direction is open to the public domain and its length is greater than its width, for it its length was like its width, it would be like a courtyard whose opening was breached to the public domain and one would need a board/bar of four handbreadths and a bit more (see Talmud Eruvin 5a) or two boards/bars of a bit of size and similarly, a courtyard which was breached into the public domain and its length was greater than its width, it is judged to be an alley which is permitted with a stake or a board. But an alley that was made valid with a stake is different than an alley made valid with a beam, for an alley which was made valid with a stake, it is as if it has four partitions and a person who throws [something] from the public domain into it is liable, but an alley made valid with a beam, even though it is permissible to carry within it through a combination, it is not like a completely private domain and a person who throws [something] from the public domain into it is exempt, for we hold that a beam is because of recognition and a stake because of a partition.
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English Explanation of Mishnah Eruvin

The validation of an alley: Bet Shammai says: a side-post and a crossbeam. And Bet Hillel says: either a side-post or a crossbeam. R. Eliezer says: two side-posts. In this version, Bet Shammai says that the alley must have the side-post and a crossbeam in order to carry in it, whereas Bet Hillel says that either is sufficient. Rabbi Eliezer says that the crossbeam is irrelevant and that what are needed are two side-posts.
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Bartenura on Mishnah Eruvin

רבי אליעזר אומר לחיים – he holds like the School of Shammai that requires a stake from one side and the other, but the Halakha is not according to Rabbi Eliezer.
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English Explanation of Mishnah Eruvin

In the name of Rabbi Ishmael one student stated in front of Rabbi Akiva: Bet Shammai and Bet Hillel did not disagree concerning an alley that was less than four cubits [in width], that it [may be validated] by either a side-post or a crossbeam. About what did they disagree? In the case of one that was wider than four, and narrower than ten cubits: Bet Shammai says: both a side-post and a crossbeam [are required] and Bet Hillel says: either a side-post or a crossbeam. Rabbi Akiva said they disagree about both cases. In this statement, a student of Rabbi Ishmael’s comes in front of Rabbi Akiva to present a more limited version of the debate. According to this version, both houses agree that if the alley is less than four cubits wide, either a side-post or crossbeam is sufficient. Probably the reason that Bet Shammai agrees in this case is that if the entrance is narrower it is clearer that this is not a public domain. The debate is only when the entrance is between four and ten cubits wide. Rabbi Akiva rejects this version and rules that in both cases, Bet Hillel and Bet Shammai disagree. The first section of the mishnah is therefore representative of Rabbi Akiva’s position. As an aside, we can learn a fair amount of rabbinic history from this mishnah. Rabbi Akiva and Rabbi Ishmael were the heads of competing academies, some time in the early part of the second century CE. Both academies produced midrashic compilations that while similar to each, have notable differences. This mishnah is one indicator that Rabbi Akiva’s academy became more dominant, perhaps especially so after Rabbi Ishmael’s demise. Rabbi Ishmael’s students come in front of Rabbi Akiva to see if their traditions are acceptable in his eyes. This is a sign of their turning to his authority, probably after their own master’s death. Rabbi Akiva rejects the Ishmaelian tradition and the anonymous piece which opens the mishnah is taught according to Rabbi Akiva. Indeed, the Mishnah is a work produced by the Akivan academy, a work in which Akiva’s students, most notably Rabbis Judah, Meir, Shimon and Yose dominate.
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Bartenura on Mishnah Eruvin

אמר תלמיד אחד – He is Rabbi Meir.
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Bartenura on Mishnah Eruvin

שהוא פחות מארבע אמות – the width of its opening.
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Bartenura on Mishnah Eruvin

אמר רבי עקיבא על זה ועל זה נחלקו – The first Tanna/teacher also this is how it should be read: It does distinguish between wide and narrow and the Talmud explains that there is a difference between them: An alley that has less than four handbreadths in the width of its opening – one of them holds that it requires neither a stake nor a beam and the other one holds a stake or a beam but it is not made clear from their words which of them holds that it is required and which of them holds that it is not required.
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