The gemara brings two more explanations regarding the Levite cities to explain how the empty space around the city comes out to a quarter – how is it measured and a quarter of what? Some questions are raised on some of the explanations. The mishna brings a debate between Rabbi Meir and the rabbis. According to Rabbi Meir, the 2,000 cubits of the techum are measured from 70.67 cubits outside the city. According to the rabbis, this is not the case – it is measured from the city borders but the 70.67 measurement is used to determine if two cities are considered as one for techum. There is a debate between emoraim whether it is a space of 70.67 per city or 70.67 all together. There is a situation where one city can combine two others that are on either side. What is that situation? The mishna begins to describe exactly how they did the measuring for the city.
Eruvin 57
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Eruvin 57
דַּל אַרְבַּע דִּתְחוּמִין וְאַרְבַּע דִּקְרָנוֹת. כַּמָּה הָוֵי? תְּמָנְיָא.
Subtract four million square cubits of the extended boundary for the area of the open space, which is a thousand cubits by a thousand cubits on each side, and an additional four million square cubits from the corners, a thousand cubits by a thousand cubits in each corner, which are connected to the open space. How much is the sum total? It is eight million square cubits.
תִּילְתָּא הָווּ! מִי סָבְרַתְּ בְּרִבּוּעָא קָאָמַר? בְּעִיגּוּלָא קָאָמַר. כַּמָּה מְרוּבָּע יָתֵר עַל הֶעָגוֹל — רְבִיעַ, דַּל רְבִיעַ — פָּשׁוּ לַהּ שִׁיתָּא. וְשִׁיתָּא מֵעֶשְׂרִים וְאַרְבַּע, רִיבְעָא הָוֵי.
The Gemara asks: According to this calculation, the eight million square cubits of open space are one-third of the total area of the extended boundary, which is twenty-four million square cubits. The Gemara answers as it answered above: Do you think that this halakha was stated with regard to a square city? It was stated with regard to a round city. How much larger is the area of a square than the area of a circle? It is one quarter of the area of the circle. Subtract one quarter from the eight million square cubits of open space, and six million square cubits are left; and six is precisely one quarter of twenty-four.
רָבִינָא אָמַר: מַאי רְבִיעַ, רְבִיעַ דִּתְחוּמִין.
Ravina said: What is the meaning of the statement that the open space is one quarter? It is one quarter of the boundary. This halakha was indeed stated with regard to a square city. However, there is open space only along the sides of the city but not at its corners. Accordingly, a city that is two thousand cubits by two thousand cubits has a total extended boundary of thirty-two million square cubits, of which eight million square cubits, two thousand cubits by one thousand cubits on each side, is open space. The open space is thus one quarter of the total.
רַב אָשֵׁי אָמַר: מַאי רְבִיעַ, רְבִיעַ דִּקְרָנוֹת.
Rav Ashi said the opposite: What is the meaning of the statement that the open space is one quarter of the total extended boundary? One quarter of the corners. Open space is granted only in the corners, and not along the sides. Accordingly, the open space is one thousand cubits by a thousand cubits in each corner, for a total of four million square cubits. The total extended boundary in each corner is two thousand cubits by two thousand cubits, or four million square cubits per corner, which equals a grand total of sixteen million square cubits. Consequently, the open space is one quarter of the total extended boundary.
אֲמַר לֵיהּ רָבִינָא לְרַב אָשֵׁי: וְהָא ״סָבִיב״ כְּתִיב!
Ravina said to Rav Ashi: Isn’t it written in the verse: “And the open spaces of the cities, that you shall give to the Levites, shall be from the wall of the city and outward one thousand cubits around” (Numbers 35:4)? The verse indicates that the city is provided with open space on all sides and not merely at its corners
מַאי ״סָבִיב״ — סָבִיב דִּקְרָנוֹת, דְּאִי לָא תֵּימָא הָכִי, גַּבֵּי עוֹלָה דִּכְתִיב: ״וְזָרְקוּ (בְּנֵי אַהֲרֹן) אֶת הַדָּם עַל הַמִּזְבֵּחַ סָבִיב״, הָכִי נָמֵי סָבִיב מַמָּשׁ?! אֶלָּא מַאי ״סָבִיב״ — סָבִיב דִּקְרָנוֹת, הָכִי נָמֵי: מַאי ״סָבִיב״ — סָבִיב דִּקְרָנוֹת.
Rav Ashi responded: What is the meaning of around? Around at the corners, i.e., an open space of this size is provided at each corner. As, if you do not say so, that the area of the corners is also called around, with regard to the burnt-offering, as it is written: “And they shall sprinkle the blood around upon the altar” (Leviticus 1:5), here, too, will you say that the blood must be sprinkled literally “around” the altar on all sides? The blood is sprinkled only upon the corners of the altar. Rather, what is the meaning of around? Around the corners, i.e., the mitzva is to sprinkle the blood at the corners, and this is considered sprinkling blood “around upon the altar.” Here too, with regard to the open space of the cities of the Levites, what is the meaning of around? Around the corners.
אֲמַר לֵיהּ רַב חֲבִיבִי מָחוֹזְנָאָה לְרַב אָשֵׁי: וְהָא אִיכָּא מוּרְשָׁא דְקַרְנָתָא!
The Gemara returns to its previous statement that the open space around a city of the Levites is one quarter of the total extended boundary when the city is round. It questions this statement based upon the mishna’s ruling that the boundaries of a city are always delineated as a square. Rav Ḥavivi from Meḥoza said to Rav Ashi: But aren’t there the protrusions of the corners? How can there be a thousand cubits of open space on each side; when the city is squared, the corners of the square protrude into the open space, thus reducing its area?
בְּמָתָא עִיגּוּלְתָּא. וְהָא רַיבְּעוּהָ? אֵימוֹר דְּאָמְרִינַן חֲזֵינַן כְּמַאן דִּמְרַבְּעָא. רַבּוֹעֵי וַדַּאי מִי מְרַבַּעְנָא?!
Rav Ashi replied: We are dealing with a circular city. Rav Ḥavivi responded: But haven’t they squared the city? Rav Ashi responded: Say that we say the following: We view the city as if it were squared. Do we actually add houses and square it? Although for the purpose of calculating the extended boundary we view the city as a square, in actuality the uninhabited sections are part of the open space.
אֲמַר לֵיהּ רַב חֲנִילַאי מָחוֹזְנָאָה לְרַב אָשֵׁי: מִכְּדִי כַּמָּה מְרוּבָּע יָתֵר עַל הֶעָגוֹל — רְבִיעַ, הָנֵי תַּמְנֵי מְאָה? שֵׁית מְאָה וְשִׁיתִּין וּשְׁבַע נָכֵי תִּילְתָּא הָוֵי!
Rav Ḥanilai from Meḥoza said to Rav Ashi: Now, how much larger is the area of a square than the area of a circle? One quarter. Therefore, if we calculate how much area a circular city with a diameter of two thousand cubits gains when it is squared, does it add up to these eight hundred cubits mentioned above? The extra area added is only 667 minus one-third cubits.
אֲמַר לֵיהּ: הָנֵי מִילֵּי בְּעִיגּוּלָא מִגּוֹ רִבּוּעַ. אֲבָל בַּאֲלַכְסוֹנָא — בָּעֵינָא טְפֵי. דְּאָמַר מָר, כׇּל אַמְּתָא בְּרִיבּוּעַ — אַמְּתָא וּתְרֵי חוּמְּשֵׁי בַּאֲלַכְסוֹנָא.
Rav Ashi said to him: This statement applies only to a circle enclosed within a square, as the area of a circle is three-quarters the area of the square around it. However, with regard to the additional diagonal [alakhsona] space added in the corners of the square, more is required. As the Master said: Every cubit in the side of a square is one and two-fifths cubits in its diagonal. Based on this rule, the calculation is exact.
מַתְנִי׳ נוֹתְנִין קַרְפֵּף לָעִיר, דִּבְרֵי רַבִּי מֵאִיר. וַחֲכָמִים אוֹמְרִים: לֹא אָמְרוּ קַרְפֵּף אֶלָּא בֵּין שְׁתֵּי עֲיָירוֹת, אִם יֵשׁ לָזוֹ שִׁבְעִים אַמָּה וְשִׁירַיִים וּלָזוֹ שִׁבְעִים אַמָּה וְשִׁירַיִים — עוֹשֶׂה קַרְפֵּף אֶת שְׁתֵּיהֶן לִהְיוֹת אֶחָד.
MISHNA: One allocates a karpef to every city, i.e., the measure of a karpef, which is slightly more than seventy cubits, is added to every city, and the two thousand cubits of the Shabbat limit are measured from there; this is the statement of Rabbi Meir. And the Rabbis say: They spoke of the addition of a karpef only with regard to the space between two adjacent cities. How so? If this city has seventy cubits and a remainder vacant on one side, and that city has seventy cubits and a remainder vacant on the adjacent side, and the two areas of seventy-plus cubits overlap, the karpef combines the two cities into one.
וְכֵן שְׁלֹשָׁה כְּפָרִים הַמְשׁוּלָּשִׁין, אִם יֵשׁ בֵּין שְׁנַיִם חִיצוֹנִים מֵאָה וְאַרְבָּעִים וְאַחַת וּשְׁלִישׁ — עָשָׂה אֶמְצָעִי אֶת שְׁלָשְׁתָּן לִהְיוֹת אֶחָד.
And likewise, in the case of three villages that are arranged as a triangle, if there are only 141⅓ cubits separating between the two outer villages, the middle village combines the three villages into one.
גְּמָ׳ מְנָא הָנֵי מִילֵּי? אָמַר רָבָא: דְּאָמַר קְרָא: ״מִקִּיר הָעִיר וָחוּצָה״. אָמְרָה תּוֹרָה: תֵּן חוּצָה, וְאַחַר כָּךְ מְדוֹד.
GEMARA: The Gemara asks: From where are these matters, that a karpef is added to a city, derived? Rava said: As the verse states: “And the open spaces of the cities, that you shall give to the Levites, shall be from the wall of the city and outward a thousand cubits around. And you shall measure from outside the city on the east side two thousand cubits” (Numbers 35:4–5). The Torah says: Provide a certain vacant space outside the city, and only afterward measure the two thousand cubits.
וַחֲכָמִים אוֹמְרִים לֹא אָמְרוּ וְכוּ׳. אִיתְּמַר, רַב הוּנָא אָמַר: נוֹתְנִין קַרְפֵּף לָזוֹ וְקַרְפֵּף לָזוֹ. חִיָּיא בַּר רַב אָמַר: קַרְפֵּף [אֶחָד] לִשְׁתֵּיהֶן.
We learned in the mishna: And the Rabbis say: They spoke of the addition of a karpef only with regard to the space between two adjacent cities. It was stated that the amora’im disagreed with regard to this issue. Rav Huna said: One allocates a karpef to this city and a karpef to that city, so that the two cities together are granted a total of slightly more than 141 cubits. Ḥiyya bar Rav said: One allocates only one common karpef to the two of them.
תְּנַן, וַחֲכָמִים אוֹמְרִים: לֹא אָמְרוּ קַרְפֵּף אֶלָּא בֵּין שְׁתֵּי עֲיָירוֹת, תְּיוּבְתָּא דְרַב הוּנָא!
The Gemara raises possible proofs for each opinion. We learned in the mishna: And the Rabbis say: They spoke of the addition of a karpef only with regard to the space between two adjacent cities. This appears to be a conclusive refutation of the opinion of Rav Huna, as it states that one karpef is allocated rather than two.
אָמַר לְךָ רַב הוּנָא: מַאי קַרְפֵּף, תּוֹרַת קַרְפֵּף, וּלְעוֹלָם קַרְפֵּף לָזוֹ וְקַרְפֵּף לָזוֹ.
The Gemara answers that Rav Huna could have said to you in response to this difficulty: What is meant here by a karpef ? It means the principle of a karpef. In actuality, one allocates a karpef to this city and a karpef to that city.
הָכִי נָמֵי מִסְתַּבְּרָא, מִדְּקָתָנֵי סֵיפָא: אִם יֵשׁ לָזוֹ שִׁבְעִים אַמָּה וְשִׁירַיִים וְלָזוֹ שִׁבְעִים אַמָּה וְשִׁירַיִים — עוֹשֶׂה קַרְפֵּף לִשְׁתֵּיהֶן לִהְיוֹת אֶחָד. שְׁמַע מִינַּהּ.
The Gemara comments: So, too, it is reasonable to explain the mishna in the following manner: From the fact that it teaches in the latter clause: If this city has seventy cubits and a remainder vacant on one side, and that city has seventy cubits and a remainder vacant on the adjacent side, and the two areas of seventy-plus cubits overlap, the karpef combines the two cities into one. This indicates that an area of seventy cubits and a remainder is added to each city. The Gemara concludes: Indeed, learn from this that this is the correct understanding of the mishna.
לֵימָא תֶּיהְוֵי תְּיוּבְתֵּיהּ דְּחִיָּיא בַּר רַב! אָמַר לְךָ חִיָּיא בַּר רַב:
The Gemara asks: Let us say that this mishna is a conclusive refutation of the opinion of Ḥiyya bar Rav, that two adjacent cities are granted only one karpef. The Gemara answers that Ḥiyya bar Rav could have said to you:
הָא מַנִּי — רַבִּי מֵאִיר הִיא.
In accordance with whose opinion is this clause of the mishna? It is the opinion of Rabbi Meir, who maintains that one allocates a karpef to each city.
אִי רַבִּי מֵאִיר הִיא, הָא תָּנֵי לֵיהּ רֵישָׁא: נוֹתְנִין קַרְפֵּף לָעִיר, דִּבְרֵי רַבִּי מֵאִיר?
The Gemara continues to ask: If it is in accordance with the opinion of Rabbi Meir, didn’t we already learn in the first clause: One allocates a karpef to each city; this is the statement of Rabbi Meir? What need is there to mention Rabbi Meir’s opinion again?
צְרִיכָא, דְּאִי מֵהַהִיא, הֲוָה אָמֵינָא: חַד לַחֲדָא, וְחַד לְתַרְתֵּי. קָא מַשְׁמַע לַן דִּלְתַרְתֵּי תְּרֵי יָהֲבִינַן לְהוּ.
The Gemara answers: It was necessary to mention his opinion again, as, if we had learned his opinion only from that first clause, I might have said that one allocates one karpef for one city and also one karpef for two cities. Therefore, the mishna teaches us that for two cities, one allocates two karpef areas.
וְאִי אַשְׁמְעִינַן הָכָא, מִשּׁוּם דִּדְחִיקָא תַּשְׁמִישְׁתַּיְיהוּ, אֲבָל הָתָם דְּלָא דְּחִיקָא תַּשְׁמִישְׁתַּיְיהוּ, אֵימָא לָא, צְרִיכָא.
And conversely, if the mishna had taught us this law only here, with regard to two cities, one might have said that only in that case is each city granted a separate karpef, because a smaller space between the two adjacent cities would be too crowded for the use of both cities. But there, with regard to one city, where the area of the city itself is not too crowded for the use of its residents, one might say that it is not given any karpef whatsoever. Therefore, it was necessary for the mishna to teach both clauses.
תְּנַן: וְכֵן שְׁלֹשָׁה כְּפָרִים הַמְשׁוּלָּשִׁין, אִם יֵשׁ בֵּין שְׁנַיִם הַחִיצוֹנִים מֵאָה וְאַרְבָּעִים וְאַחַת אַמָּה וּשְׁלִישׁ — עוֹשֶׂה אֶמְצָעִי אֶת שְׁלָשְׁתָּן לִהְיוֹת אֶחָד. טַעְמָא דְּאִיכָּא אֶמְצָעִי, הָא לֵיכָּא אֶמְצָעִי — לֹא. תְּיוּבְתָּא דְרַב הוּנָא!
The Gemara tries again to adduce proof from the mishna, in which we learned: And likewise, in the case of three villages that are aligned in a row, if there is only 141⅓ cubits separating between the two outer ones, the middle village combines the three villages into one. At this point the Gemara understands that the mishna here is dealing with three villages arranged in a straight line. Therefore, it makes the following inference: The reason that the three villages are considered as one is only because there is a middle village, but were there no middle village, they would not be considered as one. This appears to be a conclusive refutation of the opinion of Rav Huna. According to Rav Huna, the two villages should be considered as one even without the middle village, due to the double karpef.
אָמַר לְךָ רַב הוּנָא: הָא אִתְּמַר עֲלַהּ, אָמַר רַבָּה אָמַר רַב אִידִי אָמַר רַבִּי חֲנִינָא: לֹא מְשׁוּלָּשִׁין מַמָּשׁ, אֶלָּא רוֹאִין כׇּל שֶׁאִילּוּ מֵטִיל אֶמְצָעִי בֵּינֵיהֶן וְיִהְיוּ מְשׁוּלָּשִׁין, וְאֵין בֵּין זֶה לָזֶה אֶלָּא מֵאָה וְאַרְבָּעִים אַמָּה וְאַחַת וּשְׁלִישׁ — עָשָׂה אֶמְצָעִי אֶת שְׁלָשְׁתָּן לִהְיוֹת אֶחָד.
The Gemara rejects this argument: Rav Huna could have said to you: Wasn’t it stated with regard to that mishna that Rabba said that Rav Idi said that Rabbi Ḥanina said: It does not mean that the villages are actually aligned in a row of three villages in a straight line. Rather, even if the middle village is off to one side and the outer villages are more than two karpef lengths apart, we see their spacing and make the following assessment: Any case where, if the middle village were placed between the other two so that they were three villages aligned in a row, there would be only a distance of 141⅓ cubits between one and the other, then the middle village turns the three villages into one. According to this explanation, the mishna can be understood even as a support for the opinion of Rav Huna.
אֲמַר לֵיהּ רָבָא לְאַבָּיֵי: כַּמָּה יְהֵא בֵּין חִיצוֹן לָאֶמְצָעִי? אֲמַר לֵיהּ: אַלְפַּיִם אַמָּה.
With regard to this case, Rava said to Abaye: How much distance can there be between an outer village and the middle one, if the latter is still to combine the three villages into one? Abaye said to him: Two thousand cubits.
וְהָא אַתְּ הוּא דְּאָמְרַתְּ: כְּווֹתֵיהּ דְּרָבָא בְּרֵיהּ דְּרַבָּה בַּר רַב הוּנָא מִסְתַּבְּרָא, דְּאָמַר: יוֹתֵר מֵאַלְפַּיִם אַמָּה!
Rava replied: Wasn’t it you yourself who said: It is reasonable to rule in accordance with the opinion of Rava, son of Rabba bar Rav Huna, who said: The Shabbat limit of a bow-shaped city is measured from the imaginary bowstring stretched between the two ends of the city, even if the distance between the center of the string and the center of the bow is more than two thousand cubits. Why shouldn’t the three villages in this case be considered a single village also, even if they are separated by more than two thousand cubits?
הָכִי הַשְׁתָּא? הָתָם, אִיכָּא בָּתִּים. הָכָא, לֵיכָּא בָּתִּים.
Abaye rejected the comparison: How can you compare? There, in the case of the bow-shaped city, there are houses that combine the city into a single unit, whereas here, there are no houses linking the outer villages. Therefore, if two villages are separated by more than two thousand cubits, the measure of the Shabbat limit, they cannot be considered a single entity.
וַאֲמַר לֵיהּ רָבָא לְאַבָּיֵי: כַּמָּה יְהֵא בֵּין חִיצוֹן לְחִיצוֹן? כַּמָּה יְהֵא?! מַאי נָפְקָא לָךְ מִינַּהּ? כׇּל שֶׁאִילּוּ מַכְנִיס אֶמְצָעִי בֵּינֵיהֶן וְאֵין בֵּין זֶה לָזֶה אֶלָּא מֵאָה וְאַרְבָּעִים וְאַחַת וּשְׁלִישׁ.
And Rava said to Abaye: How much distance can there be between one outer village and the other outer village? Abaye expressed surprise at this question: How much distance can there be between them? What is the practical difference to you? Any case where, if the middle village were placed between them, there would be only a distance of 141⅓ cubits between one and the other, the middle village turns the three villages into one. Therefore, the critical detail is not the distance between the outer villages but the size of the middle village.
וַאֲפִילּוּ אַרְבַּעַת אַלְפַּיִם אַמָּה? אֲמַר לֵיהּ: אִין. וְהָאָמַר רַב הוּנָא: עִיר הָעֲשׂוּיָה כְּקֶשֶׁת, אִם יֵשׁ בֵּין שְׁנֵי רָאשֶׁיהָ פָּחוֹת מֵאַרְבַּעַת אֲלָפִים אַמָּה מוֹדְדִין לָהּ מִן הַיֶּתֶר, וְאִם לָאו מוֹדְדִין לָהּ מִן הַקֶּשֶׁת!
Rava continued his line of questioning: Is this true even if the distance between the two outer villages is four thousand cubits? Abaye said to him: Yes. Rava asked: Didn’t Rav Huna say the following with regard to a city shaped like a bow: If the distance between its two ends is less than four thousand cubits, one measures the Shabbat limit from the imaginary bowstring stretched between the two ends of the bow; and if not, one measures the Shabbat limit from the bow itself? This indicates that even if there is an uninterrupted string of houses linking the two ends of the city, if the two ends are separated by more than four thousand cubits, the distance is too great for it to be considered a single city.
אֲמַר לֵיהּ: הָתָם לֵיכָּא לְמֵימַר ״מַלֵּי״. הָכָא אִיכָּא לְמֵימַר ״מַלֵּי״.
Abaye said to him: There, in the case of the bow-shaped city, there is no room to say: Fill it in, as there is nothing with which to fill in the empty space between the two ends of the city. However, here, in the case of the villages, there is room to say: Fill it in, as the middle village is seen as though it were projected between the two outer villages, and therefore all three combine into a single village.
אֲמַר לֵיהּ רַב סָפְרָא לְרָבָא: הֲרֵי בְּנֵי אֲקִיסְטְפוֹן, דְּמָשְׁחִינַן לְהוּ תְּחוּמָא מֵהַאי גִּיסָא דְּאַרְדָּשִׁיר, וּבְנֵי תְּחוּמָא דְאַרְדָּשִׁיר מָשְׁחִינַן לְהוּ תְּחוּמָא מֵהַאי גִּיסָא דַּאֲקִיסְטְפוֹן. הָא אִיכָּא דִּגְלַת דְּמַפְסְקָא יָתֵר מִמֵּאָה וְאַרְבָּעִים וְאַחַת וּשְׁלִישׁ?
Rav Safra said to Rava: With regard to the people of the city of Akistefon, for whom we measure the Shabbat limit from the far end of the city of Ardeshir, and the people of Ardeshir, for whom we measure the Shabbat limit from the far end of Akistefon, as though the two settlements were a single city; isn’t there the Tigris River, which separates them by more than 141⅓ cubits? How can two cities that are separated by more than two karpef-lengths be considered a single entity?
נְפַק, אַחְוִי לֵיהּ הָנָךְ אַטְמָהָתָא דְשׁוּרָא, דְּמִבַּלְעִי בְּדִגְלַת בְּשִׁבְעִים אַמָּה וְשִׁירַיִים.
Rava went out and showed Rav Safra the foundations of a wall of one of the cities, which were submerged in the Tigris River at a distance of seventy cubits and a remainder from the other city. In other words, the two cities were in fact linked through the remnants of a wall submerged in the river.
מַתְנִי׳ אֵין מוֹדְדִין אֶלָּא בְּחֶבֶל שֶׁל חֲמִשִּׁים אַמָּה, לֹא פָּחוֹת וְלֹא יוֹתֵר. וְלֹא יִמְדּוֹד אֶלָּא כְּנֶגֶד לִבּוֹ.
MISHNA: One may measure a Shabbat limit only with a rope fifty cubits long, no less and no more, as will be explained in the Gemara. And one may measure the limit only at the level of one’s heart, i.e., whoever comes to measure the limit must hold the rope next to his chest.
הָיָה מוֹדֵד וְהִגִּיעַ לְגַיְא אוֹ לְגָדֵר, מַבְלִיעוֹ, וְחוֹזֵר לְמִדָּתוֹ. הִגִּיעַ לְהַר, מַבְלִיעוֹ וְחוֹזֵר לְמִדָּתוֹ.
If one was measuring the limit and he reached a canyon or a fence, the height of the fence and the depth of the canyon are not counted toward the two thousand cubits; rather, he spans it and then resumes his measurement. Two people hold the two ends of the rope straight across the canyon or the fence, and the distance is measured as though the area were completely flat. If one reached a hill, he does not measure its height; rather, he spans the hill as if it were not there and then resumes his measurement,
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Eruvin 57
דַּל אַרְבַּע דִּתְחוּמִין וְאַרְבַּע דִּקְרָנוֹת. כַּמָּה הָוֵי? תְּמָנְיָא.
Subtract four million square cubits of the extended boundary for the area of the open space, which is a thousand cubits by a thousand cubits on each side, and an additional four million square cubits from the corners, a thousand cubits by a thousand cubits in each corner, which are connected to the open space. How much is the sum total? It is eight million square cubits.
תִּילְתָּא הָווּ! מִי סָבְרַתְּ בְּרִבּוּעָא קָאָמַר? בְּעִיגּוּלָא קָאָמַר. כַּמָּה מְרוּבָּע יָתֵר עַל הֶעָגוֹל — רְבִיעַ, דַּל רְבִיעַ — פָּשׁוּ לַהּ שִׁיתָּא. וְשִׁיתָּא מֵעֶשְׂרִים וְאַרְבַּע, רִיבְעָא הָוֵי.
The Gemara asks: According to this calculation, the eight million square cubits of open space are one-third of the total area of the extended boundary, which is twenty-four million square cubits. The Gemara answers as it answered above: Do you think that this halakha was stated with regard to a square city? It was stated with regard to a round city. How much larger is the area of a square than the area of a circle? It is one quarter of the area of the circle. Subtract one quarter from the eight million square cubits of open space, and six million square cubits are left; and six is precisely one quarter of twenty-four.
רָבִינָא אָמַר: מַאי רְבִיעַ, רְבִיעַ דִּתְחוּמִין.
Ravina said: What is the meaning of the statement that the open space is one quarter? It is one quarter of the boundary. This halakha was indeed stated with regard to a square city. However, there is open space only along the sides of the city but not at its corners. Accordingly, a city that is two thousand cubits by two thousand cubits has a total extended boundary of thirty-two million square cubits, of which eight million square cubits, two thousand cubits by one thousand cubits on each side, is open space. The open space is thus one quarter of the total.
רַב אָשֵׁי אָמַר: מַאי רְבִיעַ, רְבִיעַ דִּקְרָנוֹת.
Rav Ashi said the opposite: What is the meaning of the statement that the open space is one quarter of the total extended boundary? One quarter of the corners. Open space is granted only in the corners, and not along the sides. Accordingly, the open space is one thousand cubits by a thousand cubits in each corner, for a total of four million square cubits. The total extended boundary in each corner is two thousand cubits by two thousand cubits, or four million square cubits per corner, which equals a grand total of sixteen million square cubits. Consequently, the open space is one quarter of the total extended boundary.
אֲמַר לֵיהּ רָבִינָא לְרַב אָשֵׁי: וְהָא ״סָבִיב״ כְּתִיב!
Ravina said to Rav Ashi: Isn’t it written in the verse: “And the open spaces of the cities, that you shall give to the Levites, shall be from the wall of the city and outward one thousand cubits around” (Numbers 35:4)? The verse indicates that the city is provided with open space on all sides and not merely at its corners
מַאי ״סָבִיב״ — סָבִיב דִּקְרָנוֹת, דְּאִי לָא תֵּימָא הָכִי, גַּבֵּי עוֹלָה דִּכְתִיב: ״וְזָרְקוּ (בְּנֵי אַהֲרֹן) אֶת הַדָּם עַל הַמִּזְבֵּחַ סָבִיב״, הָכִי נָמֵי סָבִיב מַמָּשׁ?! אֶלָּא מַאי ״סָבִיב״ — סָבִיב דִּקְרָנוֹת, הָכִי נָמֵי: מַאי ״סָבִיב״ — סָבִיב דִּקְרָנוֹת.
Rav Ashi responded: What is the meaning of around? Around at the corners, i.e., an open space of this size is provided at each corner. As, if you do not say so, that the area of the corners is also called around, with regard to the burnt-offering, as it is written: “And they shall sprinkle the blood around upon the altar” (Leviticus 1:5), here, too, will you say that the blood must be sprinkled literally “around” the altar on all sides? The blood is sprinkled only upon the corners of the altar. Rather, what is the meaning of around? Around the corners, i.e., the mitzva is to sprinkle the blood at the corners, and this is considered sprinkling blood “around upon the altar.” Here too, with regard to the open space of the cities of the Levites, what is the meaning of around? Around the corners.
אֲמַר לֵיהּ רַב חֲבִיבִי מָחוֹזְנָאָה לְרַב אָשֵׁי: וְהָא אִיכָּא מוּרְשָׁא דְקַרְנָתָא!
The Gemara returns to its previous statement that the open space around a city of the Levites is one quarter of the total extended boundary when the city is round. It questions this statement based upon the mishna’s ruling that the boundaries of a city are always delineated as a square. Rav Ḥavivi from Meḥoza said to Rav Ashi: But aren’t there the protrusions of the corners? How can there be a thousand cubits of open space on each side; when the city is squared, the corners of the square protrude into the open space, thus reducing its area?
בְּמָתָא עִיגּוּלְתָּא. וְהָא רַיבְּעוּהָ? אֵימוֹר דְּאָמְרִינַן חֲזֵינַן כְּמַאן דִּמְרַבְּעָא. רַבּוֹעֵי וַדַּאי מִי מְרַבַּעְנָא?!
Rav Ashi replied: We are dealing with a circular city. Rav Ḥavivi responded: But haven’t they squared the city? Rav Ashi responded: Say that we say the following: We view the city as if it were squared. Do we actually add houses and square it? Although for the purpose of calculating the extended boundary we view the city as a square, in actuality the uninhabited sections are part of the open space.
אֲמַר לֵיהּ רַב חֲנִילַאי מָחוֹזְנָאָה לְרַב אָשֵׁי: מִכְּדִי כַּמָּה מְרוּבָּע יָתֵר עַל הֶעָגוֹל — רְבִיעַ, הָנֵי תַּמְנֵי מְאָה? שֵׁית מְאָה וְשִׁיתִּין וּשְׁבַע נָכֵי תִּילְתָּא הָוֵי!
Rav Ḥanilai from Meḥoza said to Rav Ashi: Now, how much larger is the area of a square than the area of a circle? One quarter. Therefore, if we calculate how much area a circular city with a diameter of two thousand cubits gains when it is squared, does it add up to these eight hundred cubits mentioned above? The extra area added is only 667 minus one-third cubits.
אֲמַר לֵיהּ: הָנֵי מִילֵּי בְּעִיגּוּלָא מִגּוֹ רִבּוּעַ. אֲבָל בַּאֲלַכְסוֹנָא — בָּעֵינָא טְפֵי. דְּאָמַר מָר, כׇּל אַמְּתָא בְּרִיבּוּעַ — אַמְּתָא וּתְרֵי חוּמְּשֵׁי בַּאֲלַכְסוֹנָא.
Rav Ashi said to him: This statement applies only to a circle enclosed within a square, as the area of a circle is three-quarters the area of the square around it. However, with regard to the additional diagonal [alakhsona] space added in the corners of the square, more is required. As the Master said: Every cubit in the side of a square is one and two-fifths cubits in its diagonal. Based on this rule, the calculation is exact.
מַתְנִי׳ נוֹתְנִין קַרְפֵּף לָעִיר, דִּבְרֵי רַבִּי מֵאִיר. וַחֲכָמִים אוֹמְרִים: לֹא אָמְרוּ קַרְפֵּף אֶלָּא בֵּין שְׁתֵּי עֲיָירוֹת, אִם יֵשׁ לָזוֹ שִׁבְעִים אַמָּה וְשִׁירַיִים וּלָזוֹ שִׁבְעִים אַמָּה וְשִׁירַיִים — עוֹשֶׂה קַרְפֵּף אֶת שְׁתֵּיהֶן לִהְיוֹת אֶחָד.
MISHNA: One allocates a karpef to every city, i.e., the measure of a karpef, which is slightly more than seventy cubits, is added to every city, and the two thousand cubits of the Shabbat limit are measured from there; this is the statement of Rabbi Meir. And the Rabbis say: They spoke of the addition of a karpef only with regard to the space between two adjacent cities. How so? If this city has seventy cubits and a remainder vacant on one side, and that city has seventy cubits and a remainder vacant on the adjacent side, and the two areas of seventy-plus cubits overlap, the karpef combines the two cities into one.
וְכֵן שְׁלֹשָׁה כְּפָרִים הַמְשׁוּלָּשִׁין, אִם יֵשׁ בֵּין שְׁנַיִם חִיצוֹנִים מֵאָה וְאַרְבָּעִים וְאַחַת וּשְׁלִישׁ — עָשָׂה אֶמְצָעִי אֶת שְׁלָשְׁתָּן לִהְיוֹת אֶחָד.
And likewise, in the case of three villages that are arranged as a triangle, if there are only 141⅓ cubits separating between the two outer villages, the middle village combines the three villages into one.
גְּמָ׳ מְנָא הָנֵי מִילֵּי? אָמַר רָבָא: דְּאָמַר קְרָא: ״מִקִּיר הָעִיר וָחוּצָה״. אָמְרָה תּוֹרָה: תֵּן חוּצָה, וְאַחַר כָּךְ מְדוֹד.
GEMARA: The Gemara asks: From where are these matters, that a karpef is added to a city, derived? Rava said: As the verse states: “And the open spaces of the cities, that you shall give to the Levites, shall be from the wall of the city and outward a thousand cubits around. And you shall measure from outside the city on the east side two thousand cubits” (Numbers 35:4–5). The Torah says: Provide a certain vacant space outside the city, and only afterward measure the two thousand cubits.
וַחֲכָמִים אוֹמְרִים לֹא אָמְרוּ וְכוּ׳. אִיתְּמַר, רַב הוּנָא אָמַר: נוֹתְנִין קַרְפֵּף לָזוֹ וְקַרְפֵּף לָזוֹ. חִיָּיא בַּר רַב אָמַר: קַרְפֵּף [אֶחָד] לִשְׁתֵּיהֶן.
We learned in the mishna: And the Rabbis say: They spoke of the addition of a karpef only with regard to the space between two adjacent cities. It was stated that the amora’im disagreed with regard to this issue. Rav Huna said: One allocates a karpef to this city and a karpef to that city, so that the two cities together are granted a total of slightly more than 141 cubits. Ḥiyya bar Rav said: One allocates only one common karpef to the two of them.
תְּנַן, וַחֲכָמִים אוֹמְרִים: לֹא אָמְרוּ קַרְפֵּף אֶלָּא בֵּין שְׁתֵּי עֲיָירוֹת, תְּיוּבְתָּא דְרַב הוּנָא!
The Gemara raises possible proofs for each opinion. We learned in the mishna: And the Rabbis say: They spoke of the addition of a karpef only with regard to the space between two adjacent cities. This appears to be a conclusive refutation of the opinion of Rav Huna, as it states that one karpef is allocated rather than two.
אָמַר לְךָ רַב הוּנָא: מַאי קַרְפֵּף, תּוֹרַת קַרְפֵּף, וּלְעוֹלָם קַרְפֵּף לָזוֹ וְקַרְפֵּף לָזוֹ.
The Gemara answers that Rav Huna could have said to you in response to this difficulty: What is meant here by a karpef ? It means the principle of a karpef. In actuality, one allocates a karpef to this city and a karpef to that city.
הָכִי נָמֵי מִסְתַּבְּרָא, מִדְּקָתָנֵי סֵיפָא: אִם יֵשׁ לָזוֹ שִׁבְעִים אַמָּה וְשִׁירַיִים וְלָזוֹ שִׁבְעִים אַמָּה וְשִׁירַיִים — עוֹשֶׂה קַרְפֵּף לִשְׁתֵּיהֶן לִהְיוֹת אֶחָד. שְׁמַע מִינַּהּ.
The Gemara comments: So, too, it is reasonable to explain the mishna in the following manner: From the fact that it teaches in the latter clause: If this city has seventy cubits and a remainder vacant on one side, and that city has seventy cubits and a remainder vacant on the adjacent side, and the two areas of seventy-plus cubits overlap, the karpef combines the two cities into one. This indicates that an area of seventy cubits and a remainder is added to each city. The Gemara concludes: Indeed, learn from this that this is the correct understanding of the mishna.
לֵימָא תֶּיהְוֵי תְּיוּבְתֵּיהּ דְּחִיָּיא בַּר רַב! אָמַר לְךָ חִיָּיא בַּר רַב:
The Gemara asks: Let us say that this mishna is a conclusive refutation of the opinion of Ḥiyya bar Rav, that two adjacent cities are granted only one karpef. The Gemara answers that Ḥiyya bar Rav could have said to you:
הָא מַנִּי — רַבִּי מֵאִיר הִיא.
In accordance with whose opinion is this clause of the mishna? It is the opinion of Rabbi Meir, who maintains that one allocates a karpef to each city.
אִי רַבִּי מֵאִיר הִיא, הָא תָּנֵי לֵיהּ רֵישָׁא: נוֹתְנִין קַרְפֵּף לָעִיר, דִּבְרֵי רַבִּי מֵאִיר?
The Gemara continues to ask: If it is in accordance with the opinion of Rabbi Meir, didn’t we already learn in the first clause: One allocates a karpef to each city; this is the statement of Rabbi Meir? What need is there to mention Rabbi Meir’s opinion again?
צְרִיכָא, דְּאִי מֵהַהִיא, הֲוָה אָמֵינָא: חַד לַחֲדָא, וְחַד לְתַרְתֵּי. קָא מַשְׁמַע לַן דִּלְתַרְתֵּי תְּרֵי יָהֲבִינַן לְהוּ.
The Gemara answers: It was necessary to mention his opinion again, as, if we had learned his opinion only from that first clause, I might have said that one allocates one karpef for one city and also one karpef for two cities. Therefore, the mishna teaches us that for two cities, one allocates two karpef areas.
וְאִי אַשְׁמְעִינַן הָכָא, מִשּׁוּם דִּדְחִיקָא תַּשְׁמִישְׁתַּיְיהוּ, אֲבָל הָתָם דְּלָא דְּחִיקָא תַּשְׁמִישְׁתַּיְיהוּ, אֵימָא לָא, צְרִיכָא.
And conversely, if the mishna had taught us this law only here, with regard to two cities, one might have said that only in that case is each city granted a separate karpef, because a smaller space between the two adjacent cities would be too crowded for the use of both cities. But there, with regard to one city, where the area of the city itself is not too crowded for the use of its residents, one might say that it is not given any karpef whatsoever. Therefore, it was necessary for the mishna to teach both clauses.
תְּנַן: וְכֵן שְׁלֹשָׁה כְּפָרִים הַמְשׁוּלָּשִׁין, אִם יֵשׁ בֵּין שְׁנַיִם הַחִיצוֹנִים מֵאָה וְאַרְבָּעִים וְאַחַת אַמָּה וּשְׁלִישׁ — עוֹשֶׂה אֶמְצָעִי אֶת שְׁלָשְׁתָּן לִהְיוֹת אֶחָד. טַעְמָא דְּאִיכָּא אֶמְצָעִי, הָא לֵיכָּא אֶמְצָעִי — לֹא. תְּיוּבְתָּא דְרַב הוּנָא!
The Gemara tries again to adduce proof from the mishna, in which we learned: And likewise, in the case of three villages that are aligned in a row, if there is only 141⅓ cubits separating between the two outer ones, the middle village combines the three villages into one. At this point the Gemara understands that the mishna here is dealing with three villages arranged in a straight line. Therefore, it makes the following inference: The reason that the three villages are considered as one is only because there is a middle village, but were there no middle village, they would not be considered as one. This appears to be a conclusive refutation of the opinion of Rav Huna. According to Rav Huna, the two villages should be considered as one even without the middle village, due to the double karpef.
אָמַר לְךָ רַב הוּנָא: הָא אִתְּמַר עֲלַהּ, אָמַר רַבָּה אָמַר רַב אִידִי אָמַר רַבִּי חֲנִינָא: לֹא מְשׁוּלָּשִׁין מַמָּשׁ, אֶלָּא רוֹאִין כׇּל שֶׁאִילּוּ מֵטִיל אֶמְצָעִי בֵּינֵיהֶן וְיִהְיוּ מְשׁוּלָּשִׁין, וְאֵין בֵּין זֶה לָזֶה אֶלָּא מֵאָה וְאַרְבָּעִים אַמָּה וְאַחַת וּשְׁלִישׁ — עָשָׂה אֶמְצָעִי אֶת שְׁלָשְׁתָּן לִהְיוֹת אֶחָד.
The Gemara rejects this argument: Rav Huna could have said to you: Wasn’t it stated with regard to that mishna that Rabba said that Rav Idi said that Rabbi Ḥanina said: It does not mean that the villages are actually aligned in a row of three villages in a straight line. Rather, even if the middle village is off to one side and the outer villages are more than two karpef lengths apart, we see their spacing and make the following assessment: Any case where, if the middle village were placed between the other two so that they were three villages aligned in a row, there would be only a distance of 141⅓ cubits between one and the other, then the middle village turns the three villages into one. According to this explanation, the mishna can be understood even as a support for the opinion of Rav Huna.
אֲמַר לֵיהּ רָבָא לְאַבָּיֵי: כַּמָּה יְהֵא בֵּין חִיצוֹן לָאֶמְצָעִי? אֲמַר לֵיהּ: אַלְפַּיִם אַמָּה.
With regard to this case, Rava said to Abaye: How much distance can there be between an outer village and the middle one, if the latter is still to combine the three villages into one? Abaye said to him: Two thousand cubits.
וְהָא אַתְּ הוּא דְּאָמְרַתְּ: כְּווֹתֵיהּ דְּרָבָא בְּרֵיהּ דְּרַבָּה בַּר רַב הוּנָא מִסְתַּבְּרָא, דְּאָמַר: יוֹתֵר מֵאַלְפַּיִם אַמָּה!
Rava replied: Wasn’t it you yourself who said: It is reasonable to rule in accordance with the opinion of Rava, son of Rabba bar Rav Huna, who said: The Shabbat limit of a bow-shaped city is measured from the imaginary bowstring stretched between the two ends of the city, even if the distance between the center of the string and the center of the bow is more than two thousand cubits. Why shouldn’t the three villages in this case be considered a single village also, even if they are separated by more than two thousand cubits?
הָכִי הַשְׁתָּא? הָתָם, אִיכָּא בָּתִּים. הָכָא, לֵיכָּא בָּתִּים.
Abaye rejected the comparison: How can you compare? There, in the case of the bow-shaped city, there are houses that combine the city into a single unit, whereas here, there are no houses linking the outer villages. Therefore, if two villages are separated by more than two thousand cubits, the measure of the Shabbat limit, they cannot be considered a single entity.
וַאֲמַר לֵיהּ רָבָא לְאַבָּיֵי: כַּמָּה יְהֵא בֵּין חִיצוֹן לְחִיצוֹן? כַּמָּה יְהֵא?! מַאי נָפְקָא לָךְ מִינַּהּ? כׇּל שֶׁאִילּוּ מַכְנִיס אֶמְצָעִי בֵּינֵיהֶן וְאֵין בֵּין זֶה לָזֶה אֶלָּא מֵאָה וְאַרְבָּעִים וְאַחַת וּשְׁלִישׁ.
And Rava said to Abaye: How much distance can there be between one outer village and the other outer village? Abaye expressed surprise at this question: How much distance can there be between them? What is the practical difference to you? Any case where, if the middle village were placed between them, there would be only a distance of 141⅓ cubits between one and the other, the middle village turns the three villages into one. Therefore, the critical detail is not the distance between the outer villages but the size of the middle village.
וַאֲפִילּוּ אַרְבַּעַת אַלְפַּיִם אַמָּה? אֲמַר לֵיהּ: אִין. וְהָאָמַר רַב הוּנָא: עִיר הָעֲשׂוּיָה כְּקֶשֶׁת, אִם יֵשׁ בֵּין שְׁנֵי רָאשֶׁיהָ פָּחוֹת מֵאַרְבַּעַת אֲלָפִים אַמָּה מוֹדְדִין לָהּ מִן הַיֶּתֶר, וְאִם לָאו מוֹדְדִין לָהּ מִן הַקֶּשֶׁת!
Rava continued his line of questioning: Is this true even if the distance between the two outer villages is four thousand cubits? Abaye said to him: Yes. Rava asked: Didn’t Rav Huna say the following with regard to a city shaped like a bow: If the distance between its two ends is less than four thousand cubits, one measures the Shabbat limit from the imaginary bowstring stretched between the two ends of the bow; and if not, one measures the Shabbat limit from the bow itself? This indicates that even if there is an uninterrupted string of houses linking the two ends of the city, if the two ends are separated by more than four thousand cubits, the distance is too great for it to be considered a single city.
אֲמַר לֵיהּ: הָתָם לֵיכָּא לְמֵימַר ״מַלֵּי״. הָכָא אִיכָּא לְמֵימַר ״מַלֵּי״.
Abaye said to him: There, in the case of the bow-shaped city, there is no room to say: Fill it in, as there is nothing with which to fill in the empty space between the two ends of the city. However, here, in the case of the villages, there is room to say: Fill it in, as the middle village is seen as though it were projected between the two outer villages, and therefore all three combine into a single village.
אֲמַר לֵיהּ רַב סָפְרָא לְרָבָא: הֲרֵי בְּנֵי אֲקִיסְטְפוֹן, דְּמָשְׁחִינַן לְהוּ תְּחוּמָא מֵהַאי גִּיסָא דְּאַרְדָּשִׁיר, וּבְנֵי תְּחוּמָא דְאַרְדָּשִׁיר מָשְׁחִינַן לְהוּ תְּחוּמָא מֵהַאי גִּיסָא דַּאֲקִיסְטְפוֹן. הָא אִיכָּא דִּגְלַת דְּמַפְסְקָא יָתֵר מִמֵּאָה וְאַרְבָּעִים וְאַחַת וּשְׁלִישׁ?
Rav Safra said to Rava: With regard to the people of the city of Akistefon, for whom we measure the Shabbat limit from the far end of the city of Ardeshir, and the people of Ardeshir, for whom we measure the Shabbat limit from the far end of Akistefon, as though the two settlements were a single city; isn’t there the Tigris River, which separates them by more than 141⅓ cubits? How can two cities that are separated by more than two karpef-lengths be considered a single entity?
נְפַק, אַחְוִי לֵיהּ הָנָךְ אַטְמָהָתָא דְשׁוּרָא, דְּמִבַּלְעִי בְּדִגְלַת בְּשִׁבְעִים אַמָּה וְשִׁירַיִים.
Rava went out and showed Rav Safra the foundations of a wall of one of the cities, which were submerged in the Tigris River at a distance of seventy cubits and a remainder from the other city. In other words, the two cities were in fact linked through the remnants of a wall submerged in the river.
מַתְנִי׳ אֵין מוֹדְדִין אֶלָּא בְּחֶבֶל שֶׁל חֲמִשִּׁים אַמָּה, לֹא פָּחוֹת וְלֹא יוֹתֵר. וְלֹא יִמְדּוֹד אֶלָּא כְּנֶגֶד לִבּוֹ.
MISHNA: One may measure a Shabbat limit only with a rope fifty cubits long, no less and no more, as will be explained in the Gemara. And one may measure the limit only at the level of one’s heart, i.e., whoever comes to measure the limit must hold the rope next to his chest.
הָיָה מוֹדֵד וְהִגִּיעַ לְגַיְא אוֹ לְגָדֵר, מַבְלִיעוֹ, וְחוֹזֵר לְמִדָּתוֹ. הִגִּיעַ לְהַר, מַבְלִיעוֹ וְחוֹזֵר לְמִדָּתוֹ.
If one was measuring the limit and he reached a canyon or a fence, the height of the fence and the depth of the canyon are not counted toward the two thousand cubits; rather, he spans it and then resumes his measurement. Two people hold the two ends of the rope straight across the canyon or the fence, and the distance is measured as though the area were completely flat. If one reached a hill, he does not measure its height; rather, he spans the hill as if it were not there and then resumes his measurement,
