Eruvin 57

דל ארבע דתחומין וארבע דקרנות כמה הוי תמניא

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.

תילתא הוו מי סברת ברבועא קאמר בעיגולא קאמר כמה מרובע יתר על העגול רביע דל רביע פשו לה שיתא ושיתא מעשרים וארבע ריבעא הוי

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.

רבינא אמר מאי רביע רביע דתחומין

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.

רב אשי אמר מאי רביע רביע דקרנות

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.

אמר ליה רבינא לרב אשי והא סביב כתיב

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

מאי סביב סביב דקרנות דאי לא תימא הכי גבי עולה דכתיב וזרקו (בני אהרן) את הדם על המזבח סביב הכי נמי סביב ממש אלא מאי סביב סביב דקרנות הכי נמי מאי סביב סביב דקרנות

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.

אמר ליה רב חביבי מחוזנאה לרב אשי והא איכא מורשא דקרנתא

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?

במתא עיגולתא והא ריבעוה אימור דאמרינן חזינן כמאן דמרבעא רבועי ודאי מי מרבענא

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.

אמר ליה רב חנילאי מחוזנאה לרב אשי מכדי כמה מרובע יתר על העגול רביע הני תמני מאה שית מאה ושיתין ושבע נכי תילתא הוי

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.

אמר ליה הני מילי בעיגולא מגו רבוע אבל באלכסונא בעינא טפי דאמר מר כל אמתא בריבוע אמתא ותרי חומשי באלכסונא:

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.

מתני׳ נותנין קרפף לעיר דברי רבי מאיר וחכמים אומרים לא אמרו קרפף אלא בין שתי עיירות אם יש לזו שבעים אמה ושיריים ולזו שבעים אמה ושיריים עושה קרפף את שתיהן להיות אחד

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.

וכן שלשה כפרים המשולשין אם יש בין שנים חיצונים מאה וארבעים ואחת ושליש עשה אמצעי את שלשתן להיות אחד:

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.

גמ׳ מנא הני מילי אמר רבא דאמר קרא מקיר העיר וחוצה אמרה תורה תן חוצה ואחר כך מדוד:

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.

וחכמים אומרים לא אמרו וכו׳: איתמר רב הונא אמר נותנין קרפף לזו וקרפף לזו חייא בר רב אמר קרפף [אחד] לשתיהן

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.

תנן וחכמים אומרים לא אמרו קרפף אלא בין שתי עיירות תיובתא דרב הונא

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.

אמר לך רב הונא מאי קרפף תורת קרפף ולעולם קרפף לזו וקרפף לזו

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.

הכי נמי מסתברא מדקתני סיפא אם יש לזו שבעים אמה ושיריים ולזו שבעים אמה ושיריים עושה קרפף לשתיהן להיות אחד שמע מינה

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.

לימא תיהוי תיובתיה דחייא בר רב אמר לך חייא בר רב

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:

הא מני רבי מאיר היא

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.

אי רבי מאיר היא הא תני ליה רישא נותנין קרפף לעיר דברי רבי מאיר

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?

צריכא דאי מההיא הוה אמינא חד לחדא וחד לתרתי קא משמע לן דלתרתי תרי יהבינן להו

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.

ואי אשמעינן הכא משום דדחיקא תשמישתייהו אבל התם דלא דחיקא תשמישתייהו אימא לא צריכא

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.

תנן וכן שלשה כפרים המשולשין אם יש בין שנים החיצונים מאה וארבעים ואחת אמה ושליש עושה אמצעי את שלשתן להיות אחד טעמא דאיכא אמצעי הא ליכא אמצעי לא תיובתא דרב הונא

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.

אמר לך רב הונא הא אתמר עלה אמר רבה אמר רב אידי אמר רבי חנינא לא משולשין ממש אלא רואין כל שאילו מטיל אמצעי ביניהן ויהיו משולשין ואין בין זה לזה אלא מאה וארבעים אמה ואחת ושליש עשה אמצעי את שלשתן להיות אחד

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.

אמר ליה רבא לאביי כמה יהא בין חיצון לאמצעי אמר ליה אלפים אמה

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.

והא את הוא דאמרת כוותיה דרבא בריה דרבה בר רב הונא מסתברא דאמר יותר מאלפים אמה

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?

הכי השתא התם איכא בתים הכא ליכא בתים

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.

ואמר ליה רבא לאביי כמה יהא בין חיצון לחיצון כמה יהא מאי נפקא לך מינה כל שאילו מכניס אמצעי ביניהן ואין בין זה לזה אלא מאה וארבעים ואחת ושליש

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.

ואפילו ארבעת אלפים אמה אמר ליה אין והאמר רב הונא עיר העשויה כקשת אם יש בין שני ראשיה פחות מארבעת אלפים אמה מודדין לה מן היתר ואם לאו מודדין לה מן הקשת

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.

אמר ליה התם ליכא למימר מלי הכא איכא למימר מלי

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.

אמר ליה רב ספרא לרבא הרי בני אקיסטפון דמשחינן להו תחומא מהאי גיסא דארדשיר ובני תחומא דארדשיר משחינן להו תחומא מהאי גיסא דאקיסטפון הא איכא דגלת דמפסקא יתר ממאה וארבעים ואחת ושליש

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?

נפק אחוי ליה הנך אטמהתא דשורא דמבלעי בדגלת בשבעים אמה ושיריים:

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.

מתני׳ אין מודדין אלא בחבל של חמשים אמה לא פחות ולא יותר ולא ימדוד אלא כנגד לבו

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.

היה מודד והגיע לגיא או לגדר מבליעו וחוזר למדתו הגיע להר מבליעו וחוזר למדתו

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,