## Eruvin Daf 57a

###### Eruvin 57a:1
[Eruvin 57a:1](https://torahapp.org/share/book/Eruvin/r/57a:1)

דַּל אַרְבַּע דִּתְחוּמִין וְאַרְבַּע דִּקְרָנוֹת. כַּמָּה הָוֵי? תְּמָנְיָא.

**William Davidson Edition - English:**
**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.


###### Eruvin 57a:2
[Eruvin 57a:2](https://torahapp.org/share/book/Eruvin/r/57a:2)

תִּילְתָּא הָווּ! מִי סָבְרַתְּ בְּרִבּוּעָא קָאָמַר? בְּעִיגּוּלָא קָאָמַר. כַּמָּה מְרוּבָּע יָתֵר עַל הֶעָגוֹל — רְבִיעַ, דַּל רְבִיעַ — פָּשׁוּ לַהּ שִׁיתָּא. וְשִׁיתָּא מֵעֶשְׂרִים וְאַרְבַּע, רִיבְעָא הָוֵי.

**William Davidson Edition - English:**
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.**


###### Eruvin 57a:3
[Eruvin 57a:3](https://torahapp.org/share/book/Eruvin/r/57a:3)

רָבִינָא אָמַר: מַאי רְבִיעַ, רְבִיעַ דִּתְחוּמִין.

**William Davidson Edition - English:**
**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.


###### Eruvin 57a:4
[Eruvin 57a:4](https://torahapp.org/share/book/Eruvin/r/57a:4)

רַב אָשֵׁי אָמַר: מַאי רְבִיעַ, רְבִיעַ דִּקְרָנוֹת.

**William Davidson Edition - English:**
**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.


###### Eruvin 57a:5
[Eruvin 57a:5](https://torahapp.org/share/book/Eruvin/r/57a:5)

אֲמַר לֵיהּ רָבִינָא לְרַב אָשֵׁי: וְהָא ״סָבִיב״ כְּתִיב!

**William Davidson Edition - English:**
**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


###### Eruvin 57a:6
[Eruvin 57a:6](https://torahapp.org/share/book/Eruvin/r/57a:6)

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.

**William Davidson Edition - English:**
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.**


###### Eruvin 57a:7
[Eruvin 57a:7](https://torahapp.org/share/book/Eruvin/r/57a:7)

אֲמַר לֵיהּ רַב חֲבִיבִי מָחוֹזְנָאָה לְרַב אָשֵׁי: וְהָא אִיכָּא מוּרְשָׁא דְקַרְנָתָא!

**William Davidson Edition - English:**
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?


###### Eruvin 57a:8
[Eruvin 57a:8](https://torahapp.org/share/book/Eruvin/r/57a:8)

בְּמָתָא עִיגּוּלְתָּא. וְהָא רַיבְּעוּהָ? אֵימוֹר דְּאָמְרִינַן חֲזֵינַן כְּמַאן דִּמְרַבְּעָא. רַבּוֹעֵי וַדַּאי מִי מְרַבַּעְנָא?!

**William Davidson Edition - English:**
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.


###### Eruvin 57a:9
[Eruvin 57a:9](https://torahapp.org/share/book/Eruvin/r/57a:9)

אֲמַר לֵיהּ רַב חֲנִילַאי מָחוֹזְנָאָה לְרַב אָשֵׁי: מִכְּדִי כַּמָּה מְרוּבָּע יָתֵר עַל הֶעָגוֹל — רְבִיעַ, הָנֵי תַּמְנֵי מְאָה? שֵׁית מְאָה וְשִׁיתִּין וּשְׁבַע נָכֵי תִּילְתָּא הָוֵי!

**William Davidson Edition - English:**
**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.


###### Eruvin 57a:10
[Eruvin 57a:10](https://torahapp.org/share/book/Eruvin/r/57a:10)

אֲמַר לֵיהּ: הָנֵי מִילֵּי בְּעִיגּוּלָא מִגּוֹ רִבּוּעַ. אֲבָל בַּאֲלַכְסוֹנָא — בָּעֵינָא טְפֵי. דְּאָמַר מָר, כׇּל אַמְּתָא בְּרִיבּוּעַ — אַמְּתָא וּתְרֵי חוּמְּשֵׁי בַּאֲלַכְסוֹנָא.

**William Davidson Edition - English:**
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.


###### Eruvin 57a:11
[Eruvin 57a:11](https://torahapp.org/share/book/Eruvin/r/57a:11)

**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.

**William Davidson Edition - English:**
**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.**


###### Eruvin 57a:12
[Eruvin 57a:12](https://torahapp.org/share/book/Eruvin/r/57a:12)

וְכֵן שְׁלֹשָׁה כְּפָרִים הַמְשׁוּלָּשִׁין, אִם יֵשׁ בֵּין שְׁנַיִם חִיצוֹנִים מֵאָה וְאַרְבָּעִים וְאַחַת וּשְׁלִישׁ — עָשָׂה אֶמְצָעִי אֶת שְׁלָשְׁתָּן לִהְיוֹת אֶחָד.

**William Davidson Edition - English:**
**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.**


###### Eruvin 57a:13
[Eruvin 57a:13](https://torahapp.org/share/book/Eruvin/r/57a:13)

**גְּמָ׳** מְנָא הָנֵי מִילֵּי? אָמַר רָבָא: דְּאָמַר קְרָא: ״מִקִּיר הָעִיר וָחוּצָה״. אָמְרָה תּוֹרָה: תֵּן חוּצָה, וְאַחַר כָּךְ מְדוֹד.

**William Davidson Edition - English:**
**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.


###### Eruvin 57a:14
[Eruvin 57a:14](https://torahapp.org/share/book/Eruvin/r/57a:14)

וַחֲכָמִים אוֹמְרִים לֹא אָמְרוּ וְכוּ׳. אִיתְּמַר, רַב הוּנָא אָמַר: נוֹתְנִין קַרְפֵּף לָזוֹ וְקַרְפֵּף לָזוֹ. חִיָּיא בַּר רַב אָמַר: קַרְפֵּף [אֶחָד] לִשְׁתֵּיהֶן.

**William Davidson Edition - English:**
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.**


###### Eruvin 57a:15
[Eruvin 57a:15](https://torahapp.org/share/book/Eruvin/r/57a:15)

תְּנַן, וַחֲכָמִים אוֹמְרִים: לֹא אָמְרוּ קַרְפֵּף אֶלָּא בֵּין שְׁתֵּי עֲיָירוֹת, תְּיוּבְתָּא דְרַב הוּנָא!

**William Davidson Edition - English:**
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.


###### Eruvin 57a:16
[Eruvin 57a:16](https://torahapp.org/share/book/Eruvin/r/57a:16)

אָמַר לְךָ רַב הוּנָא: מַאי קַרְפֵּף, תּוֹרַת קַרְפֵּף, וּלְעוֹלָם קַרְפֵּף לָזוֹ וְקַרְפֵּף לָזוֹ.

**William Davidson Edition - English:**
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.


###### Eruvin 57a:17
[Eruvin 57a:17](https://torahapp.org/share/book/Eruvin/r/57a:17)

הָכִי נָמֵי מִסְתַּבְּרָא, מִדְּקָתָנֵי סֵיפָא: אִם יֵשׁ לָזוֹ שִׁבְעִים אַמָּה וְשִׁירַיִים וְלָזוֹ שִׁבְעִים אַמָּה וְשִׁירַיִים — עוֹשֶׂה קַרְפֵּף לִשְׁתֵּיהֶן לִהְיוֹת אֶחָד. שְׁמַע מִינַּהּ.

**William Davidson Edition - English:**
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.


###### Eruvin 57a:18
[Eruvin 57a:18](https://torahapp.org/share/book/Eruvin/r/57a:18)

לֵימָא תֶּיהְוֵי תְּיוּבְתֵּיהּ דְּחִיָּיא בַּר רַב! אָמַר לְךָ חִיָּיא בַּר רַב:

**William Davidson Edition - English:**
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:**