Eruvin 113

דל ארבע דתחומין וארבע דקרנות כמה הוי תמניא

Deducting [for the open space] four [million square cubits]<span class="x" onmousemove="('comment',' One thousand by one thousand sq. cubits on each of the four sides of the city amount to four million sq. cubits, cf. supra p. 398, n. 2.');">¹</span> from the limits and four [million square cubits] from the corners,<span class="x" onmousemove="('comment',' Cf. loc. cit. n. 3.');">²</span> to what area would this space amount?

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

To one of eight million square cubits. But is not such an open space a third of the area?<span class="x" onmousemove="('comment',' Which, as has just been shown, amounted to 8,000,000 + 16,000,000 = 24,000,000 sq. cubits; 8,000,000/24,000,000 = 1/3.');">³</span> - Do you think that the reference is to a square town?

רבינא אמר מאי רביע רביע דתחומין

No, a circular town was spoken of. For by how much does the area of a square exceed that of a circle? By one quarter approximately.

רב אשי אמר מאי רביע רביע דקרנות

Deduct a quarter from the measurements given<span class="x" onmousemove="('comment',' Sc. from the strip of open space around the town which, if square shaped, contains an area of eight million sq. cubits.');">⁴</span> and there would remain six [million square cubits];<span class="x" onmousemove="('comment',' The area of the city (1,000 X 1,000 sq. cubits) plus the area of the open space (a strip of a thousand cubits in width on the four sides of the town) amounts to 3,000 X 3,000 = 9,000,000 sq. cubits, when the city, and the open space around it are square shaped. When they are circular the total of their area amounts to 9,000,000 X 1/4 sq. cubits. The area of the open space alone amounts, therefore, to 9,000,000 X 3/4 - 1,000,000 X 3/4');">⁵</span> and six [million] represent a quarter of twenty-four [million].<span class="x" onmousemove="('comment',' The latter figure representing the total area of the limits of the land and the corners (v. supra 56b ad fin) which, unlike the open space, are not affected by the shape of the city.');">⁶</span>

אמר ליה רבינא לרב אשי והא סביב כתיב

Rabina explained: What is meant by 'a quarter'? A quarter of the area of the limits.<span class="x" onmousemove="('comment',' According to Rabina the reference is, as was first assumed (cf. supra text and notes) , to a city whose area was 2,000 by 2,000 sq. cubits, and the area of whose limits, (i.e., the strips of 2,000 cubits perpendicular distance from its confines) plus the area of the corners between them, is 2,000 X 2,000 X 8 = 32,000,000 sq. cubits, while the area of its open spaces along the limits, amounts to 2,000 X 1,000 X 4= 8,000,000 sq. cubits, 8,000,000/32,000,000 = 1/4 which is the 'quarter' spoken of. Rabina is of the opinion that no land for the purpose of open space was set aside in htn the corners. V. Tosaf. s.v. thhk');">⁷</span> R'Ashi explained: What is meant by 'a quarter'?

מאי סביב סביב דקרנות דאי לא תימא הכי גבי עולה דכתיב (ויקרא א, ה) וזרקו (בני אהרן) את הדם על המזבח סביב ה"נ סביב ממש אלא מאי סביב סביב דקרנות ה"נ מאי סביב סביב דקרנות

A quarter of the area of the corners.<span class="x" onmousemove="('comment',' No open space being allowed along the limits. Cf. previous note, the Tosaf. cited and Rashi s.v. a.l. The area of each corner being 4,000,000 sq. cubits and the area of the open space in each corner being 1,000,000 sq. cubits the latter area equals (1,000,000/4,000,000 =) 1/4 'a quarter' of that of the former in each corner. The total area of the corners equals 4 X 4,000,000 while the total area of open spaces in these corners equals 4 X 1,000,000 the proportion of the latter to the former is, therefore, 4 X 1,000,000/4 X 4,000,000 = 1/4 which is also 'a quarter'.');">⁸</span> Said Rabina to R'Ashi: Is it not written i Scripture: 'round about'?<span class="x" onmousemove="('comment',' Num. XXXV, 4. How then could it be maintained that the open spaces were restricted (cf. prev. n.) to the corners only?');">⁹</span> - By 'round about' the corners were meant - For, if you were not to admit this, would you also contend that the expression.

א"ל רב חביבי מחוזנאה לרב אשי והא איכא מורשא דקרנתא

And<span class="x" onmousemove="('comment',' 'The sons of Aaron' is enclosed in cur. edd. in parenthesis.');">¹⁰</span> dash the blood round about against the altar,<span class="x" onmousemove="('comment',' Lev. I. 5.');">¹¹</span> written in connection with a burnt-offering, also meant round about the very altar?<span class="x" onmousemove="('comment',' But this, surely, is contrary to the adopted practice of sprinkling the blood round the corners of the altar only. htnk');">¹²</span>

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

Consequently you must admit that by 'round about' was meant round about the corners; well then, here also by 'round about' was meant round about the corners. Said R'Habibi<span class="x" onmousemove="('comment',' MS.M 'Aha'; Rashi (s.v. a.l.) 'Habiba'.');">¹³</span> of Hoza'ah<span class="x" onmousemove="('comment',' The modern Khuzistan.');">¹⁴</span>

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

to R'Ashi: Are there not, however, the projections of the corners?<span class="x" onmousemove="('comment',' Which reduce the area of the open spaces which, in consequence, would represent less than a quarter of the corners.');">¹⁵</span> - The reference is to a circular city.<span class="x" onmousemove="('comment',' A circle has no projecting corners.');">¹⁶</span> Was it not, however, made square?<span class="x" onmousemove="('comment',' As stated supra.');">¹⁷</span>

אמר ליה ה"מ בעיגולא מגו רבוע אבל באלכסונא בעינא טפי דאמר מר כל אמתא בריבוע אמתא ותרי חומשי באלכסונא:

- You might contend that it was said that we imagine it to be a square<span class="x" onmousemove="('comment',' For the purpose of extending its Sabbath limits or the land around it in favour of the Levites.');">¹⁸</span> but can you contend that it was actually made square?<span class="x" onmousemove="('comment',' Obviously not. An imaginary square causes no actual reduction.');">¹⁹</span> Said R'Hanilai<span class="x" onmousemove="('comment',' MS.M., Habi; Bomb. ed. Hinai.');">²⁰</span>

<big><strong>מתני׳</strong></big> נותנין קרפף לעיר דברי רבי מאיר וח"א לא אמרו קרפף אלא בין שתי עיירות אם יש לזו שבעים אמה ושיריים ולזו שבעים אמה ושיריים עושה קרפף את שתיהן להיות אחד

of Hoza'ah to R'Ashi: Consider! By how much does the area of a square exceed that of a circle? By a quarter approximately. Are not then the so called 'eight hundred'<span class="x" onmousemove="('comment',' Supra 56b; 'The Sabbath limits gain eight hundred cubits' by the application to the corners of the diagonal of the tablet of two thousand cubits in length.');">²¹</span>

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

only six hundred and sixty-seven minus a third?<span class="x" onmousemove="('comment',' If the difference between a square and a circle is a quarter of the former it is also (since the proportion of the two figures is 3:4) a third of the latter. The difference consequently between a line of two thousand cubits (which may be regarded as the diameter of a circle) and the diagonal of a square whose sides measure two thousand cubits should be a third of two thousand 2000/3 = 666 2/3 or 667 - 1/3.');">²²</span> - The other replied: This<span class="x" onmousemove="('comment',' That the approximate difference between the area of a square and that of a circle is a quarter of the former or a third of the latter.');">²³</span> applies only to a circle inscribed within a square, but in the case of the diagonal - of a square<span class="x" onmousemove="('comment',' In relation to any of its sides.');">²⁴</span>

<big><strong>גמ׳</strong></big> מנא הני מילי אמר רבא דאמר קרא (במדבר לה, ד) מקיר העיר וחוצה אמרה תורה תן חוצה ואחר כך מדוד:

more must be added; for a Master stated: Every cubit in the side of a square corresponds to one and two fifths of a cubit in its diagonal.<span class="x" onmousemove="('comment',' A side of the square spoken of being equal to 2,000 cubits, the diagonal of such a square must be equal to 2,000 X 7/5 cubits. The gain, therefore, is 2,000 X 7/5 - 2,000 = 2,000 X 2/5 = 400 X 2,000 cubits.');">²⁵</span> <big><b>MISHNAH: </b></big>A KARPAF<span class="x" onmousemove="('comment',' V. Glos., a stretch of land extending to seventy and two thirds cubits away from the town.');">²⁶</span> IS ALLOWED FOR EVERY TOWN;<span class="x" onmousemove="('comment',' Sc. the Sabbath limits begin at such a distance from the town and not from the town boundary.');">²⁷</span>

וחכ"א לא אמרו וכו': איתמר רב הונא אמר נותנין קרפף לזו וקרפף לזו חייא בר רב אמר קרפף [א'] לשתיהן

SO R'MEIR, BUT THE SAGES RULED: [THE LAW OF] KARPAF<span class="x" onmousemove="('comment',' Sc. the Sabbath limits begin at such a distance from the town and not from the town boundary.');">²⁷</span> WAS INSTITUTED ONLY BETWEEN TWO TOWNS<span class="x" onmousemove="('comment',' This is explained in the Gemara infra.');">²⁸</span> SO THAT BY ADDING TO EACH ONE<span class="x" onmousemove="('comment',' Or 'EITHER' (v. Gemara infra) . Lit., 'if there is to this . . and if etc,'');">²⁹</span>

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

A STRETCH OF LAND OF SEVENTY AND A FRACTION<span class="x" onmousemove="('comment',' I.e., two thirds of a cubit.');">³⁰</span> THE KARPAF COMBINES THE TWO TOWNS INTO ONE.<span class="x" onmousemove="('comment',' This is explained in the Gemara infra.');">²⁸</span> SO ALSO WHERE THREE VILLAGES ARE ARRANGED IN THE SHAPE OF A TRIANGLE,<span class="x" onmousemove="('comment',' This is explained in the Gemara infra.');">²⁸</span>

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

IF BETWEEN THE TWO OUTER ONES THERE WAS A DISTANCE OF A HUNDRED AND FORTY-ONE AND A THIRD CUBITS, THE MIDDLE ONE CAUSES ALL THE THREE OF THEM TO BE REGARDED AS ONE.<span class="x" onmousemove="('comment',' This is explained in the Gemara infra.');">²⁸</span> <big><b>GEMARA: </b></big>Whence is this<span class="x" onmousemove="('comment',' That a karpaf is allowed for every town. vmuj');">³¹</span> inferred? - Raba replied: From Scripture which says: From the wall of the city and outward,<span class="x" onmousemove="('comment',' Num. XXXV, 4, emphasis on 'outward' . vmuj');">³²</span>

ה"נ מסתברא מדקתני סיפא אם יש לזו ע' אמה ושיריים ולזו ע' אמה ושיריים עושה קרפף לשתיהן להיות אחד שמע מינה

the Torah having thereby enjoined: Allow an outward area,<span class="x" onmousemove="('comment',' , Sc. KARPAF.');">³³</span> and then begin your measuring.<span class="x" onmousemove="('comment',' Of the Sabbath limit.');">³⁴</span> BUT THE SAGES RULED.

לימא תיהוי תיובתיה דחייא בר רב אמר לך חייא בר רב

WAS INSTITUTED ONLY etc. It was stated: R'Huna laid down: A karpaf is allowed for each town. Hiyya B'Rab laid down: Only one karpaf is allowed for both towns. We learned: BUT THE SAGES RULED: [THE LAW OF] KARPAF WAS INSTITUTED ONLY BETWEEN TWO TOWNS. Is not this<span class="x" onmousemove="('comment',' The use of KARPAF in the sing.');">³⁵</span> an objection against R'Huna? - R'Huna can answer you: What is meant by 'KARPAF'?<span class="x" onmousemove="('comment',' The use of KARPAF in the sing.');">³⁵</span> The law of karpaf, but in fact a karpaf is allowed for each town. This may also be supported by reason, since in the final clause it was stated: SO THAT BY ADDING TO EACH ONE A STRETCH OF LAND OF SEVENTY AND A FRACTION CUBITS THE KARPAF COMBINES THE TWO TOWNS INTO ONE. This is conclusive. Must it be said that this<span class="x" onmousemove="('comment',' The final clause just cited, according to which a karpaf is allowed to each town.');">³⁶</span> presents an objection against Hiyya B'Rab?<span class="x" onmousemove="('comment',' Who allows only one karpaf for both towns.');">³⁷</span> - Hiyya B'Rab can answer you: