עירובין 57 — Soncino English Talmud

¹Deducting [for the open space] four [million square cubits] from the limits and four [million square cubits] from the corners, to what area would this space amount? To one of eight million square cubits. But is not such an open space a third of the area? — Do you think that the reference is to a square town? 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. Deduct a quarter from the measurements given and there would remain six [million square cubits]; and six [million] represent a quarter of twenty-four [million]. Rabina explained: What is meant by ‘a quarter’? A quarter of the area of the limits. R. Ashi explained: What is meant by ‘a quarter’? A quarter of the area of the corners. Said Rabina to R. Ashi: Is it not written in Scripture: ‘round about’? — By ‘round about’ the corners were meant — For, if you were not to admit this, would you also contend that the expression. And dash the blood round about against the altar, written in connection with a burnt-offering, also meant round about the very altar? 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 of Hoza'ah to R. Ashi: Are there not, however, the projections of the corners? — The reference is to a circular city. Was it not, however, made square? — You might contend that it was said that we imagine it to be a square but can you contend that it was actually made square? Said R. Hanilai 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’ only six hundred and sixty-seven minus a third? — The other replied: This applies only to a circle inscribed within a square, but in the case of the diagonal — of a square 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. MISHNAH. A KARPAF IS ALLOWED FOR EVERY TOWN; SO R. MEIR, BUT THE SAGES RULED: [THE LAW OF] KARPAF WAS INSTITUTED ONLY BETWEEN TWO TOWNS SO THAT BY ADDING TO EACH ONE A STRETCH OF LAND OF SEVENTY AND A FRACTION THE KARPAF COMBINES THE TWO TOWNS INTO ONE. SO ALSO WHERE THREE VILLAGES ARE ARRANGED IN THE SHAPE OF A TRIANGLE, 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. GEMARA. Whence is this inferred? — Raba replied: From Scripture which says: From the wall of the city and outward, the Torah having thereby enjoined: Allow an outward area, and then begin your measuring. BUT THE SAGES RULED . . . 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 an objection against R. Huna? — R. Huna can answer you: What is meant by ‘KARPAF’? 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 presents an objection against Hiyya b. Rab? — Hiyya b. Rab can answer you:^ᵃ^ᵇ^ᶜ^ᵈ^ᵉ^ᶠ^ᵍ^ʰ^ⁱ^ʲ^ᵏ^ˡ^ᵐ^ⁿ^ᵒ^ᵖ^ᵠ^ʳ^ˢ^ᵗ^ᵘ^ᵛ^ʷ^ˣ^ʸ^ᶻ^ᵃᵃ^ᵃᵇ^ᵃᶜ^ᵃᵈ^ᵃᵉ^ᵃᶠ^ᵃᵍ^ᵃʰ^ᵃⁱ^ᵃʲ^ᵃᵏ

^ᵃnote: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.
^ᵇnote:Cf. loc. cit. n. 3.
^ᶜnote: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.
^ᵈnote:Sc. from the strip of open space around the town which, if square shaped, contains an area of eight million sq. cubits.
^ᵉnote: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 (area of circular city) = 3/4 (9,000,000 — 1,000,000) = 3/4 x 8,000,000 = 6,000,000 sq. cubits.
^ᶠnote: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.
^ᵍnote: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 the corners. V. Tosaf. s.v. htn.
^ʰnote:No open space being allowed along the limits. Cf. previous note, the Tosaf. cited and Rashi s.v. thhk 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’.
^ⁱnote:Num. XXXV, 4. How then could it be maintained that the open spaces were restricted (cf. prev. n.) to the corners only?
^ʲnote:‘The sons of Aaron’ is enclosed in cur. edd. in parenthesis.
^ᵏnote:Lev. I. 5.
^ˡnote:But this, surely, is contrary to the adopted practice of sprinkling the blood round the corners of the altar only.
^ᵐnote:MS.M ‘Aha’; Rashi (s.v. htnk a.l.) ‘Habiba’.
^ⁿnote:The modern Khuzistan.
^ᵒnote:Which reduce the area of the open spaces which, in consequence, would represent less than a quarter of the corners.
^ᵖnote:A circle has no projecting corners.
^ᵠnote:As stated supra.
^ʳnote:For the purpose of extending its Sabbath limits or the land around it in favour of the Levites.
^ˢnote:Obviously not. An imaginary square causes no actual reduction.
^ᵗnote:MS.M., Habi; Bomb. ed. Hinai.
^ᵘnote: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.
^ᵛnote: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.
^ʷnote: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.
^ˣnote:In relation to any of its sides.
^ʸnote: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.
^ᶻnote:V. Glos., a stretch of land extending to seventy and two thirds cubits away from the town.
^ᵃᵃnote:Sc. the Sabbath limits begin at such a distance from the town and not from the town boundary.
^ᵃᵇnote:This is explained in the Gemara infra.
^ᵃᶜnote:Or ‘EITHER’ (v. Gemara infra). Lit., ‘if there is to this . . . and if etc,’
^ᵃᵈnote:I.e., two thirds of a cubit.
^ᵃᵉnote:That a karpaf is allowed for every town.
^ᵃᶠnote:Num. XXXV, 4, emphasis on ‘outward’ vmuj.
^ᵃᵍnote:vmuj, Sc. KARPAF.
^ᵃʰnote:Of the Sabbath limit.
^ᵃⁱnote:The use of KARPAF in the sing.
^ᵃʲnote:The final clause just cited, according to which a karpaf is allowed to each town.
^ᵃᵏnote:Who allows only one karpaf for both towns.

²This is the view of R. Meir. But if this is the view of R. Meir [the objection arises:] Was it not already enunciated in the first clause: A KARPAF IS ALLOWED FOR EVERY TOWN; SO R. MEIR? — [Both were] required. For if [the law were to be derived] from the former only it might have been presumed that one karpaf is allowed for one town and one is also allowed for two towns, hence we were informed that for two towns two karpafs are allowed. And if we had been informed of the latter only it might have been assumed [that R. Meir's view applied to such a case only] because [one karpaf is too] cramped for the use of two towns, but not in the former case where the space is not too cramped. [Hence both were] required. We learned: SO ALSO WHERE THREE VILLAGES ARE ARRANGED IN THE SHAPE OF A TRIANGLE, 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. The reason then is because there was one in the middle, but if there had been none in the middle the outer two villages would not have been combined. Is not this an objection against R. Huna? — R. Huna can answer you: Surely, in connection with this ruling it was stated: Rabbah in the name of R. Idi who had it from R. Hanina explained: There is no need for the villages to be arranged in the shape of an equilateral triangle but that if on observation it is found that with the middle one placed between the other two they would form a triangle, and there would be between the one and the other a distance of no more than a hundred and forty-one and a third cubits the middle one causes all the three of then, to be regarded as one. Said Raba to Abaye: What [maximum distance] is allowed between an outer village and the middle one? — ‘Two thousand cubits’, the other replied. ‘But did you not say’, the former asked: ‘that logical reasoning is in agreement with Raba the son of Rabbah son of R. Huna who ruled that a perpendicular distance of more than two thousand cubits was allowed?’ ‘What a comparison! There, houses are in existence, but here there are no houses’. Raba further asked Abaye: What [maximum distance] is allowed between the two outer ones? — ‘What [distance] is allowed’! What difference does this make in view of the ruling that ‘if . . . with the middle one placed between the other two’ there remains between them ‘a distance of no more than a hundred and forty-one and a third cubits’ they are all regarded as one? — Even if they are four thousand cubits distant from one another? — ‘Yes’, the other replied. ‘But did not R. Huna lay down: If a town is shaped like a bow then if the distance between its two ends is less than four thousand cubits the Sabbath limits are measured from the bow string, otherwise measuring must begin from the arch?’ — ‘There’, the other replied. ‘you cannot say that the distance is filled up but here you can well say so’. Said R. Safra to Raba: Behold the people of Ktesifon for whom we measure the Sabbath limits from the further side of Ardashir and the people of Ardashir for whom we measure the Sabbath limit from the further side of Ktesifon; does not the Tigris in fact cut between them a gap wider than a hundred and forty-one and a third cubits? — The other thereupon went out and showed him the flanks of a wall that projected seventy and two thirds cubits across the Tigris. MISHNAH. SABBATH LIMITS MAY BE MEASURED ONLY WITH A ROPE OF THE LENGTH OF FIFTY CUBITS NEITHER LESS NOR MORE; AND A MAN MAY MEASURE ONLY WHILE HOLDING THE END OF THE ROPE ON A LEVEL WITH HIS HEART. IF IN THE COURSE OF MEASURING THE SURVEYOR REACHED A GLEN OR A FALLEN WALL HE SPANS IT AND RESUMES HIS MEASURING; IF HE REACHED A HILL HE SPANS IT AND RESUMES HIS MEASURING;^ᵃˡ^ᵃᵐ^ᵃⁿ^ᵃᵒ^ᵃᵖ^ᵃᵠ^ᵃʳ^ᵃˢ^ᵃᵗ^ᵃᵘ^ᵃᵛ^ᵃʷ^ᵃˣ^ᵃʸ^ᵃᶻ^ᵇᵃ^ᵇᵇ^ᵇᶜ^ᵇᵈ^ᵇᵉ^ᵇᶠ^ᵇᵍ^ᵇʰ^ᵇⁱ^ᵇʲ^ᵇᵏ^ᵇˡ^ᵇᵐ^ᵇⁿ^ᵇᵒ^ᵇᵖ^ᵇᵠ^ᵇʳ^ᵇˢ^ᵇᵗ^ᵇᵘ^ᵇᵛ^ᵇʷ^ᵇˣ^ᵇʸ

^ᵃˡnote:The final clause just cited.
^ᵃᵐnote:Lit., ‘this according to whom?’
^ᵃⁿnote:It is not the conclusion of the ruling of the Sages, but a continuation of R. Meir's ruling with which our Mishnah began.
^ᵃᵒnote:The purpose of the ruling being that every town shall have a karpaf but not one exclusively for itself.
^ᵃᵖnote:By the final clause.
^ᵃᵠnote:That karpafs are at all allowed.
^ᵃʳnote:One town surrounded by open country.
^ᵃˢnote:In such a case, it might have been assumed, R. Meir allows no karpaf at all.
^ᵃᵗnote:Why the two outer villages may be regarded as one despite the distance of a hundred and forty-one and a third cubits intervening.
^ᵃᵘnote:The requirement of a third village between the other two.
^ᵃᵛnote:Who allowed a karpaf for every town (or village) and according to whom the two outer villages would have been combined into one, even in the absence of the third village, owing to the fact that no more than the space of two karpafs (2 X 70 2/3 = 141 1/3 cubits) intervened between them.
^ᵃʷnote:Var. lec. ‘Raba’, ‘It. Adda’.
^ᵃˣnote:Lit., ‘actually’.
^ᵃʸnote:Sc. that ‘the distance between any two of them shall be no greater than a hundred and forty-one and a third cubits.
^ᵃᶻnote:l.e., ‘the middle village and any of the other two.
^ᵇᵃnote:A distance that is equal to that of two karpafs on either side of the middle village.
^ᵇᵇnote:Even though the distance between the two outer ones is much greater than a hundred and forty-one and a third cubits.
^ᵇᶜnote:If it is desired that the middle one shall cause ALL THE THREE OF THEM TO BE REGARDED AS ONE.
^ᵇᵈnote:A Sabbath limit. Since it is permitted to walk without an ‘erub between the middle one and either of the others it is also permitted to regard the former as placed between the latter.
^ᵇᵉnote:Between the middle point of the bow-string and the arch, in the case of a town that was built in the shape of a bow (supra 55b).
^ᵇᶠnote:Lit., ‘thus now’.
^ᵇᵍnote:Throughout the area of the arch to either end of the imaginary string, so that it is possible to reach the ‘string’ via the bow.
^ᵇʰnote:Between the middle village and the others, and all the distance between them must be traversed across open country.
^ᵇⁱnote:I.e., , the confines on either side of the middle one and each of the others.
^ᵇʲnote:Which shows that the distance between the outer ones subject to this reservation is of no consequence.
^ᵇᵏnote:The outer ones.
^ᵇˡnote:Supra 55a q.v. notes.
^ᵇᵐnote:Lit., ‘there is no (reason) to say: Fill’, between the houses at the two ends of the bow.
^ᵇⁿnote:Since there is nothing wherewith to fill it.
^ᵇᵒnote:Lit., ‘there is (reason) to say: Fill’, by regarding the third village as breaking up the distance and reducing it on either side.
^ᵇᵖnote:[Two neighbouring places, the former on the eastern and the latter on the western bank of the Tigris, v. Obermeyer pp. 164ff.] Thus assuming that the two towns are combined into one.
^ᵇᵠnote:In its course between the two towns.
^ᵇʳnote:How then could the two towns be regarded as one?
^ᵇˢnote:Lit.,’remnants.
^ᵇᵗnote:And thus reduced the gap between the buildings of the two towns to less than a hundred and forty one and a third cubits.
^ᵇᵘnote:The reason follows in the Gemara.
^ᵇᵛnote:Sc. each of the two surveyors must hold his end of the measuring rope at a level with his heart, in order to ensure correctness and in the process of measuring. Correctness is impossible where one end of the rope is held at one level and the other end at a higher or lower level, since the distance measured would in this case be less than the full length of the rope.
^ᵇʷnote:That collapsed in a heap and across which people pass.
^ᵇˣnote:[I.e., he takes into consideration only the horizontal span provided it is not more than fifty cubits]. Sc. one man stands on its near side while another stands on its far side, each of them holding one end of the rope which is thus stretched across the glen or the collapsed wall. By this method of measuring one gains for the Sabbath limit the distances taken up by the slopes.
^ᵇʸnote:This refers to a glen, for instance, that was wider then fifty cubits (cf. n. 7) in a part that faced the town and narrower than fifty cubits in another part that was removed from the town sideways. The surveyor, when reaching the edge of the glen, is in such circumstances allowed to make a detour to the narrower section of the glen, to span it there with the rope, and to continue his measuring until the rope is perpendicular to the line drawn from the point furthest from the town on the far side of the glen. He then RESUMES his measuring from that point to the end of the Sabbath limit.