Eruvin

Deducting [for the open space] four [million square cubits]1 from the limits and four [million square cubits] from the corners,2 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?3 — 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 given4 and there would remain six [million square cubits];5 and six [million] represent a quarter of twenty-four [million].6 Rabina explained: What is meant by ‘a quarter’? A quarter of the area of the limits.7 R. Ashi explained: What is meant by ‘a quarter’? A quarter of the area of the corners.8 Said Rabina to R. Ashi: Is it not written in Scripture: ‘round about’?9 — By ‘round about’ the corners were meant — For, if you were not to admit this, would you also contend that the expression. And10 dash the blood round about against the altar,11 written in connection with a burnt-offering, also meant round about the very altar?12 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. Habibi13 of Hoza'ah14 to R. Ashi: Are there not, however, the projections of the corners?15 — The reference is to a circular city.16 Was it not, however, made square?17 — You might contend that it was said that we imagine it to be a square18 but can you contend that it was actually made square?19 Said R. Hanilai20 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’21 only six hundred and sixty-seven minus a third?22 — The other replied: This23 applies only to a circle inscribed within a square, but in the case of the diagonal — of a square24 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. 25 MISHNAH. A KARPAF26 IS ALLOWED FOR EVERY TOWN;27 SO R. MEIR, BUT THE SAGES RULED: [THE LAW OF] KARPAF27 WAS INSTITUTED ONLY BETWEEN TWO TOWNS28 SO THAT BY ADDING TO EACH ONE29 A STRETCH OF LAND OF SEVENTY AND A FRACTION30 THE KARPAF COMBINES THE TWO TOWNS INTO ONE.28 SO ALSO WHERE THREE VILLAGES ARE ARRANGED IN THE SHAPE OF A TRIANGLE,28 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.28 GEMARA. Whence is this31 inferred? — Raba replied: From Scripture which says: From the wall of the city and outward,32 the Torah having thereby enjoined: Allow an outward area,33 and then begin your measuring.34 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 this35 an objection against R. Huna? — R. Huna can answer you: What is meant by ‘KARPAF’?35 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 this36 presents an objection against Hiyya b. Rab?37 — Hiyya b. Rab can answer you: supra p. 398, n. 2. = 1/3. cubits. 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. unlike the open space, are not affected by the shape of the city. 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. 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’. only? tablet of two thousand cubits in length. 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. of the latter. 7/5 cubits. The gain, therefore, is 2,000 X 7/5 — 2,000 = 2,000 X 2/5 = 400 X 2,000 cubits.