Yerushalmi Eruvin 2:5 ירושלמי עירובין ב׳:ה׳

MISHNAH: In addition, Rebbi Jehudah ben Bava said, if a garden patch or a corral are seventy cubits and a remainder by seventy cubits and a remainder surrounded by a wall ten hand-breadths high¹¹Since 70.71…² = 5’000, the area enclosed is 2 bet se’ah. In an enclosed area of up to 2 bet se’ah one may carry. One of more than 2 bet se’ah may be turned into a domain for carrying only if it is used for human dwelling. one carries inside on condition that it contain a watchman’s hut or a dwelling or be close to a village¹²Within 70.71 cubits of the village.

HALAKHAH: Paragraph. “In addition, Rebbi Jehudah ben Bava said,” etc. Rebbi Samuel bar Naḥman in the name of Rebbi Jonathan, they inferred it from the courtyard of the Tabernacle: the length of the courtyard 100 cubits wide 50 by 50⁸¹Ex. 27:18. Babli 23b. The expression “50 by 50” is read as meaning that the standard measure of area shall be a square of 5’000 square cubits.. 50 times 100 are 5’000. 70 by 70 are 5’000 minus 100, and we have stated “seventy cubits and a remainder.” And Samuel stated, they stated cubits and two thirds of a cubit. Seventy times two thirds and seventy times two thirds make 140 thirds each; 140 thirds and 140 thirds are 93⅓. There is missing from there 4/9 for the corner, there remain nineteen thirds minus one ninth. As we have stated, there is a slight difference which the Sages could not compute⁸²Since 70² = 4900 and 71²= 5041 the square root of 5’000 is between 70 and 71. In order to compute 70⅔² one uses the binomial formula in its geometric form: A square of sides 70⅔ is composed of a square of sides 70 + two rectangles 70 by ⅔ + a square of area 4/9 for a total of 49937/9. The difference to 5000 is 62/9 = 19/3 -1/9. The additional correction was a problem. Not only is the square root of 5000 irrational, not expressible as a fraction, but of the two square root algorithms used in Antiquity, the Babylonian, using a kind of Newton approximation, is an approximation from above and the Hellenistic, using an equivalent of modern continued fractions, starts with an approximation from above, when the legal situation here demands an approximation from below. 70⅔, is a reasonable rational approximation from below to √5000 since 707/9² already is >5009. The second term of the continued fraction development is an approximation from below, 70140/197, not a practical expression. The systematic approximation of square roots from below which used to be taught in our schools is essentially dependent on the notion of place values underlying Indian- Arabic numerals. The first approximation of √5000 both in the Babylonian and the Hellenistic methods, 705/7, is an exceedingly good low-denominator approximation from above, (705/7)² = 500025/49, and therefore not usable in this context. The approximation of 70⅔ cubits allows a measuring error of 1 digit without exceeding √5000. Tosephta 4:9..

In a corral which covers two bet se’ah one is permitted only to carry a distance of four cubits⁸³This refers to areas enclosed by a makeshift fence such as is authorized for a caravan. The moment it is a full two bet se’ah one requires a wall or a fence with woof and warp (Mishnah 5).. If there were two, each one a bet se’ah minus four cubits; Rebbi Zeˋira in the name of Rebbi Joḥanan: one carries in the second as complement of the first⁸⁴Cf. Babli 93a. Two people enclosed adjacent areas with makeshift fences. R. La notes that they cannot combine their areas to one authorized for caravans, cf. Chapter 1 Note 296.. Rebbi La in the name of Rebbi Joḥanan, one may not carry in the second as complement of the first. Rebbi Zeˋira said, Rebbi La agrees that if there were three⁸⁵Three people camping together form a caravan and follow the rules explained in Chapter 1.. Each of the three a bet se’ah, one agrees that one carries in the second as complement of the first⁸⁶Since as member of a caravan he has two bet se’ah at his disposal..

A corral which covers up to two bet se’ah. Rebbi Abbahu said, since it can be permitted by a caravan, if somebody threw from the public domain into it he is liable⁸⁷Even though the enclosure made by a caravan does not qualify as wall of a private domain under normal circumstances, the area becomes a private domain for the rules of the Sabbath.. Rebbi Samuel bar Rav Isaac asked, (not after it was permitted) [if it was chosen by]⁸⁸The text in parentheses was originally written by the scribe, the text in brackets is the corrector’s. The original text is preferable. the caravan it becomes forbidden in a prohibition; therefore here is no liability for a purification sacrifice⁸⁹R. Abbahu’s statement is refuted. Since the entire arrangement is rabbinical, no biblical liability is possible.. By the same argument, an alley whose beam is higher than twenty cubits since it is qualified in the opinion of Rebbi Jehudah (more than thirteen)⁹⁰The text in parentheses should be deleted; it is appropriate only in the next sentence.
Since practice does not follow R. Jehudah, the rules of private domain cannot be applied to areas which may become private domains only according to him., if somebody threw from the public domain into it would he be liable? An alley which was breached more than ten [cubits], since a breach of an alley in the opinion of Rebbi Jehudah is more than thirteen, if somebody threw from the public domain into it would he be liable?

If a courtyard is open into a corral one may carry from the courtyard to the corral but not from the corral to the courtyard⁹¹Courtyard and corral must have a common owner. Since the corral (enclosed by a makeshift fence) is an appendix to the courtyard but not vice-versa, cf. Note 48, Mishnah 9:2.. Rebbi Judah from Anthodriya asked, may one carry from one corral to another corral through the courtyard⁹²Since from courtyard to corral is permitted, may one move from one corral to the other without stopping in the courtyard? The question is not answered since if half of the way is forbidden the entire way cannot be permitted.? ⁹³Chapter 1, Note 194. The opinion of Rebbi Jehudah seems inverted, as we have stated there, “what is a corral? Anything close to a village, the words of Rebbi Jehudah.” And here he says so? Rebbi Mana said, Rebbi Jehudah treated it as a house.