Eruvin

GEMARA. ONE HANDBREADTH! Is not a handbreadth and a half required?1 — Since it is wide enough to hold [an ariah of the size of] one handbreadth one may provide a foundation2 for the remaining half of the handbreadth by plastering [the beam] with clay, a little on one side3 and a little on the other,3 so [that the ariah can be] kept in position. Rabbah son of R. Huna said: The cross-beam of which [the Rabbis] spoke must be strong enough to support an ariah;4 the supports5 of the beam, however, need not be so strong as to be capable of bearing the beam and the ariah.6 R. Hisda, however, ruled: They7 must be strong enough to support both the beam and the ariah. R. Shesheth said: If one laid a beam across [an entrance to] an alley and spread a mat over it, raising [the lower end of the mat to a height of] three handbreadths from the ground, there is here neither valid cross-beam nor valid partition. There is here no valid cross-beam, since it is covered up; and no valid partition, since it is one through which kids can push their way. 8 Our Rabbis taught: If a cross-beam projects from one wall and does not touch the wall opposite, and so also if two cross-beams one of which projects from one wall and the other from the wall opposite, do not touch one another, it is not necessary to provide9 another beam, [if the gap is] less than three handbreadths, [but if it was one of] three handbreadths it is necessary to provide another cross-beam. R. Simeon b. Gamaliel ruled: [if the gap was] less than four handbreadths it is not necessary to provide another cross-beam [and only where it was one of] four handbreadths it is necessary to provide another cross-beam. Similarly where there were two parallel cross-beams, neither of which was wide enough to hold an ariah, it is unnecessary to provide10 another cross-beam if the two together can hold the width of one handbreadth of an ariah, otherwise11 it is necessary to provide another cross-beam. R. Simeon b. Gamaliel ruled: If they can hold an ariah of the length of three handbreadths it is unnecessary to provide10 another cross-beam, otherwise11 it is necessary to provide another cross-beam. If they were [fixed] one higher than the other,12 the higher one, said R. Jose son of R. Judah, is looked upon as if it lay lower13 or the lower one, as if it lay higher,13 provided only that the higher one was not higher than twenty cubits14 and the lower one [was not] lower than ten cubits.14 Abaye remarked: R. Jose son of R. Judah holds the same view as his father in one respect and differs from him in another. He ‘holds the same view as his father in one respect’ in that he also adopts the principle of ‘IS LOOKED UPON’; ‘and differs from him in another’, for whereas R. Judah holds [that a cross-beam may be] higher than twenty cubits,14 R. Jose son of R. Judah holds [that it is valid] only within, but not above twenty cubits. R. JUDAH RULED: [THE BEAM IS VALID IF IT IS SUFFICIENTly] WIDE, ALTHOUGH IT IS NOT STRONG. Rab Judah taught Hiyya b. Rab in the presence of Rab, ‘WIDE, ALTHOUGH IT IS NOT STRONG’, when the latter said to him: Teach him, ‘Wide and strong enough’. Did not, however, R. Ela'i state in the name of Rab, ‘[a cross-beam that is] four [handbreadths] wide [is valid] although it is not strong,’? — One that is four [handbreadths] wide is different [from one that is less than the prescribed width]. IF IT WAS MADE OF STRAW etc. What does he thereby teach us? That we adopt the principle of ‘IS LOOKED UPON’?15 But, then, is not this exactly the same [principle as was already enunciated]?16 — It might have been assumed that [the principle] is applied only to one of its own kind17 but not to one of a different kind;18 hence we were taught [that any material is valid]. [IF IT WAS] CURVED IT IS LOOKED UPON AS THOUGH IT WERE STRAIGHT. Is not this obvious?19 — He taught us [thereby a ruling] like that of R. Zera, for R. Zera stated: If it20 was within an alley and its curve without the alley, or if it was below twenty cubits21 and its curve above twenty, or if it was above ten cubits21 but its curve was below ten, attention must be paid [to this]:22 Whenever no [gap of] three handbreadths23 would have remained if its curve had been removed, it is not necessary to provide another cross-beam; otherwise, another cross-beam must be provided. Is not this also obvious? — It was necessary [to enunciate the ruling in the case where the beam] was within the alley and its curve was without the alley. As it might have been presumed that the possibility must be taken into consideration that the residents might be guided by it;24 hence we were informed [that no such possibility need be considered]. [IF IT WAS] ROUND IT IS LOOKED UPON AS THOUGH IT WERE SQUARE. What need again was there for this ruling?25 It was necessary [on account of its] final clause: WHATSOEVER HAS A CIRCUMFERENCE OF THREE HANDBREADTHS IS ONE HANDBREADTH IN DIAMETER. Whence are these calculations26 deduced? — R. Johanan replied: Scripture stated: And he made the ‘molten sea of ten cubits from brim to brim, round in compass, and the height thereof was five cubits; and a line of thirty cubits did compass it round about.27 But surely there was [the thickness of] its brim?28 — R. Papa replied: Of its brim, it is written in Scripture [that it was as thin as] the flower of a lily;29 for it is written: And it30 was a handbreadth thick, and the brim thereof was wrought like the brim of a cup, like the flower of a lily; it held two thousand baths.31 But there was [still] a fraction at least?28 — When [the measurement of the circumference]32 was computed33 it was that of the inner circumference.34 R. Hiyya taught:35 The sea that Solomon made contained one hundred and fifty ritual baths.36 But consider: How much is [the volume of] a ritual bath? Forty se'ah,37 as it was taught: And he shall bathe . . . OF STRAW’ is obviously not strong. beams can be made of it. totally unfit. alley. statement. This, as Zuckermann points out (Das Mathematische im Talmud, p. 23) proves that the Rabbis were well aware of the more exact ratio between the diameter and circumference and that the ratio of 1:3 was accepted by them simply as a workable number for religious purposes. Hence the question, ‘Whence are these calculations deduced?’ V. Feldman, Rabbinical Mathematics etc., p. 23]. circumference, the ratio of a diameter to a circumference must consequently be 10:30 = 1:3 approx. greater than 1:3.