Commentary for Eruvin 27:23

תניא רבי חייא ים שעשה שלמה היה מחזיק מאה וחמשים מקוה טהרה מכדי מקוה כמה הוי ארבעים סאה כדתניא (ויקרא טו, טז) ורחץ (את בשרו)

Whenever no [gap of] three handbreadths<span class="x" onmousemove="('comment',' Between the two parts of the beam at which the curve begins.');">²³</span> 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;<span class="x" onmousemove="('comment',' Lit., 'he might come to be drawn after it'; and so use a section of the public domain as if it had been a part of their alley.');">²⁴</span> 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?<span class="x" onmousemove="('comment',' v. supra note 3.');">²⁵</span> It was necessary [on account of its] final clause: WHATSOEVER HAS A CIRCUMFERENCE OF THREE HANDBREADTHS IS ONE HANDBREADTH IN DIAMETER'Whence are these calculations<span class="x" onmousemove="('comment',' Lit., 'things'. [This is the only instance where a doubt is raised in the Talmud in connection with a mathematical 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].');">²⁶</span> 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.<span class="x" onmousemove="('comment',' I Kings VII, 23. As the molten sea which had a diameter of ten cubits was approximately thirty cubits in circumference, the ratio of a diameter to a circumference must consequently be 10:30 = 1:3 approx.');">²⁷</span> But surely there was [the thickness of] its brim?<span class="x" onmousemove="('comment',' Which increased the diameter to more than ten cubits: so that the ratio between diameter and circumference was greater than 1:3.');">²⁸</span> - R'Papa replied: Of its brim, it is written in Scripture [that it was as thin as] the flower of a lily;<span class="x" onmousemove="('comment',' Its thickness, therefore, amounted to very little and might be disregarded.');">²⁹</span> for it is written: And it<span class="x" onmousemove="('comment',' The lower portion of the sea.');">³⁰</span> 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.<span class="x" onmousemove="('comment',' I Kings VII, 26.');">³¹</span> But there was [still] a fraction at least?<span class="x" onmousemove="('comment',' Which increased the diameter to more than ten cubits: so that the ratio between diameter and circumference was greater than 1:3.');">²⁸</span> - When [the measurement of the circumference]<span class="x" onmousemove="('comment',' Of the molten sea.');">³²</span> was computed<span class="x" onmousemove="('comment',' As thirty cubits.');">³³</span> it was that of the inner circumference.<span class="x" onmousemove="('comment',' The diameter of which was exactly ten cubits.');">³⁴</span> R'Hiyya taught:<span class="x" onmousemove="('comment',' So Bomb. ed. Cur. edd., 'it was taught'.');">³⁵</span> The sea that Solomon made contained one hundred and fifty ritual baths.<span class="x" onmousemove="('comment',' Lit., 'a gathering together for purification'.');">³⁶</span> But consider: How much is [the volume of] a ritual bath? Forty se'ah,<span class="x" onmousemove="('comment',' V. Glos.');">³⁷</span> as it was taught: And he shall bathe.

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