Midrash 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 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 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 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 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.

Sifrei Bamidbar

One verse states (Ibid. 3) "Is there any number to His angelic hosts?" and another (Daniel 7:10) "A thousand thousands were serving Him, and myriad myriads were standing before Him." How are these two verses to be reconciled? Before they were exiled from their land — "Is there any number to His angelic hosts?" After they were exiled from their land — "A thousand thousands were serving Him." As it were, the celestial retinue was diminished. Rebbi says in the name of Abba b. Yossi: One verse states: "Is there any number to His angelic hosts?" and another, "A thousand thousands were serving Him." How are these two verses to be reconciled? "A thousand thousands were serving Him" — this is one host. And how many hosts are there? — "Is there any number to His angelic hosts?" One verse states (Psalms 147:4) "He counts the number of the stars, (which implies that He calls each by name), and another (Isaiah 40:26) "Raise your eyes on high and see who created these. He brings forth their legions by number; he calls to all of them by name," (which implies that He calls all of them as one). (How is this to be understood?) When the Holy One Blessed be He calls, all answer, something impossible for flesh and blood, to call two names at the same time. Similarly, (Shemot 20:1) "And G-d spoke all of these things (in one utterance) saying, etc.", and (Psalms 62:12) "One thing has G-d spoken; these two have I heard," and (Jeremiah 23:29) "Is My word not like fire, says the L-rd, and like a hammer shattering rock?" Rebbi says in the name of Abba Yossi b. Dostai: One verse states "He brings forth their legions by number, etc.", and another "He counts the number of the stars." How are these two verses to be reconciled? We are hereby taught there is no changing of the (essential) name there. The name that it is called by now is not the name that it will be called by later, (but its "name" is simply a function of its embassy.) And thus is it written (Judges 12:18) "And the angel of the L-rd said to him: Why do you ask my name? It is hidden." I do not know what "name" I will be converted to (in the future). One verse states (II Samuel 24:24) "And David bought the threshing floor and the cattle for fifty silver shekels," and another (I Chronicles 21:25) "And David gave Arnon for the place gold shekels weighing six hundred." How are these two verses to be reconciled? For the place of the threshing floor, six hundred; for the place of the altar, fifty. Rebbi says, in the name of Abba Yossi b. Dostai: One verse states "And David bought the threshing floor, etc." and another verse states "And David gave Arnon for the place gold shekels weighing six hundred." How are these two verses to be reconciled? There were twelve tribes, and he took from each fifty shekels, six hundred shekels in all. R. Elazar says "And David bought the threshing floor," as explained elsewhere. Where? "And David gave Arnon for the place, etc." But the cattle for the burnt-offering and the threshing sledges and the cattle gear for the wood for fifty shekalim. One verse states (I Kings 5:6) "And Solomon had forty thousand stables of horses for his chariots," and another, (II Chronicles 9:28) "four thousand stables of horses." How are these two verses to be reconciled? Four thousand stables for forty thousand (horses). One verse states (Ibid. 4:5) "Its capacity was three thousand bath measures," and another (I Kings 7:26) "Its capacity was two thousand bath measures." How are these two verses to be reconciled? Two thousand in wet measure, which are three thousand in dry measure — whence the sages ruled: Forty sa'ah in wet measure is equal to two kor in dry measure.

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