Mishnah
Mishnah

Commentary for Eruvin 1:5

הָיְתָה שֶׁל קַשׁ אוֹ שֶׁל קָנִים, רוֹאִין אוֹתָהּ כְּאִלּוּ הִיא שֶׁל מַתֶּכֶת. עֲקֻמָּה, רוֹאִין אוֹתָהּ כְּאִלּוּ הִיא פְשׁוּטָה. עֲגֻלָּה, רוֹאִין אוֹתָהּ כְּאִלּוּ הִיא מְרֻבַּעַת. כֹּל שֶׁיֵּשׁ בְּהֶקֵּפוֹ שְׁלֹשָׁה טְפָחִים, יֶשׁ בּוֹ רֹחַב טָפַח:

If it (the korah) were of straw or of reeds, it is viewed as if it were made of metal. [R. Yehudah says this. The halachah is not in accordance with him.] If it were crooked, [so that an ariach could not rest upon it (as it also could not if it were round)], it is viewed as if it were straight. If it were round, it is viewed as if it were square. Whatever is three tefachim in circumference is one tefach in width. [That is, what is the required measure for a round korah? Whatever is three tefachim in circumference — i.e., whatever requires a cord three tefachim long to go around it — would, if squared, have a width of a tefach. For thus do we find with the yam (the reservoir) made by Solomon, viz. (I Kings 7:23): "And he made the molten yam, ten cubits from brim to brim, round all about … and a line of thirty cubits compassed it roundabout" — whence it is seen that for every cubit of width in the circle, there are three cubits of circumference.]

Bartenura on Mishnah Eruvin

היתה של קש ושל קנים – Rabbi Yehuda stated this but the Halakha is not according to him.
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English Explanation of Mishnah Eruvin

Introduction This mishnah is a continuation of Rabbi Judah’s words from yesterday’s mishnah. Rabbi Judah held that the cross-beam need not actually be strong enough to support a half-brick.
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Bartenura on Mishnah Eruvin

עקומה – the small bricks are not able to rest upon it (when it is curved) and similarly when it is round, a small brick cannot rest upon it.
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English Explanation of Mishnah Eruvin

If [the cross-beam] was made of straw or reeds, we look at it as if it was of metal. If the cross-beam was made of a material which could not hold a half-brick, Rabbi Judah considers it nevertheless as if it was strong enough to do so.
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Bartenura on Mishnah Eruvin

if it has in its circumference: Which is to say, what is the round measurement required to render [the beam] proper? Anything that has in its circumference three handbreadths, which requires a string of three handbreadths to encircle it around, it is known that it has a width (diameter) of one handbreadth, if you divide [it]. As so do we find with the basin that Shlomo made (II Chronicles 4:2), "ten ells from its edge to its edge and five ells of height and a line of thirty ells encircling it around." Hence for every ell in width (diameter), there are three ells in circumference.
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English Explanation of Mishnah Eruvin

[If it was] curved we look at it as if it were straight. If it was curved, it also could not hold a half-brick. Nevertheless, Rabbi Judah holds that it is valid.
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English Explanation of Mishnah Eruvin

[If it was] round we look at it as if it were square. Whatever has a circumference of three handbreadths has a diameter of one handbreadth. Again, a round cross-beam could not hold a half-brick. However, it still must be wide enough to hold a one handbreadth half-brick. In order for this to be true, it must have a circumference of three handbreadths (the rabbis knew that pi was roughly three to one, and they knew that this was not exact).
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