פירוש על עירובין 1:5

היתה של קש ושל קנים – Rabbi Yehuda stated this but the Halakha is not according to him.

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.

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.

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.

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.

[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.

[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).