GEMARA: The Gemara questions the statement in the mishna with regard to the minimum width of the cross beam: A handbreadth? A handbreadth and a half is required, as a small brick is a handbreadth and a half wide.

The Gemara answers: Since the cross beam is wide enough to receive and hold a handbreadth, one can affix the remaining half handbreadth with plaster, a small amount on this side and a small amount on that side, and the brick will stand in place.

Rabba bar Rav Huna said: The cross beam of which the Sages spoke must be sturdy enough to receive and hold a small brick; however, the supports of the cross beam need not be sturdy enough to receive and hold a cross beam and a small brick. Criteria were established for the cross beam itself, which renders the alleyway fit for one to carry within it; criteria were not established for its supports. Rav Ḥisda disagreed and said: Both this, the beam, and that, its supports, must be sturdy enough to hold a cross beam and a small brick.

Rav Sheshet said: If one placed a cross beam over the entrance of an alleyway, and draped a mat over it, and raised the lower end of the mat three handbreadths from the ground, there is neither a cross beam here, nor is there a partition here to render the alleyway fit for one to carry within it. There is neither a cross beam here, as it is obscured and therefore inconspicuous. Nor is there a partition here, as it is a partition that is more than three handbreadths off the ground through which goats can pass, and therefore it does not have the legal status of a partition.

Our Sages taught in the Tosefta: If a cross beam projects from this wall of an alleyway but does not touch that wall opposite, and similarly, if there are two cross beams, one projecting from this wall and one projecting from that wall opposite, and they do not touch one another, if there is a gap of less than three handbreadths between the beam and the wall, or between the two beams respectively, one need not bring another cross beam to render the alleyway fit for one to carry within it, as they are considered joined based on the principle of lavud. However, if there is a gap of three handbreadths, one must bring another cross beam.

Rabban Shimon ben Gamliel says: If the gap is less than four handbreadths, one need not bring another cross beam. However, if it is four handbreadths, he must bring another cross beam, as in his opinion the principle of lavud applies to a gap up to four handbreadths wide.

And similarly, if two matching, extremely narrow cross beams are placed alongside each other, even though there is not sufficient width in this beam to receive a small brick, and there is not sufficient width in that beam, if the two beams together can receive a small brick along its handbreadth width, one need not bring another cross beam to render the alleyway fit for one to carry within it; but if not, one is required to bring another cross beam.

Rabban Shimon ben Gamliel says: If the two cross beams can receive a small brick along its length, which is three handbreadths, one need not bring another cross beam, but if not, one must bring another cross beam.

If these two narrow cross beams are placed one above and one below, Rabbi Yosei, son of Rabbi Yehuda, says: One considers the upper one as though it were below, and the lower one as though it were above, i.e., close together. If the two together are fit to hold a small brick, they render the alleyway fit for one to carry within it, although they are not actually close to each other, provided that the upper cross beam is not above twenty cubits and the lower one is not below ten handbreadths, between which a cross beam renders an alleyway fit for one to carry within it.

Abaye said: Rabbi Yosei, son of Rabbi Yehuda, holds in accordance with the opinion of his father with regard to one matter, and disagrees with his opinion with regard to one matter. He holds in accordance with the opinion of his father in one matter, as he is of the opinion that the principle: One considers, applies. Just as Rabbi Yehuda stated in the mishna that the cross beam is considered as though it were sturdy even though it is not, his son, Rabbi Yosei, holds that one considers two cross beams placed apart as though they were adjacent.

And Rabbi Yosei disagrees with his father’s opinion with regard to one matter. While Rabbi Yehuda holds that a cross beam renders an alleyway fit for one to carry within it even if it is higher than twenty cubits, Rabbi Yosei, son of Rabbi Yehuda, holds: Within twenty cubits, yes, it renders the alleyway fit for one to carry within it; above twenty, it does not.

It was stated in the mishna that Rabbi Yehuda says: It suffices if the cross beam is wide enough to hold a small brick, even though it is not sturdy enough to actually support it. Rav Yehuda taught this clause of the mishna to Ḥiyya bar Rav in the presence of Rav: It suffices if the cross beam is wide enough to hold a small brick, even though it is not sturdy enough to actually support it. Rav said to him: Teach it to him as follows: Wide enough and sturdy enough to hold a small brick.

The Gemara challenges this statement: Didn’t Rabbi Elai say that Rav said: A cross beam that is four handbreadths wide renders an alleyway fit for one to carry within it even if it is not sturdy enough to hold a small brick? The Gemara answers: A cross beam that is four handbreadths wide is different, as a beam of that width is considered a roof and not a beam. It is considered as though the edge of the roof descended and constituted an actual partition, not merely a conspicuous distinction.

It was stated in the mishna: Even if the cross beam is made of straw or reeds, one considers it as though it were made of metal. The Gemara asks: What is the mishna teaching us? If it is teaching that we say one considers the cross beam as though it were fit to bear a brick, then this clause is the same as the previous clause in the mishna: Wide enough even though it is not sturdy enough.

The Gemara answers: There is a novel point here, lest you say that with regard to a cross beam made of material that other beams of its own kind are sturdy, e.g., wood, we say that even the flimsiest of cross beams is considered sturdy. However, with regard to a cross beam made of material that only beams not of its own kind are sturdy, e.g., straw, which can never support a brick, we do not say that one considers the cross beam as if it were made of metal. Therefore, the mishna teaches us that there is no difference between the cases.

It was taught in the mishna: If the cross beam is curved, one considers it as though it were straight. The Gemara challenges: That is obvious. The Gemara answers that this is in accordance with the opinion of Rabbi Zeira, as Rabbi Zeira said: If the cross beam is inside the alleyway, and its curved section is outside the alleyway; or it is within twenty cubits of the ground, and its curved section is above twenty cubits; or it is above ten handbreadths, and its curved section is below ten handbreadths, meaning that the curved part of the beam is outside the area where a cross beam is effective, one considers the situation: In any case where, were the curved section outside the area where a cross beam is effective removed, there would not be a gap of three handbreadths between this effective part of the cross beam and that effective part of the cross beam, one need not bring another cross beam. And if not, if the gap would be greater, he must bring another cross beam.

The Gemara comments: That too is obvious, as the curved portion of the cross beam is considered as though it were straight. The Gemara explains: In a case where the cross beam is inside the alleyway and its curved portion is outside the alleyway, it was necessary for him to teach the halakha. Lest you say: Let us be concerned that he will come to be drawn after it and carry in the area where the curvature extends beyond the alleyway, Rabbi Zeira teaches us that this is not a concern.

The mishna continues: If the cross beam is round, one considers it as though it were square. The Gemara asks: Why do I need this clause as well? Similar cases were already taught in the mishna. The Gemara answers: It was necessary to teach the last clause of this section, i.e., the principle that any circle with a circumference of three handbreadths is a handbreadth in diameter.

The Gemara asks: From where are these matters, this ratio between circumference and diameter, derived? Rabbi Yoḥanan said that the verse said with regard to King Solomon: ''And he made a molten sea, ten cubits from the one brim to the other: It was round all about, and its height was five cubits; and a line of thirty cubits did circle it round about'' (I Kings 7:23).

The Gemara asks: But isn’t there its brim that must be taken into account? The diameter of the sea was measured from the inside, and if its circumference was measured from the outside, this ratio is no longer accurate.

Rav Pappa said: With regard to its brim, it is written that the brim is as the petals of a lily, as stated in the verse: ''And it was a handbreadth thick; and its brim was wrought as the brim of a cup, as the petals of a lily; it contained two thousand bat'' (I Kings 7:26). The brim was very thin.

The Gemara asks: But nevertheless, isn’t there the minimal amount of the thickness of the brim? The Gemara answers: When one calculates the circumference, he calculates from the inside.

Rabbi Ḥiyya taught in a baraita: The sea that Solomon fashioned contained a volume of one hundred and fifty baths of ritual purification. The Gemara asks: After all, with regard to a ritual bath, how much is its volume? It is forty se’a, as it was taught in a baraita: And he shall bathe his flesh