Rif Eruvin 3b {Eruvin 12b continues ... 14a}

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3b

{Eruvin 12b continues}
One {an alleyway} whose length exceeds its width, and houses and courtyards enter it. And what is considered a courtyard, such that it is not permitted via a lechi or korah but rather with a strip of 4 {handbreadths on the side of the breach}? One whose length does not exceed its width. But if its length exceeds its width even by the slightest amount, it is reckoned to be an alleyway, and an alleyway suffices with a lechi or a korah.

{Eruvin 13b}
Mishna:
The korah in question must be wide enough to hold an {a half sized brick, and an ariach is half the width of a brick which is three handbreadths. {Thus, the ariach is 1.5 handbreadths wide.}
It is {therefore} sufficient for the korah to be a handbreadth wide, in order to support the width of an ariach. {1/4 handbreadth could stick out on each side.}
It {the korah} must be wide enough to support an ariach and strong enough to support an ariach.
Rabbi Yehuda says: It need be sufficiently wide even though it need not be strong {enough to support an ariach}.
If it {the korah} was made of straw or reed, we consider it as if it were made of metal.
If crooked, we consider it as if it were straight.
Rounded, we consider it as if it were square - if there is in its circumference 3 handbreadths, it had 1 handbreadth in width.

{Eruvin 14a}
Gemara:
Rabba bar Rav Huna said: The korah of which they spoke needs to be strong enough to support the ariach, but the supports of the korah need not be strong enough to support both the korah and an ariach.
And Rav Chisda said: Both this and that - it needs to be strong enough to support a korah and the ariach.

The Sages learnt {in a brayta}: A korah which comes out from {on top} of one wall but does not reach the other wall; and also, two korot, one coming out from this wall and the other from the other wall, and they do not reach each other, if {the gap between korot or between korah and wall is} less than 3 {handbreadths}, he need not bring another korah. If 3 {handbreadths} he needs to bring another korah. Rabban Shimon ben Gamliel says: Less than 4 {handbreadths}, he need not bring another korah. If 4 {handbreadths} he needs to bring another korah. And so too, two parallel korot {next to one another, at the same height}, this one cannot support {in width} an ariach, and that one cannot support an ariach, if they can {together} support an ariach to its width of a handbreadth, he need not bring another korah. And if not, he needs to bring another korah. Rabban Shimon ben Gamliel says: if they can support an ariach to its length of 3 handbreadths he need not bring another korah, and if not he needs to bring another korah.

If one {korah} was below and another was above {thus, they were not at the same height} - Rabbi Yossi beRabbi Yehuda says: we view the upper one as if it were below {at the level of the lower one}, assuming that the uppoer one is not above 20 cubits and the lower one is not lower than 10 handbreadths.

{From the Mishna:} "Rabbi Yehuda says: It need be sufficiently wide even though it need not be strong {enough to support an ariach}":
And we do not hold like Rabbi Yehuda, for we need it to be sufficiently wide and strong.
And also, this of Rabbi Yossi beRabbi Yehuda, that we view the upper one as if it were below, we do not hold.

{And from the Mishna:} "If it {the korah} was made of straw or reed {we consider it as if it were made of metal}" is Rabbi Yehuda, and the halacha is not like him.

Rabbi Zera said: If it {the korah} is within the alleyway, and its bend {for the korah curves} is outside the alleyway; if it is within 20 {cubits}, and its bend it above 20; if it is higher than 10 {handbreadths}