(Mishnah): We measure only from a Mumcheh.

If a Techum (e.g. to the east) was measured in two places (e.g. from the northeast and southeast corners), and one of them extends further [east] than the other, we follow the place where it is larger;

If one measured a larger [Techum] and one measured a smaller, we follow the larger.

Even a male or female slave is believed to say 'the Techum extends to this place', for Chachamim did not say [the law of Techumim] to be stringent, rather, to be lenient.

(Gemara): If a commoner measured more (a greater Techum), we do not heed him.

(R. Hoshayah): (Our Mishnah teaches that Chachamim said the law of Techumim to be lenient.) This shows that Techumim are not mid'Oraisa.

Question (R. Mana): Granted, the Techum of 2000 Amos is not mid'Oraisa. The Techum of 4000 Amos is mid'Oraisa!

Answer (R. Shimon bar Karsenah citing R. Acha): The only Techum that is mid'Oraisa is 12 Mil, like Machaneh Yisrael.

(Mishnah): If an individual's city became a public city, we may be Me'arev all of it.

If a public city (even if it was not Reshus ha'Rabim) became an individual's city, we may be Me'arev it only if we leave outside [the Eruv] the size of the city 'Chadashah' of Yehudah, which has 50 residents. R. Yehudah says so;

R. Shimon says, [one must leave over] three Chatzeros, each with at least two houses.

(Gemara - Beraisa, in the name of R. Yehudah): [If an individual's city became a public city,] we may not be Me'arev half of it.

Contradiction: R. Yehudah contradicts himself!

(R. Chiyah - Beraisa): How do we permit [a Mavuy Mefulash to] Reshus ha'Rabim? R. Yehudah says, he puts a Lechi on this side and a Lechi on the other side, or a Korah on this side and a Korah on the other side;

Chachamim say, he puts a Lechi or Korah on this side, and Tzuras ha'Pesach on the other side.

[There, he permits every Mavuy by itself,] and here he says so (he forbids to be Me'arev half a city)?!

Answer #1: He did not say so [that we may not be Me'arev half] about this, rather, about the following. Even a great city like Antuchiya, and it has only one door, one may be Me'arev all of it;

It was taught in the name of R. Yehudah that we may not be Me'arev half of it. (Since they must share the opening to Reshus ha'Rabim, they cannot separate from each other.)

Inference (R. Yosah): If people of a Mavuy put their Korah in the middle of the Mavuy, these (who put it) are permitted, and these (the others) are forbidden. If both of them put [Koros], both of them are forbidden.

How does he do [to permit the entire Mavuy]? He puts the Korah at the opening of the Mavuy.

If five Mavo'os open to a Mavuy, if [the five] put their Koros [at their openings, which are] in the middle of the [central] Mavuy, these [that put] are permitted, and these [that did not put] are forbidden. If these and these put (the central Mavuy put at its opening to Reshus ha'Rabim), these and these are forbidden. (This is like above. Only a Mavuy that fixed itself forbids others.)

How does he do [to permit all of them]? He puts the Korah at the opening of the [central] Mavuy [and all of them make Shituf together. We explained this like PNEI MEIR.]

Once, R. Pinchas came to here. He saw an opening of the market of [wood] cutters. (Their Mavuy was open to a big Mavuy.) He told them, did you divide your Eruvin?! (The only way to permit everyone is to be Me'arev together!)

R. Yudah bar Shalom told him, [the Korah at our opening] is to strengthen the houses. (It is not to permit our Mavuy by itself.)

(Mishnah): [If a public city became an individual's city, we may be Me'arev it] only if we leave outside like the city 'Chadashah' of Yehudah.

Examples of this are Tzanan Chadashah and Migdal Gad, which has 50 residents.

Even men, women and minors [count towards the 50]. Asi says, they must be Yisraelim.

(R. Ba bar Mamal citing Shimon bar Chiyah citing Rav): (R. Shimon requires leaving over three Chatzeros, each with at least two houses.) This is when [the houses] open to [the Chatzer].

(R. Mana): Since they open to it, they all become one Reshus.