(Gemara) Question: Do we follow only the larger Techum?! (Rashi - automatically, this implies that the smaller Techum is permitted! Tosfos - surely, we should follow the smaller Techum in its place (e.g. southeast), and attribute the difference to swallowing and Mekadrin, and not to error!)

Version #1 (Rashi) Answer: We follow even the larger Techum.

Version #2 (Tosfos) Answer: We follow even the smaller Techum [in its place].

(Mishnah): If a larger Techum was measured for one...

Question: This is just like the previous clause! (Why is it repeated?)

Answer: It means that if two people measured and obtained different Techumim, we follow the larger one.

Version #1 - Rashi - (Abaye): This is only if the difference is less than the excess of the diagonal over the side. (We can say that the shorter measurer was not proficient in measuring the diagonal.)

Version #2 - Tosfos - (Abaye): This is only if [the second measurement is bigger and] we can attribute the excess to additions to the city [after the first measurement] and their diagonal.

(Mishnah): Chachamim enacted Techumim to be lenient, but not to be stringent.

Contradiction (Beraisa): Chachamim enacted Techumim to be stringent, but not to be lenient.

Answer (Ravina): The Beraisa means that Chachamim did not enact Techumim to be more lenient than the Torah, rather, to be more stringent. It is only mid'Rabanan. (Therefore, they can be lenient about it.)

(Mishnah - R. Yehudah): If an individual's city became a public city, we may be Me'arev all of it. (Rashi - 600,000 people regularly pass through, but the streets are not wide enough to be Reshus ha'Rabim. R. Tam - Reshus ha'Rabim does not depend on 600,000 going through.)

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

(Gemara) Question: What is a case of an individual's city that became public?

Answer #1 (Rav Yehudah): Diskarta of the Reish Galusa is an example.

Objection (Rav Nachman): Why is this the only case?

Suggestion: Many people frequent the Reish Galusa [to get permission to judge]. Therefore, they will remind each other and will not come to permit a city of Rabim.

Rejection: All of Yisrael gather on Shabbos morning [to hear the Chacham expound. It should always be permitted]!

Answer #2 (Rav Nachman): The Mishnah applies to the city of [any individual, e.g.] Naszavai [that became public].

(Beraisa) Question: If an individual's city became public, and Reshus ha'Rabim passes through it, how may we be Me'arev it?

Answer: One puts a Lechi on each side or a Korah on each side, and then people may carry in the middle.

One may not be Me'arev half of it. Rather, one must be Me'arev all of it, or each Mavoy by itself.

If a public city is Reshus ha'Rabim, and it has only one opening, we may be Me'arev all of it.

Question: Who is our Tana, who permits to be Me'arev a Reshus ha'Rabim?

Answer (Rav Huna brei d'Rav Yehoshua): It is R. Yehudah:

(Beraisa): R. Yehudah said an even bigger Chidush. If one owns two houses on opposite sides of Reshus ha'Rabim, he puts a Lechi on each side or a Korah on each side and he may carry in the middle;

Chachamim: We cannot be Me'arev Reshus ha'Rabim like this!

(Beraisa): One may not be Me'arev half of it.

Version #1 (Rav Papa): One may not be Me'arev half of it lengthwise. (E.g. if Reshus ha'Rabim goes from north to south, the east half may not be Me'arev by itself. This is because Reshus ha'Rabim joins the Mavo'os.) One may be Me'arev half of it widthwise (e.g. the north half. See Perush Chai diagram, Perek 5 number 102, in the English Charts section.)

Suggestion: This is unlike R. Akiva, who says that [even] people who are permitted in their place (e.g. a Mavoy in the south) forbid elsewhere!

Rejection: It is even like R. Akiva. He discusses an inner Chatzer and an outer Chatzer, when the only opening of the inner Chatzer is through the outer. Here, each side can use its own opening!

Version #2 (Rav Papa): Don't say that one may not be Me'arev half lengthwise, but one may be Me'arev half widthwise. Rather, even widthwise is forbidden.

Suggestion: This is like R. Akiva, who says that people who are permitted in their place forbid elsewhere!

Rejection: It is even like Chachamim. They [say that people who are permitted] do not forbid regarding an inner Chatzer, for they can close the door [between the Chatzeros] and carry by themselves. [We force people to benefit others if they will not lose through this.] Here, nothing separates one part of Reshus ha'Rabim from the other!

(Beraisa): One must be Me'arev all of it, or each Mavoy by itself.

Question: One may not be Me'arev half of it, for it forbids the other half. The same should apply if one is Me'arev each Mavoy by itself!

Answer: The case is, there is a Dakah (Rashi, according to Ritva - a small opening to outside the city; Tosfos - a low wall) at the end of each Mavoy. (This shows that it withdraws from the other Mavo'os):

(Rav Idi bar Avin): If a Chatzer made a Dakah in front of its opening [to the Mavoy], it does not forbid the Mavoy.

(Beraisa): If a public city is Reshus ha'Rabim...

R. Zeira was Me'arev the [public] city of R. Chiya's household. He did not leave a remnant.

Abaye: Why did you do this?

R. Zeira: Their elders told me that R. Chiya bar Asi was Me'arev all of it. I inferred that it was an individual's city that became a public city.

Abaye: The elders told me that there used to be a wasteheap blocking one opening. It was removed, so now there are two openings and one may not be Me'arev all of it!

R. Zeira: I did not realize this.

Question (Rav Ami bar Ada): If there is a ladder at one end [from the wall to outside the city] and it is open at the other end, what is the law?

Answer #1 (Rabah): Rav says that a ladder is like an opening. (One may not be Me'arev the entire city, for it has two openings.)

Answer #2 (Rav Nachman): Rav Ada [bar Ahavah] said in the name of Rav that a ladder is like an opening, and like a wall:

It is like a wall in this case. (It does not invalidate the wall);

It is like an opening when it is between two Chatzeros. It permits the residents to be Me'arev together or separately.