Eruvin 5:7 - 5:8

מי שהיה במזרח – in the field, and he sanctified for himself the [Sabbath] day and he was far from his Eruv more than two-thousand [cubits], for his Eruv is not an Eruv, since he is not able to walk and to carry, it would be for him a Sabbath camp in his house when his Eruv is not an Eruv.

בעיבורה של עיר (within the outskirts of the city) – in one of the houses that stands within seventy cubits and left-overs.

לא עשה ולא כלום – for without an Eruv also, he has from the city/town two-thousand cubits in every direction, and the entire city/town with its outskirts are considered to him as four cubits.

נתנו חוץ לתחום – outside of the outskirts of the city/town. And this is explained in the Gemara (Tractate Eruvin 60b).

מה שנשכר –[what he gains] in this direction, he loses in the direction that is opposite it. For he counts from the Eruv two-thousand [cubits] in every direction if it and if he placed [something] at the end of one-thousand [cubits] to the east, it is found that the two-thousand [cubits] of the east end at the conclusion of three-thousand [cubits] of the city and he has gained one-thousand, but the two-thousand [cubits] of the west end at the end of one-thousand [cubits] of the west of the city, and he lost one-thousand [cubits]. And this comes to tell us that the city does not count in the total of the two-thousand [cubits] of the west but rather all of it is like four cubits. And these words [apply] when the two-thousand [cubits] do not end from the Eruv to the side of the city/town, but rather, at the end of the city/town or outside of it, but if they end in the middle or the city or at whatever place within it, he cannot walk within the city/town other than up to the point where the two-thousand cubits of the Eruv end, and not further, as it is taught nearby (in the next Mishnah).

אנשי איש גדולה – that they (i.e., the residents of a large town) had a small town within the two-thousand [cubits] and they depart from their city and count and walk the path of the small [city/town] that is adjacent/nearby, they walk through all of the small town/city that is adjacent to them like four cubits and complete their measurement outside of it.

ואין אנשי עיר קטנה מהלכין את הגדולה – [the large town/city] in its entirety like four cubits, because the measurement of the [Sabbath] limits ended in the middle of the large city/town, therefore, the large city/town is not considered for them like four cubits and they don’t go there, but rather only until the end of their [Sabbath] limits.

כיצד מי שהיה מעיר גדולה – Our Mishnah is deficient and should be read as follows: The people of a large town/city walk through the entire small town/city but the people of a small town/city do not walk through all of the large city/town; in what case are these words said? When he measures two-thousand cubits. But, a person who places his Eruv within the city/town, whether the people of a large town/city placed it in a small town/city or whether the people of a small town/city placed it in a small town/city, they walk all the city/town that the Eruv is placed in it like four cubits. How so? He who was from a large city/town and placed his Eruv in a small town/city etc.

ור' עקיבא – disputes on the first Tanna/teacher and holds that the Eruv does not make the city/town in which it is placed like four cubits, and we don’t count two-thousand cubits other than from the place of the Eruv. But the Halakha is not according to Rabbi Akiva.