Eruvin, Chapter 2, Mishnah 5. This mishnah opens with the words of Rabbi Yehudah ben Bava, continuing directly from the previous mishnah in which he proposed a stringency in the laws of the upright boards around wells - and here too the mishnah opens with a further stringency of his.
A garden and a karpef - an area not enclosed for dwelling:
Rabbi Yehudah ben Bava discusses a garden and a karpef. A 'karpef' is an area outside the city used for storing wood and the like. These are the examples the mishnah brought earlier for areas whose enclosure was not made for human habitation, and therefore it was established there that carrying in an area not enclosed for dwelling is limited to "beis sa'atayim" alone.
The stringency of Rabbi Yehudah ben Bava:
In his view, even in a garden or a karpef surrounded by a fence one may carry, provided that two conditions are met:
A limit on the area: up to "shivim amah ushnei shelishim al shivim amah ushnei shelishim" - seventy amos and two thirds by seventy amos and two thirds, which is the measure of beis sa'atayim, a little under five thousand square amos.
A connection to human dwelling: that some form of human habitation be attached to it - a watchman's hut or a place where a person could live - or that it be close enough to the city that the owner visits it on a regular basis. When it lies within the Shabbos boundary, within two thousand amos, the owner would go there and walk about in it even on Shabbos itself, and this is as though he lives there.
It emerges that Rabbi Yehudah ben Bava insists that even a karpef must be 'enclosed for dwelling,' and even then the permission extends only to the measure of beis sa'atayim.
The view of Rabbi Yehudah:
Rabbi Yehudah comes and narrows the stringency: there is no need to restrict matters as Rabbi Yehudah ben Bava holds, and it is enough that the area contains a well or a cave, or any place that serves human needs to some degree - and with that one may carry throughout that entire area of beis sa'atayim.
The view of Rabbi Akiva:
Rabbi Akiva is more lenient still: even if there is no dwelling place at all connected to the area, and even though it serves no human habitation whatsoever, one may carry in it - provided it is no larger than that same measure of seventy amos and two thirds by seventy amos and two thirds, a little under five thousand square amos.
The shape of the area - Rabbi Eliezer and Rabbi Yosi:
The Tannaim further disagree about the geometric shape of the area:
Rabbi Eliezer: the shape is critical. Even if the length exceeds the width by a single amah, so that it is not an exact square, one may not carry in the area, and it must be a perfect square. It is worth noting that a baraisa in the Gemara presents another version of his view, with a different perspective: if the length exceeds double the width, one may not carry in it. That is, it should be a rectangle whose width is half its length, and no more than one amah beyond double. The Gemara says that this is in fact how our mishnah is to be understood.
Rabbi Yosi: even if the length is double the width, one may carry there.
What, then, is the difference between Rabbi Eliezer and Rabbi Yosi? If Rabbi Eliezer is interpreted according to the baraisa as saying that the area may not exceed by more than one amah a rectangle whose length is double its width, then Rabbi Yosi too says that double is acceptable.
The Gemara explains that the difference lies in what is required at the outset:
For Rabbi Eliezer, at the outset a rectangle is required - like the dimensions of the Mishkan, a rectangle of five thousand amos.
For Rabbi Yosi, at the outset a square is required; but if it happens that the length is double the width, that too is acceptable.
In summary: in this mishnah we examined three approaches to permitting carrying in a garden and a karpef that were not enclosed for dwelling - Rabbi Yehudah ben Bava, who requires a connection to human dwelling within the measure of beis sa'atayim; Rabbi Yehudah, who is satisfied with a well or a cave; and Rabbi Akiva, who permits it even with no human use at all - as well as the dispute between Rabbi Eliezer and Rabbi Yosi about the shape of the area, the difference between them being the question of what is required at the outset: a rectangle or a square.