If he does not recognize [a tree or a fence] or if he is not expert in the halachah [and does not know that it will avail him to say: "My habitation is in that place"] and he says: "My habitation is in my place" (i.e., wherever he finds himself), his place effects habitation for him, two thousand cubits in a circle on all sides, [for in respect to the cities of refuge from which the two thousand cubits of the tchum Shabbath are derived it is written (Numbers 35:5): "This shall be for them the open spaces of the cities" — For this (i.e., for the cities of refuge) you add the corners (around the circle), but you do not add corners for those acquiring habitation on Shabbath.] These are the words of R. Chanina b. Antignos. The sages say: (two thousand cubits in a) square, as in a square tablet, so that the corners be gained. [The rabbis expound "This" (above) as inclusive, i.e., As this shall be (the ruling for) all who acquire habitation on Shabbath. The halachah is in accordance with the sages. ("as in a square tablet":) Rambam explains that because it is impossible to make an exact square, it is taught: "as in a square tablet." That is, in the manner that men are wont to square, though it not be exact. ("so that the corners be gained":) the four corners of the diagonal, which are an addition to the circle in the midst of the square.]
Bartenura on Mishnah Eruvin
ואם אינו מכיר – a tree or a fence.
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English Explanation of Mishnah Eruvin
Introduction
In this mishnah we learn of a debate concerning the measuring of the 2000 cubits which a person may walk on Shabbat.
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Bartenura on Mishnah Eruvin
או אינו בקי בהלכה – but he doesn’t know that it will benefit him when he says, that my Sabbath resting place is in a certain place, but he said “my Sabbath resting place is in its place,” he has acquired his place.
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English Explanation of Mishnah Eruvin
If he does not recognize [any tree or fence], or if he is not familiar with the halakhah, and said, “Let my present position be my Shabbat place”, his position acquires for him the right of movement two thousand cubits in any direction. In a circle, the words of Rabbi Hanina ben Antigonus. But the sages say: the distances are square, in the shape of a square tablet, so that he may gain the area of the corners. The mishnah deals with a person who is traveling on the road and doesn’t recognize anything in the distance (as the person did in yesterday’s mishnah) or with a person who doesn’t know that the halakhah allows him to establish his Shabbat place at a distance by making an oral statement. He thinks that because he is far away from the point he recognizes that he can’t set up his 2000 cubit ring from there. The person then says that his present position is where he will spend Shabbat. He now has 2000 cubits within which to move in all directions. This halakhah is actually obvious; even if he didn’t make any statement he still has 2000 cubits in which to move. The halakhah is probably here as an introduction to the next section.
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Bartenura on Mishnah Eruvin
עגולות – that regarding the Cities of Refuge, when we appoint them, we derive two thousand cubits of the Sabbath limit, as it is written (Numbers 35:5): “[You shall measure off two thousand cubits outside the town on the east side, two thousand on the south side, two thousand on the west side, and two thousand on the north side, with the town in the center.] That shall be the pasture for their towns.” To this one you give corners (see Talmud Eruvin 51a) which are corner-pieces, but you don’t give corner-pieces to those who set up Sabbath resting places, but the Rabbis who required square expound upon this to include like this (i.e., square) it will be for all Sabbath resting places, and the Halakha is according to the Sages.
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English Explanation of Mishnah Eruvin
According to Rabbi Hanina ben Antigonus, the 2000 cubits form a circle. That is to say one simply draws a circle with a 2000 cubit radius around the person and that is the area within which he may walk. The Sages hold that this area is actually a square, drawn around the 2000 cubit radius circle. The advantage to the sages’ position is that the corners of the square increase the area. The square’s total area is 4004 x 4004=16,032,016 cubits. Note that the additional four cubits takes into account the person’s personal four cubits which his body occupies. In contrast the circle’s area is 10022 (radius, including 2 for his own body) x 3.14 (pi)= 12,585,132 (approximately).
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Bartenura on Mishnah Eruvin
כטבלא מרובעת – Maimonides wrote that because it is impossible to make an exactly defined quadrangular, the Mishnah purposely taught "כטבלא מרובעת"/a square board, that is to say, as people are accustomed to make something square, even though it is not an exactly defined quadrangular.
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Bartenura on Mishnah Eruvin
נשכר את הזויות – four corners in its diameter of the quadrangular which is greater than the circle that is within it.
