We measure [the two thousand cubits of the tchum Shabbath] only with a [flaxen] rope of fifty cubits, not less, [for when the rope is short, it is stretched more and the measure increases], and not more, [for when it is longer, its weight doubles it in the middle and it shortens.] And one measures only against his heart. [The sages fixed a place for the end of the rope, each against his heart. For if one placed it against his heart and the other against his feet, the rope would shorten and the tchumin would diminish.] If he were measuring and he came to a valley or a fence [a fallen stone wall that became a high, slanted heap], he "swallows it up" [If it were not fifty cubits wide from edge to edge above, even if its incline were more than a thousand, we do not say that it is included in the measurement of the tchum; but one stands on one side and one on the other, and the incline is swallowed up with one rope], and he returns to his measure. ["He returns to his measure" implies that if its width in the direction of the city were more than fifty, so that he could not swallow it up there with the rope, and with one of its ends not in the direction of the city, he could swallow it up — he goes and swallows it up there, and he keeps on walking and measuring from the edge onwards until the spot where the width of the valley ends in the direction of the city, and he continues measuring in the direction of the city and completes the measure of the tchum.] If he came to a mountain, he swallows it up [This, if the mountain is not very steep, but on an incline, so that walking five cubits of it lifts one only ten handbreadths; but if it is so steep that less than five cubits of walking lifts one ten handbreadths, he does not swallow it up, but only estimates (its distance) and goes on.], so long as he does not go outside the tchum. [When the measurer goes to "swallow up" the mountain or the valley, he may not go outside the tchum to a place where the heads of the valley are so narrow that he can swallow them up, in order to return thence to his measurement in the direction of the city — a decree by reason of the possibility of one's seeing him going and measuring there and saying that the tchum measurement of the sides of the city extends that far.] If he is unable to swallow it up, about this R. Dostai said: I heard that mountains are "bored through." [("about this R. Dostai said":) "about this," to exclude (the measurements for) cities of refuge and for the red heifer, (the city) closest to the slain man, where there is no boring through. ("bored through":) They (the mountains) are regarded as bored through, and they are measured through the hole to exclude the measurement of the slope, as stated in the gemara. It is measured with a four cubit rope. The lower (measurer) places the rope against his heart, and the higher, against his feet, and they measure the whole, four cubits after four cubits progressively, so that a four cubit slope loses half a man's height. The halachah is in accordance with R. Dostai.]
Bartenura on Mishnah Eruvin
אין מודדין – two-thousand cubits of the Sabbath limit other than with a flax rope that is fifty cubits long.
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English Explanation of Mishnah Eruvin
Introduction
This mishnah discusses how they actually go out and measure the Shabbat limit.
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Bartenura on Mishnah Eruvin
לא פחות – that if the rope is short, it is greatly stretched and lengthens [one must say, the measurement].
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English Explanation of Mishnah Eruvin
They measure the Shabbat limit only with a rope fifty cubits long, neither less nor more. The mishnah mandates the use of a fifty cubit rope in measuring the Shabbat limit. A shorter rope will stretch and yield to large of an area, whereas too long of a rope will not stretch enough the area will be too small.
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Bartenura on Mishnah Eruvin
ולא יותר – when it is too long, it becomes heavy, he doubles it at its middle and shortens it.
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English Explanation of Mishnah Eruvin
And one should measure only while holding the end of the rope on a level with his heart. Measuring with a rope requires two people, one to hold each end of the rope. If the two hold the rope in different places the measurement will be off. Therefore, the rabbis said that the rope should be held at the level of one’s heart.
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Bartenura on Mishnah Eruvin
אלא כנגד לבו (at level with his heart) – The Sages established for him a place to put the head of the rope, every person level with his heart, for if this person would place it corresponding to his neck and the other corresponding to his feet, the rope would shorten and the [Sabbath] limits would grow shorter.
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English Explanation of Mishnah Eruvin
If he was measuring and he reached a valley or a wall he spans it and resumes his measuring. If when measuring they come to a small valley (we might call this a large ditch) or a wall, the elevation of the wall or the descent into the ditch should not count as part of the measuring of the Shabbat limit. What they should do is span the rope over the valley, with one person standing on one side and the other person standing on the other. Similarly, if they get to a wall they do not run the rope over the wall, measuring the incline and decline leading up to the wall. Rather they measure up to the wall, then the thickness of the wall and then they proceed from the other side.
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English Explanation of Mishnah Eruvin
If he reached a hill he spans it and resumes his measuring, provided he does not go beyond the Shabbat limit. The same way they measure the wall and valley is how they measure a hill. However, in all of these cases they cannot go beyond the Shabbat limit. What this means is that if the valley, wall or hill were wide within the limit (too wide for a fifty cubit rope), but narrower outside the limit, they should not walk out of the Shabbat limit to perform their measurements and then set a place parallel to that point within the limit. The Talmud explains that the problem would be that if others saw them doing this, they might think that the point where they went to measure was the Shabbat limit, and not realize that they were measuring outside of the border in order to set up a parallel point within the border.
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Bartenura on Mishnah Eruvin
מבליעו (takes account only of the horizontal span/includes it) – if it is not fifty cubit wide from border to border from above, even though there is in its sloping going more than one-thousand, we don’t say that he should raise the measurement of his slope to the measurement of the [Sabbath] limit, but rather, this should stand on the border from here, and that should stand on its border from there and absorb (i.e., include) it from the slope with one rope.
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English Explanation of Mishnah Eruvin
If he is unable to span it in connection with this Rabbi Dostai ben Yannai stated in the name of Rabbi Meir: “I have heard that they pierce the hills.” The mishnah now deals with a valley or hill which were too big to measure with a fifty cubit rope, or were narrow only outside of the Shabbat limit. Rabbi Dostai says that we look at the mountains as if they were pierced. In other words, their ascent and descent are not taken into account. The Talmud explains how this is done. They use a small rope of four cubits, and the person holding below puts the rope next to his heart and the person holding above puts the rope next to his feet. In this way the four cubits are lessened a certain percentage for every four cubits. This is the size of the mountain’s ascent and descent, according to the rabbis. If you are having trouble picturing this, imagine a right triangle with its slope ascending, as if it was going up the mountain. If the top line is four cubits (the length of the rope) and the person hold the rope below is 3 cubits (the size of an average person), then you have a triangle whose sides are 4, 3 and 5, the side of 5 being the slope going up the hill (all of this is remembered from 10th grade geometry thank you Mr. Formica!). Thus the five cubits up the mountain are spanned with a four cubit rope, thereby gaining one cubit for every four. [I hope this helped!].
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Bartenura on Mishnah Eruvin
וחוזר למדתו – for since it teaches, “continues his measuring” – implying that if its width that corresponded to the town/city was more than fifty [cubits] and he was not able to absorb it/include it there with the rope, and with one of its heads that does not correspond to the town/city, he can absorb it/include it there, and measure and go there from the border and beyond until it corresponds to the place where the the width of the valley ends sin it corresponding to he city/town, and he returns to his measurement corresponding to the town/city and completes the measurement of its [Sabbath] limits.
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Bartenura on Mishnah Eruvin
הגיע להר מבליעו – and this is so that the mountain/hill will not be standing upright a great deal, but rather slanting, for in the walking of five cubits from it, he will not raise it (i.e., the rope) other than ten handbreadths, if it is standing straight up until with at least of the distance of five cubits it is standing upright ten handbreadths, he doesn’t include it/absorb it, but rather, estimates it alone and goes on.
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Bartenura on Mishnah Eruvin
והוא שלא יצא חוץ לתחום – when he measurer goes to include the hill/mountain or the valley, he should not leave outside of the [Sabbath] limit to a a place where the tops of the valley are short – that he is able to absorb them there in order that he can return afterwards to his measurement corresponding to the town/city, as a decree, because a person who sees it measures it and goes there would say that the measurement of the [Sabbath] limit of the sides of the city/town come up to here.
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Bartenura on Mishnah Eruvin
בזו אמר רבי דוסתאי – with this, to exclude the city of refuge and the heifer whose neck is broken that is nearest to the space/cavity that they don’t estimate the level distance between two places separated by mountains (see Talmud Eruvin 58a-b – because they are from the Written Torah).
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Bartenura on Mishnah Eruvin
מקדרין – they perforate, they see as if they perforate them and measure the path of the perforation, to exclude the measurement of its sloping, as we stated in the Gemara (Tractate Eruvin 58b) that they measure it with a rope of four cubits and the bottom they place the rope corresponding to his heart and at the top corresponding to his feet, and similarly they measure it all four cubits by four cubits and they deduct the slope of all four cubits by half the height of a person. And the Halakha is according to Rabbi Dostai.
