Explanation #1 (Rashi): This is in the Mishkan of [Sefer] Yechezkel. (Dikdukei Sofrim - this was errantly copied from the next Rashi. Surely Rashi knew where the verse was!)

Explanation #2 (R. Chananel): It is in Sefer Zecharyah, but "uv'Yad ha'Ish Keneh ha'Midah" is in Yechezkel.

Implied question: It says "Madad Ru'ach ha'Kadim bi'Kenei ha'Midah... Saviv", and so it is written [that they measured with a reed] in the four directions!

Answer (Ri): They used a measuring rope to measure the length of 500 reeds.

Implied question: No rope receives Tum'ah, for [Kabalas Tum'ah] requires that it is spun and woven, like it says in Shabbos (64a)!

Answer: For a stringency of Parah Adumah, we require a material that does not receive Tum'ah.

Question: Why didn't [the Tana] teach these together, i.e. "if he reached a mountain or fence, he swallows it"? (The rope is on level ground to the side, so the incline will not increase the measure.)

Answer #1: It is due to the Seifa, which teaches "I heard that we are Mekader in mountains." Therefore, a mountain was taught by itself, even though piercing applies also to a canyon and fence.

Answer #2: If we would say that a canyon and fence are totally the same, and a mountain is somewhat different, this would be fine.

Explanation #1 (Rashi, first Perush): If the width of a canyon opposite the city goes outside the Techum, and [a measurer] goes to swallow it not opposite the city, he may not measure and go outside the Techum until he is even with the [further] edge of the canyon opposite the city, and like the number of Amos he left, he returns and enters the canyon, and marks it off [that the Techum ends here. E.g. if 2030 Amos from the city was even with the outer edge, he enters the canyon and marks the end of the Techum 30 Amos from its outer edge];

[This is a decree] lest people say "the Techum extends to here', like the Gemara explains (58b).

Rebuttal: Even without this [decree], one cannot measure like this, for if he returns into the canyon, and marks off in the place that completes the number of Amos that he left (in our example, 30 from the outer edge), he marks off outside the Techum, for the Amos the he left [the Techum] were on level land, and the Amos he entered into the canyon are sloped! (E.g. when he measures 30 Amos, due to the slope perhaps this is only 20 Amos horizontally.)

Suggestion: He puts the rope in the canyon from one end to the other [so it will be straight, and not sloped], and corresponding to the Amos that he left, he measures on the rope, and puts there a plumb line (and marks off the end of the Techum directly underneath it. If he cannot reach the rope from the bottom of the canyon, he puts the plumb line on the rope before extending it from one end of the canyon to the other.)

Rejection: Since the canyon is wider than 50 Amos, Chachamim said that a rope does not help there. Even through poles, it does not help to stretch a rope of 50 Amos from one to another!

Conclusion: Rather, he goes to a place corresponding [to the end of the Techum] and swallows or is Mekader.

Explanation: He cannot swallow it unless he leaves the Techum, or it was a crooked canyon, like a Beraisa in the Gemara teaches.

Explanation #1 (Rashi, first Perush): The slope was easy to traverse. We are Mekader. I heard this, and it is difficult to me. Rashi did not explain what is difficult to him.

Explanation (Ri): It is difficult to him, because below [Rav Yehudah] says about this "we learned, i.e. that we are Mekader a crooked canyon, only if a plumb line does not descend [virtually] straight down (the edge is not so vertical), but if it descends [virtually] straight down, he descends and measures it well.

I.e. he skips the entire slope, and measures only the level part in the canyon.

Question: If so, how do we find what was taught "he swallows it"? Whenever the plumb line does not descend straight down, it is crooked, and he is Mekader, and he does not swallow it;

When the plumb line descends straight down, he does not need to swallow it. Rather, he measures it well, and skips the entire slope!

Observation: However, according to this Perush we could say that "we learned" does not refer to a crooked canyon, like Rashi explained. Rather, it means as follows. We learned that he swallows it, or when he cannot swallow it, we are Mekader, only if a plumb line does not descend straight down.

Implied question: We established that he swallows it when it is convenient to use it!

Answer: In a crooked canyon, which is more convenient to use, we are Mekader.

Rejection (of Explanation #1): However, since the Tosefta teaches that if it was a crooked canyon and he cannot swallow it, we must say like Explanation #2 in Rashi.

Explanation #2: The canyon is crooked and goes around the city. If he will swallow it on one side, he can err, for he needs to look and go several times.

Note: Rashi says that e.g. it is wider than 50 in the west, and it narrows to 50 only after it bends to the north. The swallowed measure in the north cannot help for the measure in the west. Tosfos explains that in theory, it could help (especially if it bent in a circle, through facing from place to place at the correct angle, one could learn the measure in the west from the measure in the north), but since one is prone to err, we do not do so.

Explanation: [We do not say that] he erects tall poles on both sides and stretches the rope from one to the other to swallow it. Rather, Chachamim were lenient to rely on mere estimation;

He estimates in his heart and goes away, like we establish it when it is not convenient to use it, and it is tedious to alight on it.

Distinction: If it is too steep, to the point that a plumb line descends straight down, even estimation is not needed. He skips the entire slope of the wall, like Shmuel says below regarding a canyon.

Limitation: Only regarding a wall and mountain, [Chachamim] were lenient when it is not convenient to use, that we estimate, because one must ascend on it when he wants to swallow it, and it is a great toil;

However, one always swallows a canyon, even if it is not convenient to use, as long as a plumb line descends straight down, like Shmuel said, for it is not such a toil to swallow it.

Explanation: Rav Yosef concludes that we discuss when a plumb line descends straight down.

Consequence: According to this conclusion, Rav Yosef does not refer to swallowing, like he did until now, for we said above that [when a plumb line descends straight down] he measures it well!

Rather, he refers to Rav Yehudah, who said that when a plumb line descends straight down, he measures it well. [Rav Yosef] teaches that even if it is more than 2000, he measures it well.

Explanation (Rashbam): There is no distinction whether it is 50 deep, or 100, or 1000 or 2000, even though a slope [with a horizontal component] of two Amos of a small matter (a small vertical component) is more convenient to use than a slope of four Amos of a big matter.

Explanation #1: Here, Rashi explained "he measures well" unlike above, that he skips the entire slope. Just the contrary, he does not swallow or Mekader. Rather, he measures the entire slope, for it is like smooth land.

Assertion: The same applies to a canyon or wall. If it slopes 10 [Tefachim] amidst five [Amos] it is like smooth land.

Summary: There are four laws of a wall and mountain. If it slopes 10 amidst five, he measures it like smooth land;

If it slopes 10 amidst four, he swallows it. If he cannot swallow it, he is Mekader;

If it is not convenient to use, he estimates it and goes away.

If a plumb line descends straight down, he skips the entire slope.

Distinction: In a canyon, there is no distinction between whether or not it is convenient to use, like I explained (58 DH DH Ein).

Question: According to this version of Rava, I do not know what is called convenient to use, and what is called not convenient to use. (It cannot be sloping 10 amidst five or amidst four, for those have different laws!)

However, in the latter version of Rava, who says that if it slopes 10 amidst five he swallows, this is convenient to use, and if it slopes 10 amidst four, this is not convenient to use.

Consequence: According to this version, a wall and mountain have only three laws. If it slopes 10 amidst five, he swallows it;

If it slopes 10 amidst four, he estimates it;

If a plumb line descends straight down, he skips the entire slope. This is how to explain the Sugya according to Rashi.

Explanation #2 (R. Tam): We call Chut ha'Mishkoles anything sloped and smooth without descents and crevices, so a person could stand there. This is Mishkoles. The Targum of "Yesa'arehu va'Sered" is Yimaser b'Miskela. (The verse discusses smoothing.)

Even if it is very sloped, it is called Mishkoles, since it is sloped and exceedingly smooth.

The Gemara means as follows. We learned only when Chut ha'Mishkoles does not descend there, i.e. there is no Chut ha'Mishkoles on which a person could descend and ascend. Since it is not proper for walking, [Chachamim] were lenient to swallow it;

However, if Chut ha'Mishkoles descends there, that it has a descent to descend and ascend, they were not lenient to swallow it. Rather, he measures it well, totally, like the case below.

According to letter of the law, we should always measure the slope, like we say below "we are not Mekader in refuge cities..." but for Techumim they were lenient to swallow it when Chut ha'Mishkoles does not descend there.

Explanation #2 (cont.): [The Gemara asks] how deep may a canyon be, and we swallow it? Rav Yosef said 2000 [Amos], but if it is more than 2000, no. Since it is like Techum Shabbos, we should not be lenient.

[In Version #2, Rav Yosef said that it may be even more than 2000. Abaye asked that this is not like Chachamim or Others. We answered that] there, Chut ha'Mishkoles does not descend. I.e. Rav Yosef discusses our Mishnah, when Chut ha'Mishkoles does not descend. Therefore, he swallows it even if it is more than 2000;

Chachamim and Others discuss when Chut ha'Mishkoles descends there. It is proper to walk. Even so, one may swallow it [if the depth is] up to 100 Amos according to [Rabanan], and up to 2000 according to [Others].

Consequence: According to this latter version of Rav Yosef, this that Rav Yehudah distinguished above when Chut ha'Mishkoles descends there, this is when it is more than 100 according to Rabanan, and more than 2000 according to Others.

Explanation #2 (cont.): [The Gemara asks] how much? I.e. how much may a canyon be and we swallow it? Until (i.e. at least a depth of) four, but less than four it is like smooth land, and we measure everything. However, if it slopes 10 amidst four, he estimates it and goes away.

Explanation (R. Tam): This is only for a mountain, which Shamayim made. They were lenient to estimate it. However, a canyon made through man, like the practice to make canyons and valleys around a city to fortify it, they were not lenient to estimate it;

Rather, even if Chut ha'Mishkoles does not descend there, and it is not proper to walk, he swallows it. The same applies to a wall.

Explanation #3 (Rashbam): The Rashbam's text in the Beraisa above (58a) says "if he reached a wall, he measures the wall." This is the text in the Tosefta (4:16).

Explanation: He measures the entire slope of the wall. We establish this when it is convenient to use, i.e. it slopes 10 amidst five. Our Mishnah says that he swallows it when it slopes [10] amidst four. Also Rava establishes it like this in Version #1.

Implied question: Why does it say (58a, about our Mishnah) "there it is convenient..."? (It is not convenient in our Mishnah!)

Answer: It is because the Beraisa was brought in passing, due to our Mishnah. It is proper to say "there, we learned that he swallows it only when a plumb line does not descend straight down. Since there are four Amos, they are not Batel, and one must swallow;

However, when a plumb line descends straight down, since there are not four Amos in the slope, and also, we established our Mishnah when it is not convenient to use, he skips the slope and measures it well.

[The Gemara asks] how deep may a canyon be and the four Amos are not Batel, and we swallow? Rav Yosef said, 2000. However, if it is more than 2000, even four Amos of space (i.e. the horizontal component of the slope) or more, we skip the entire slope.

Remark: This is the style of Chachamim. [If the space is] less than four Amos, it is not important, even if it is less than 100 [deep]. If [the space is] four Amos or more, it is important, until 2000 [depth]. Past this [depth], it is not important.

Explanation #3 (cont.): Abaye asked [from a Beraisa that says that] is it is 100 deep, he swallows it. If not, he does not swallow it, rather, he skips the entire slope. We answer that Rav Yosef holds like Others.

In the latter version, Rav Yosef says that even if it is more than 2000 Amos, the four Amos are not Batel, and he swallows.

The text says "there the plumb line does not descend straight down." I.e. Rabanan and Others, who hold that less than four is important up to [a depth of] 100 according to Rabanan, and 2000 according to Others - here that a plumb line does not [descend straight down], four Amos are important, and they are not Batel even more than 2000.

Explanation (R. Chananel): This is the straight way towards the city. "Mumcheh" is an expression of "u'Machah Al Kesef Yam Kineres";

One should not go to the sides of the city to measure there 2000, for sometimes there is there smooth land and it is easy to measure, and afterwards he will look and come opposite the city, and look even with his measure [of the Techum];

He should not do so, for sometimes there are mountains and valleys opposite the city that he should swallow or be Mekader.