Eruvin, daf (page) nun-heh. Today’s daf is being studied le-nishmat (for the soul of) Avraham ben Ester. We begin today’s daf on nun-heh, amud rishon (first side), starting at tanu Rabbanan (The rabbis taught), about ten lines down.
Tanu Rabbanan: Keitzad me'abberin et he'arim? So how do we extend cities? We learned in the Mishnah that sometimes you don’t actually count the 2,000 amot (cubits) from the end of the city. Sometimes there’s an extension. For example, we said the city becomes pregnant. So the Gemara asks, how do we do that? How do we extend cities?
It says, Keitzad me'abberin et he'arim? Arukah (long), if it’s a long city, kemoshehi (as it is), so then there’s no extension. What does arukah mean? It’s just a regular long city without any extensions from it. We’ll see what the chiddush is in that. I mean, if it’s just a regular city like this, like this tissue box, a long city, like a rectangle, then arukah kemoshehi: you judge it from the last house, 2,000 amah. The Gemara is going to ask, peshita, what’s the chiddush in a regular arukah case?
Okay, but then we have another case: agulah, let’s say it’s a circular city. So how do you count 2,000 amah? Osin lah zaviyot meruba'at. Okay? So, agulah: Osin lah zaviyot. Which means, if it’s circular, the way you judge the 2,000 amah is by drawing a square around the circle. So you gain the corners. Now you get to walk 2,000 amah from the points of the square, from the walls of the square, so you gain extra. That’s an agulah. Meruba'at, ein osin lah zaviyot. Okay, if it’s meruba'at, if it’s already squared, you don’t make zaviyot; it already has zaviyot.
Hayetah rechavah mitzad echad u-ketzarah mitzad acheir, ro'in otah ke'ilu shaveh. That’s a case where, let’s say, the city is wide at one point, and as the city progresses, it gets narrow. What you do is equalize it. You make it as if the wide part goes all the way down. Draw a line from the widest part all the way down and box it in. Therefore, your 2,000 amah are now extended at the narrow part of the city, because you widened it out, and you get an extended 2,000 amah.
Hayah bayit echad yotzei kemein pigum: if, let’s say, one wall or one house is protruding, o shenei batim yotzi'in, or, for that matter, two houses are protruding from the wall, kemein shenei pigumin, ro'in otah ke'ilu chut matu'ach aleihen, u-moded mimenu u-le-halan alpayim amah. Just as we learned in the Mishnah, if you have a house or two sticking out at the border, you draw a line from the extended house all the way across that side, and you get 2,000 amah from the extended area.
Hayetah asuyah kemein keshet: if the city was made in the shape of a bow, keshet, exactly. So now, where do you measure the 2,000 amah? If you go from the houses, you’re deep in. However, the houses do extend to the sides, because in a keshet it goes up like the letter U. You have these houses on the sides, at the end, and if you count from there, you’ll have an extension. So it says, o kemein gam. Gam would be like the reverse letter L. It’s one of the Greek letters of the alphabet. So you have a gam. The city is like this: it’s a line down and then a line across.
The din (law) is ro'in otah ke'ilu hi mele'ah batim va-chatzerot. So we look at it as if it’s filled with batim and chatzerot. What does that mean? With the L, you fill in the blank spot, so now it becomes a square, and therefore you’re able to count the 2,000 amah from the end, from the new, filled-in area. And for that matter, when it’s a keshet, the bow is like this, so you have a whole open space in between. Fill in the space, and now you’re able to walk 2,000 amah from the line. You know, in a bow there’s a line, right? We would call it the string, where they shoot the arrows. Go all the way up, and from the end, as if it’s filled in, you can carry from there. U-moded heimenu, and you count from there and measure from there, kolel chalal (including the open space), alpayim amah. So that mentions all the cases that we need to know.
Now the Gemara goes back. “Yes?” “Which one? What do you want to know?” “Yeah, exactly.” Basically, they’re putting a—because the bottom of the keshet is also like a circle, like a semicircle. So you put a rectangle or a square around the bottom of it as well, in order to gain these zaviyot. So you’re squaring the bottom and filling in the top. You’re squaring it up as well.
Okay. Now the Gemara begins. Amar mar (the master said), arukah kemoshehi. If it’s just a long city, let’s say in the shape of a rectangle, the Gemara says kemoshehi: you don’t square it. You don’t have to square it; it’s squared already. So what’s the chiddush? The Gemara says, peshita. Lo tzricha de'aricha uktina. So what we’re talking about here is that it’s long on one side and narrow on the other side, which is a rectangle.
Mahu deteima leyahav lah putya k'orka, which means maybe I would give the width, which is the shorter side, the same distance as the length. Let’s say I have a rectangle. It’s short on one side, like these boxes, like two of these boxes. This is the short side, and this is the long side. So I might have thought that you draw a square around the box. From here you go out, and from here you go out. Maybe on the width side I’d draw a line flush with the width, but then go all the way out and draw a line around it.
The picture in our books is tziyur—in fact, I’m using the Metivta ones here. See what they’re doing? They’re putting a square around it. You would have thought that you extend it like this. Look at Rashi. Rashi says, arukah kemoshehi, peshita. It’s one, two, three, four, five lines down. V'chi ta'aleh al da'atcha sheyiktzerenah? Exactly. You think that if it’s a long city, I should shorten it? Of course you get to count the 2,000 amah from the end of the city! Why do you have to tell me that you count from the end of it? Of course—what, did you mean I should count less than that?
So the Gemara says, de'aricha uktina, ketzarah b'rachbah: it’s narrow on the width side. Mahu deteima yarchivena lemizrach uma'arav ad shet'muroba yafeh. I would have thought that maybe you turn the rectangle into a square. Ka mashma lan kemoshehi manichim otah, sheharei yesh lah pe'ot. It already has corners. You see, the common denominator between all these cases is that round or keshet-shaped cities don’t have corners, so you square them off to give them corners. But a rectangle has corners already. You don’t have to square off something that already has corners.
The Gemara says, Baruch atah Hashem Elokeinu Melech ha'olam shehakol nihyeh bidvaro. Amen.
Haytah meruba'at, ein osim lah zaviyot. If it’s already squared, you don’t make corners for it. The Gemara says, peshita. Of course you don’t make corners. If it’s already a square, what do you have to make corners for? Lo tzricha d'meraba velo meraba beribua d'olam. It’s squared, but not a regular square of the world. It’s a diamond; it’s on a tilt. Mahu deteima leraba'ah beribua d'olam, ka mashma lan.
See the picture? It’s a square, but it’s a diamond, like a baseball diamond. Therefore, I would have thought that you square it in a regular square of ribua olam. Here’s a picture. It’s tziyur yud. Here’s the square, which is actually a diamond with four corners. However, I would have thought that you make a box around it in order to square it off normally, and therefore you’ll gain more amot in your 2,000 amah.
Ka mashma lan: no, since it’s a square on its own, finished, it has zaviyot. Although it’s not a normal square kedeka chazi, that it’s not a ribua olam, that’s enough. Nu, it makes it—but that’s the answer. You would have thought that since it’s not the regular flat, like a—“No, it’s not straight.” “Mm-hmm. You’re right. Because everything else, where that’s where we square it, we square it like a—” “Exactly, yeah. Directions. Directions. Exactly. Exactly.” Okay. That—the same as—which means the wall is not the ma'arav and the mizrach and the tzafon. Off.
The Gemara continues: Haya bayit echad yotze kemin pigum o shenei batim yotzim keshenei pigumim. If at the border of the city you have a house coming out, or two houses coming out, you draw the imaginary line from the extended houses, and you draw your line there. That’s where you have your extensions.
So the Gemara says, hashta bayit echad amart, shenei batim miba'ya? If you’re telling me that one house already extends the city, then two houses, of course, do. The Gemara answers, la tzricha mishtei ruchot. Ah, it’s talking about where you have extended houses on both sides of the city. Mahu deteima meruach echad amrinan, mishtei ruchot lo amrinan, ka mashma lan. You would have thought that maybe you only extend the city with a house that’s jutting out on one side. Ka mashma lan: with shenei batim, the houses on two different sides, you could extend the city on both sides. The chiddush is that the two houses were not on the same side; they were on opposite sides.
The Gemara says: Hayetah asuyah kemein keshet o kemein gam, ro'im otah ke'ilu hi mele'ah batim vechatzerot, u-moded heimena ulehallan alpayim amah. The first case we said was the keshet, the city made like a bow. We see that you fill it in. You square the bottom and fill it in, and then you count 2,000 amah from where you filled it in. Or it’s made like a gam, so you fill it in to make a square, and count 2,000 amah as well.
Rav Huna says: ir asuyah kekeshet, im yesh bein shenei rasheha pachot me'arba'ah elef me'arba'at alafim amah. If, let’s say, the distance from end to end between the points is less than 4,000 amah, that means the 2,000 amah from one side overlap the 2,000 amah from the other side. Let’s say it’s 3,999 amot. The 2,000 amah on both sides overlap each other, so then modedin lah min hayeter: you count the 2,000 amah from the yeter, from the string. Then you draw that imaginary line and count from there.
However, ve'im lav, if it’s 4,000 or more, then it’s considered a separate city, u-modedin lah min hakeshet: you only count from the actual keshet itself, from inside. There’s another prat in this law of the kemin keshet. You have to measure the distance from point to point. That’s what Rav Huna said. We’re going to get to that now as well. Which means, how much distance from the house to the—We’re going to get to that now; it’s coming up.
So the Gemara says, Umi amar Rav Huna hachi? Did Rav Huna actually say that? Veha'amar Rav Huna, chomat ha'ir shenifretzah beme'ah ve'arba'im ve'echad ushlish. Chomat ha'ir shenifretzah: you have a city, okay? Here’s a city. All of a sudden, the wall of the city splits. So now this city, which was all homogeneous, splits in half, and now you have two cities here. We said, no, as long as there are 141 amot and what, 2/3 or 1/3 between the cities, that’s still considered one, and therefore you count 2,000 amah from the ends. It’s considered together.
And where did they get that from? That’s the law of the karpef. Correct. So they give each city about 70 amah and change as an extension to the city. So, as long as you have 140—what is it, 141? Me'ah arba'im ve'echad ushlish—in the middle, that’s considered as if they’re still together. If it’s more than that, they’re considered separate, and therefore you cannot count from the ends of each city.
Now what do you see from here? If there are more than 141 amot and a third, they’re not mitztaref. And here he’s saying you have 4,000 amah, up to 4,000 amah. I’m saying it’s like two cities, right? In the keshet case, one part of the city ends here and one part ends here. There he says, “Oh, if you have 3,990 amah between the two ends, you’re okay. It’s considered one city.” When he had a city split in half, he only gave me 141. What’s the difference?
The Gemara answers: Amar Rava bar Ula, lo kashya, kan ru'ach achat (one side), kan mishtei ruchot. Which means that in the keshet case, at least it’s connected on one side. The bottom is connected. If the bottom is connected, it’s really one city, and therefore we’re lenient and allow the 2,000 amah to overlap. Mah she'ein ken, in the case where the city is split in half, it’s not connected at all. It’s mamash a clean split all the way down. They’re two cities. In that case we’re more machmir: we only give them a karpef each to extend out, so it’s 141 amah, and that’s it.
So make the chiluk between a city that’s attached on one side, where we’re more lenient, and a city that’s split all the way down. Umai ka mashma lan? He says, “Well, Rav Huna, what are you coming to teach us here? You’re telling me the magic number is 141 and a third. So you’re just teaching me here that notnin karpef lezu vekarpef lezu. Basically, you’re teaching me that you give 70 amah and two-thirds to each city. That’s called karpef. When you’re entering a city, you don’t measure from the end of the city. The city also gets what’s called a migrash, like a park, an open area that’s part of the city. So what are you telling me? When you have a city that’s split, as long as there are 141 and a third between them, it’s considered attached. Why? Because each city gets an extended 70 and two-thirds amah. We know that already. That’s what you’re teaching me? What did you have to tell me that for? You told it to us already: each city gets a karpef.”
Ha amrah Rav Huna chada zimna. Rav Huna taught this to us already one time when he taught us in the Mishnah. Now the Mishnah is not Rav Huna. The Mishnah is the Mishnah, but Rav Huna is going to explain the Mishnah. Detnan: notnin karpef la'ir, divrei Rebbi Meir. Rebbi Meir says that you give a karpef to a city, to any city. You have a city: don’t count from the end of the city. Add 70 amah and two-thirds, and continue counting from there. Vachachamim omrim, lo amru karpef ela bein shtei ayarot. He says, “No, no, no. A regular city doesn’t get a karpef. The law of karpef applies between two cities.” And Rav Huna is going to explain what Chachamim meant by two cities. Rebbi Meir is more lenient. Rebbi Meir says, “Every city—boom, go to the end, count another 70, and start from there.” Chachamim say no, it’s only between two cities.
And here it was Rav Huna, ve'itmar, and on that Rav Huna amar: karpef lezu vekarpef lezu. Ah, like we just learned, you give each city a karpef, 70 amah and 70 amah and the two-thirds. So as long as there are 141 and a third between them, you can join them. Vechiyya bar Rav amar, ein notnin ela karpef echad lishteihan. Chiyya bar Rav is machmir. Chiyya says you only give one karpef in between them, which means there have to be 70 between them.
Okay, fine, but the point is: Rav Huna, you taught us this already! Why did you have to tell me about a city that got split in half and tell me that as long as there are 141 amah between them—You taught us the law! You taught it to us on the Mishnah! That Mishnah says notnin karpef lezu vekarpef lezu when you have two cities next to each other, that you give a karpef. Rav Huna, you explained it: notnin karpef lezu vekarpef lezu—that’s the 141 law! So what did you have to repeat it for?
Amar Rava tzricha. Ta-yeh, you need it! Why do you need it? De'i ashme'inan hacha, because if you were talking about a case where the wall of the city came down, like our case, where you had a city that was connected and then the wall came down, separating it, mishum dahavei leih tzad heter me'ikara. I would say the only reason you can use karpefyot is because there it was attached at one time. Since it was attached, we’re lenient about 141. Aval hatam, eima lo. But in a city that was never attached—two cities that were never attached lechatchilah—I might have thought that maybe you don’t have the leniency of karpefyot. Maybe Rav Huna was only lenient in a city that was one originally and then the wall came down and split it. Since it was one originally, you’re lenient and use the karpefyot to attach it. But maybe in two cities that were never attached lechatchilah, Rav Huna doesn’t give me this leniency. Ka mashma lan: the Mishnah teaches that even in two cities that were never attached from the outset, we give the heiter of karpifiyot.
Go the other way: ve'i ashme'inan hatam. If you only gave me the case of the Mishnah, mishum dedechika tashmishtaihu, aval hacha delo dechika tashmishtaihu, eima lo, tzricha. In the Mishnah, these were two distinct cities, so each city got used to its space in between the cities. Dechika tashmishtaihu. In that case we give each city a karpef. Mah she'ein ken, in a city that was attached, they never enjoyed a karpef to start with, because they were attached. There was never a space between them. So I might have thought that when they separate, you don’t give each one its own karpef. They were happy without it. They would never enjoy a karpef; they were attached. Ka mashma lan: even though they never had a karpef in the city because it was attached, they still get one. Therefore, Rav Huna was not being redundant. Rav Huna was teaching his law in two separate cases: a case where the cities were separate from the beginning, and a case where they were attached and the wall came down.
The Gemara goes one more point: Vechama havei bein yeter lekashet? That’s your question, David. How far is the distance between them in the keshet case? You told me that at the string, at the end, it has to be less than 4,000 amah in order to count from the end. But now, from the wall, if it’s more than that, you can’t; then you count from the houses. Come down. But now the question is, how much distance is there from the houses to the string? Since you’ve got to be able to walk from the houses to the string, and then from the string you continue on, is there a distance between the houses and the string?
So the Gemara says, how much is the distance between the yeter lekashet? Yeter is the string on top. When you fill it in, the string is the yeter—the bowstring—and this is the keshet itself. So how much distance is there between the houses of the keshet and the yeter? The Gemara says: Rabbah bar Rav Huna amar: alpayim amah. Oho! So you see the picture? It’s obvious, but I just want to show it to you. From the end of the bow, 2,000 amah, and then we say you’re able to extend it. So there are laws here: 2,000 this way, 3,999 this way, and then we say you’re okay. However, then we fill it in. If it’s more than that, you can’t; then you go back to the houses.
Rava bereih de-Rabbah bar Rav Huna amar: afilu yeter me'alpayim amah, even if it’s more than 2,000 amah. Oh, what’s the logic here? Amar Abaye: kevatieh de-Rava bereih de-Rabbah bar Rav Huna mistabra. Makes sense! It makes sense, even if it’s more than 2,000. What do you mean? But how’s the person going to get to the end? He’s already walking more than 2,000 amah just to get there on Shabbat!
So the Gemara says—meaning, you want to tell me that you’re going to be mitztaref all this? Maybe it has to be a distance of a techum, less than a techum, so you can get there. But if it’s more than 2,000 amah, and the person in the house can’t even get to the end, maybe you don’t say this rule that it’s filled up and all that. So the Gemara says, “No, it doesn’t matter. You know why? De'i ba'ei hadar atei derech batim.” Exactly. He can go not straight—exactly, go the long way, around the houses. See the picture here? It’s obvious. He doesn’t have to walk straight. If he walks straight, he’ll go more than 2,000 amah. Let him go around the houses, and he’ll be able to get to the end.
So, as long as the techum of both of them are muvla, within 4,000 amah of each other, then that’s considered one city, and he can access it via the houses. Therefore, we consider it as if it is filled in, and there is no problem!
The Gemara goes one step further: Hayu sham gedudiyot gevohot asarah tefachim. Remember we saw that in the Mishnah? We said that if at the end of the city there are gedudiyot, gedudiyot that are 10 tefachim, these are walls extending the city, and then you count from the extension. The Gemara says: Mai gedudiyot? What are gedudiyot? Stam, what’s the peirush hamilah? Amar Rav Yehudah: shalosh mechitzot she'ein aleihen tikrah. So you see these dilapidated houses here. It has three walls, even though there’s no roof on it, and it’s okay; you count from there. They’re broken-down houses, but that’s enough. Three walls already make it a legitimate enough structure for you to start counting from its end.
Iba'ya lehu: shetei mechitzot veyesh aleihen tikrah mahu? Okay, now the Gemara asks: three walls without a roof are considered a structure to extend the city. What about two walls with a roof? Does the roof take the place of the third wall? How do you look at that?
Ta shema. It says like this: Elu shemit'abrin imah, the following items add to the city, the following items add to the wall of the city. Nefesh—what is a nefesh? A grave or tombstone—sheyesh bah arba amot al arba amot, that is four amot by four amot; that would be significant. Vehagesher, the bridge, vehakever, the cemetery, sheyesh bahen beit dirah, which has someone living there, a house, like a watchman there, can extend the city. Uveit hakeneset sheyesh bah beit dirah lechazan, the beit keneset that has a dwelling place where the chazan lives, the shamash. Uveit avodat kochavim, even a church, sheyesh bah beit dirah lechomarim, which has a dwelling place for the priests.
Veha'uravot, that’s a stable for horses; veha'otzarot, storage houses for wheat, oil, and wine, shebasadot, and they have a watchman’s house. Vehaburganin—burganin are huts where the trappers who trap the ofot, or people who watch the fruit in the field, live—shebetochan. Vehabayit shebetoch hayam: you have a house on an island. All these are within 72 70 amah of the city, so harei elu mit'abrin imah: you’re able to extend the city with all these.
Ve'elu she'ein mit'abrin imah: the following items, even though they’re extensions, do not extend the city. Nefesh, the tombstone or monument, shenifretzah mishtei ruchoteha ilach ve'ilach, meaning it was broken in half and therefore only has two walls. Vehagesher vehakever she'ein bahen beit dirah: the bridge or cemetery that doesn’t have a dwelling place for anyone. Uveit hakeneset she'ein bah beit dirah lechazan: the shul, the synagogue, doesn’t have a dwelling place for the shamash. Uveit avodat kochavim she'ein bah beit dirah lechomarim doesn’t have a dwelling place for the priests. Veha'uravot veha'otzarot shebasadot she'ein bahen beit dirah: the stable and storage houses that don’t have a dwelling place.
Vehabor vehasi'ach: bor is a circular hole in the ground; si'ach is a rectangular chafirah. Ume'arah: me'arah is a cave. Vegader: gader is made from stones, a wall or fence. Veshovach shebetochah: you have a shovach, let’s say, a dovecote where they keep birds. Vehabayit shebisefinah: or you have a house on a boat next to the city. Ein elu mit'abrin imah.
Okay, the common denominator between all these things is that none of them are ra'ui ledirah. A house on a boat is not ra'ui ledirah; a dovecote is not ra'ui ledirah. If it’s broken, you can’t live in it. As long as nobody can live in it, it’s not considered a significant house that can extend the city.
Now the Gemara is going to explain the question. We asked: two walls and a roof, is that considered enough to make an ibbur? Katanei mihat, partial quotation: nefesh shenifretzah mishtei ruchoteha ilach ve'ilach. The nefesh, the monument, was broken in half on both sides, so we said what? You cannot be mitztaref. Mai lav de'ika tikrah? It must be talking about a case where there is a roof! And now, instead of four walls, you only have two walls and a roof, and you’re still telling me that you don’t extend the city? Ah, there’s your answer!
So the Gemara says, lo, delika tikrah. Okay, no, there’s no roof. So we have no proof for our question.
Bayit, okay, now the Gemara goes back. The Gemara says, bayit shebayam lemai chazi? It was ra'ui lebeit dirah. It has to be ra'ui. As long as it’s suitable for somebody to dwell there, it’s enough. So now the Gemara says, okay, you have a house on an island. The house on the island extends the city. The Gemara asks: what are they doing there? Who’s living on an island in the middle of the ocean? Less than 70 amah from the city—but the point is, who’s living there? It has to be ra'ui? Mah zeh ra'ui? Who’s living on an island? Bayit shebayam lemai chazi? It’s in the middle of water!
Amar Rav Pappa: bayit she'asu lefanot bo kelim shebisefinah. Aha! It’s like a house there where they unload the boats, where the people have merchandise on the boats, so they put their kelim, you know, in this house.
Me'arah ein mit'aberet imah. Okay, we said here that a cave does not extend a city. Vehatani Rabbi Chiyya me'arah mit'aberet imah. Oh, we have another source that says you can extend a city with a cave. Amar Abaye: kesheyesh binyan al piha, which means if you have a structure close to the opening of the cave, then you can include it. A regular cave that nobody lives in is nothing to do with it, you know, and—but if it’s a cave with a binyan in front of it, that’s already considered a dirah, so it’s okay.
Vetipok lei mishum binyan gufeih, meaning, forget about the binyan; somebody could live in the cave itself. Why do you have to tell me that the only reason you can count the cave is because it has a binyan in front of it? Somebody could live in the cave itself. Lo tzricha, the case is talking about le'ashlumei. Okay, what’s this le'ashlumei? It’s where you want to complete something. The house itself does not have 4 amot by 4 amot. We said that for a house to be considered a house, minimally it has to be 4 amot by 4 amot. So you want to use the cave to finish the shi'ur of the house. Oh, in that case, it can be mitztaref.
Now, you mitztaref—and if it’s mitztaref? Right, the case of the binyan is talking about where you’re using the cave to mitztaref the binyan, and therefore together it’s going to be okay. I guess the cave was not ra'ui on its own, but when you have the binyan in front of it—“No, the binyan was not ra'ui because it’s less than the shi'ur, and you mitztaref the cave with it.” “Okay. No, fine. It says it’s the majority in the binyan.” “The cave is the majority?” “The binyan is three and this is one.” “Good. Let’s do that halachah (Jewish law) now.”
Okay, stop here. Let’s open up halachah a little bit. We have a lot of cases in our brain. Okay, Benny, give us the coordinates of some halachot. We have 20 minutes to do halachah. Let’s check off some halachot in Mishnah Berurah. Gentlemen, I would invite you all to get a Mishnah Berurah; it will benefit you greatly. Be'ezrat Hashem, I hope so, if I get in on time. It’s a good idea; it worked out good.
Shin-Tzadi-Chet, Shin-Tzadi-Chet—which halachah? Okay, now we’re connecting that to all the cases here. All right, you ready? Shin-Tzadi-Chet, halachah Alef. Gentlemen, this is a very important moment. This is making this round better than the last round, so get the books. David is praying already. Okay, David, yeah. Bring a tallit (prayer shawl), David. Part of my job is to teach the people to become people. It’s nice to teach them books; you’ve got to teach them the social skills.
Shin-Tzadi-Chet, halachah Alef. Let’s read it together: Haba limdod alpayim amah shel techum ha'ir. Okay, a guy is coming to count the techum. Im haytah ha'ir arichah u-ktinah—arichah is long, k'tinah is short; that’s a rectangle—or shehaytah meruba'at, or let’s say it was square, velo leribua ha'olam, even though it’s not leribua ha'olam, which we learned means it’s not a perfect square to the sides of the world, which we said was a diamond. Hu'il veyesh lahem arba zaviyot shavot, since, bottom line, it has four corners, manichim otah kemo shehi, you leave it as it is, u-modedim lah alpayim amah lechol ru'ach me'arba ruchoteha. That’s it, and you count the 2,000 amah from the corners.
Look at the Mishnah Berurah. Arukah uktanah, peirush she'ein rochbah ke'orkah, right, a rectangle. Velo leribua olam: if you have a square that’s not standing to the corners of the world, hainu she'einah omedet tzafonah litzfon ha'olam, that the north side is really not north, u-dromah lidrom ha'olam, ela be'alchason—it’s on a tilt. Arba zaviyot shavot, le'apukei kshehi rechavah mitzad echad uktzarah mitzad acher. It’s talking about when it has four corners, as opposed to when it’s wider on one side and then narrows out on the other side. That’s not considered having four corners, ve'ein zeh ribua, umerab'in otah, and then you square it.
Kemo shehi, hainu ba'arukah uktanah ein mosifin rochbah lisvivoteha le'orkah: in a rectangle, you don’t make a square around it. Vechein kshe'einah meruba'at leribua olam ein mosifim aleha lerab'otah beribua olam kemo bese'if gimmel. Beautiful! Well, that’s basically the beginning.
Now let’s go to halachah bet. Haitah agulah, let’s say the city was round, osim lah zaviyot, you give it corners. How do you give it corners? Vero'in otah ke'ilu hi betoch hameruba. You look at it as if the circle is now—you put a square around it—u-modedim chutz mitzal'ot oto meruba alpayim amah lechol ru'ach, and you count 2,000 amah from each side, shenimtza mistaker hazaviyot: you’re gaining the zaviyot, you’re gaining the corners.
Vechein im haitah ir meshuleshet—what is meshuleshet? Triangular—or sheyesh lah tzela'ot rabot, or it has many sides, a hexagon or some type of shape, merab'in otah, and then you square it, ve'az gam motzi'in chutz lameruba alpayim amah lechol ru'ach. The Mishnah Berurah says: meshuleshet merab'im otah, shemoshchin haribua lehashvot tzad hakatzar kefi orech tzad ha'orech. Yeah, you square it around to make it equal. Tzela'ot rabot, sheyesh lah shishah zaviyot—six sides, a hexagon—or shemonah, an octagon. Moshchin hachut lerab'ah keneged hamikomot hayoter rechavim bah, umerab'in otah u-modedim alpayim amah lechol tzad. Okay, that’s understood. Basically, you’re adding—
Look at the next. Look at gimmel. This is the case where we’ll do one analysis. Gimmel: keshemerab'ah, when you’re squaring it, merab'ah beribua olam. You make a regular square to the four sides, kedei shetehei kol ru'ach mimenu meshuchah keneged ru'ach meruchot ha'olam mechuvenet kenegdah. Okay, so a perfect square.
Gimmel: beribua olam, hainu she'eino yachol la'asot haribua kemo sheyirtzeh. You can’t make the square the way you want to make it. You have to make a square where there’s a north, a south, an east, and a west, ela davka kefi ruchot ha'olam, according to the directions of the world: darom keneged darom, tzafon keneged tzafon, sheme'atah modedim alpayim amah. Fine, so it has to be a square like that.
Halachah dalet: haitah rechavah mitzad echad uktzarah mitzad acher. We saw that case in the Gemara as well. It’s wide on one side and narrows down on the other side, ro'in otah ke'ilu kulah rechavah. You fill it in, right, as if it’s all wide. Haitah asuyah kemin gam—what’s the gam? Gamma, o kekeshet, which is the bow. Im yesh bein shenei rasheha—oh, sounds familiar? If you have less than 4,000 amah between the two ends, then they’re considered muvla, the two ends are considered connected. Modedim lah min hayeter: we measure from the yeter, vero'in et kol harochav shebein hayeter vehakeshet ke'ilu malei batim, and we fill it up as if it’s all filled with batim.
Ve'im hayah bein shenei rasheha arba'at alafim, but if there are 4,000 amah or more between the two ends, ein modedim lah ela min hakeshet: you only measure from the keshet. We have to see what those words mean, min hakeshet. I would have thought Maran would say, ela min habatim. Maybe that’s what he means: the keshet is where the houses are. We’ll have to see that; that’s going to be a subject of discussion.
Look at the Mishnah Berurah. Okay, that was dalet. This is the one we have to sit on a little. You ready? Look at dalet, Mishnah Berurah: ke'ilu kulah rechavah, right, that’s the case where you have wide and then narrowing. Hainu ksheba limdod hatechumin etzel mekom hakatzar. When you get to the narrow part, ein modedin min hachomah. You don’t go to the wall, because if you go to the wall, it goes in, so you’re going to lose amot. Ella mosifin techilah al ha'ir ad sheyihyeh shaveh im mekom harachav umisham vahalah modedim alpayim amah. First you extend it: you go to the widest part on top and draw a line down. Now you’ve extended the bottom, the narrow part, and you start counting the 2,000 amah from the new extended area.
Kemin gam, hu ot yevanit, it’s a Greek letter, vetzuratah kemin kaf peshutah; it looks like a kaf. Okay, we said L; it looks like a kaf, same thing. O kekeshet shebateha benuyim kechetzi igul: that’s a semicircle, uven shenei rasheha hamakom panui, and in between is open. Pachot me'arba'at alafim amah: shetechum roshah shel zo, the techum of one end, muvla betoch techum roshah ha'echad ha'acher, na'asit ir achat al yedei zeh. It becomes one city, vero'in ke'ilu hayah malei batim, as if it’s totally filled, uvimkom hachalal modedim alpaim miktzot hakeshet vahalah. You count from the end of the keshet and onward. Modedim lah min hayeter. Yeter nikra hachevel hakashur bishenei ketzot hakeshet: he’s giving you the peirush hamilim. Yeter is the string that attaches the two sides of the bow. Umisham vahalah modedim alpayim amah.
Vero'im et kol harochav: we look at the whole area. Vehachi nami be'ir asuyah kemin gam: the same thing applies to the gam. Just as you fill in the whole area of the keshet, you fill in the whole area of the gam as well, and make it a full square.
Now, in the case of the gam, where am I carrying from? What am I—I’m just saying you fill up the empty—The gam is an L. The gam is an L. So he’s just saying that, just like I told you to fill up the—“No, not make a triangle; make it a square.” “Make it a square. I want to carry here 2,000 amah even though there’s nothing there. I get to carry at the end of the gam all the way up. It’s an imaginary line. I’m filling it in, making another L, and just filling it in.” He’s just saying, ro'in ke'ilu mele'ah batim. We’ll get to your points about why don’t you just make it half a square and all that.
Ro'in ke'ilu mele'ah batim beribua mimmizrach ulema'arav latzafon uledarom. Vegam bazeh davka—now here’s the point—davka im bein shenei rashei hagam be'alchason pachot me'arba'at alafim amah. That’s a very good point to point out! In the gam, basically, you have a house here on the top of the gam and a house here on the bottom of the gam. In order to connect these two points, you have an alchason, a diagonal. There has to be less than 4,000 amah in the diagonal, just as we said there has to be less than 4,000 amah in the keshet. If there’s more than 4,000 amah, then these two are not connected, and you cannot mitztaref them to make them one. The Gemara didn’t point that out, but it’s the same logic: in order to mitztaref two points, the techumin have to be muvla'im between themselves.
Ke'ilu hu malei batim, ve'al ken yachol lelech kol hachalal shemerosh hakeshet ad hayeter: once you say it’s all filled up, I can walk from the house all the way to the string, and then from the string I can walk an additional 2,000. Ve'ein oleh lo becheshbon alpayim: you don’t start the alpayim from the house to the string. Vechen im hayah lerochav yachol lelech merosh hakeshet latzafon derech chalalo velitol alpayim amah shelemot mehaketzeh latzafon. Fine.
Ella min hakeshet. Now, if there are more than 4,000 amah between point and point, the halachah says we only count from the keshet, from down. What does that mean? Hata'am, dekeivan de'ein muvla'im hatechumin zeh bazeh: that’s the sevara (reasoning) now. Since the techumin are not absorbed in each other, ve'i efshar lehalech miktzeh hakeshet ha'echad liktzeh hasheini, you won’t be able to walk from one end to the other. If you start from the east side, you’ll walk 2,000 and have to stop. You won’t be able to access the other side. Al ken i efshar lachshov hachalal bikhlal ha'ir: you cannot consider the chalal in between as part of the city, ve'oleh betoch shi'ur alpayim.
Vehiskimu haposkim dechol zeh kesherotzeh lelech derech hachalal shel hakeshet ad hayeter ulehalah. This is only talking about where you want to go from the houses to the keshet and further; we’re not going to let you do that. Aval mutarim lehalech saviv derech habatim shebakeshet ad ketzeh hakeshet umisham va'eilach modedim lo alpayim amah me'achar sheholech hakol ba'ir ha'ir kulah ke'arba amot. But if I access the houses, I’m okay. This is only until where you want to go in the chalal area. When you want to go in the chalal area, you get 2,000 amah. But I can walk by the houses on the side, and I get to the last house. Once I get to the last house, I can go 2,000 amah from the last house, because the whole city is considered four amot. You understand what I just said? All this discussion was about where I want to go from the middle, where there are no houses. He said, “Oh, if you say it’s filled up, beautiful! So I won’t go all the way; this doesn’t count. The clock doesn’t start till I get—” But if you say it’s more than 4,000 amah, this middle is not filled up. But don’t think you can’t count 2,000 amah from here, because there’s a house here, and I can get to this house. I’ll walk around the houses on the side; it’s all considered four amot because it’s all one city. Once I get to this point, now start the clock. I just can’t start the clock in the middle here. Right, I can count from the two corners. That’s what the Mishnah Berurah is saying.
Okay. Now, look at the—Now, look at the—Now, look at the Rema. “4,000 from here to here, from point to point.” “No, but if it’s muvla—” “Okay, calm down, calm down, relax. Muvla means if the two techumin overlap each other, it becomes one.” “Since 48 BCE.” “The Gemara says it; what can I tell you?”
Basically, I could access—No, no. When I walk to my end, and this techum is in that techum over there, there is a way for me to get from point A on this side to point B on the other side. If it were more than 4,000 amah, I couldn’t get there. How am I going to get there? Once I get to 2,000 amah, I’m stuck there. Where am I going?
Okay. Now, the chiddush here is that Maran is mashma that you count from the keshet. When you don’t have—when you have more than 4,000 amah, it’s not muvla, and all that stuff—then you count from here. Now, what does “here” mean, from the houses? Now, I could argue: maybe you can count once the area narrows and you have less than 4,000 amah, so you could start counting from that area. Maybe you don’t have to go all the way down to the house. Here it’s wide, but as it goes down it narrows. So maybe I could start the clock once it’s less than 4,000.
So look at the Rema: veyesh omrim min hamakom shenitkatzer sham hakeshet. That’s the Rema. That’s the Tosafot opinion. “Right.” “She'ein bo arba'at alafim amah.” “Perfect, David.” Look at the Mishnah Berurah, and then we’ll stop here. Min hamakom, desvira—that’s yesh omrim, yeah. Desvira lehu, this opinion holds de'af deberashei hakeshet hayah rachav arba'at alafim veyoter: even though at the ends it was more than 4,000, afillu hachi keivan shebe'emtza hakeshet mitkatzer ad she'ein bein zeh lezeh arba'at alafim amah, nechshav ad oto makom ke'ilu malei batim. At least you fill up to that spot with houses, u-mat'chilim limdod alpayim af betachtito begag hakeshet rak me'oto makom ulehal'ah shesham hayah rachav yoter me'arba'at alafim. So that’s basically a machloket now between the Rishonim (the early authorities). Be'ezrat Hashem, we’ll stop here.