1)

(a)According to Ravina - we are speaking about a square town of two thousand Amos, which can be divided, as we explained earlier, into thirty-two blocks of one thousand square Amos. However, according to him, the corners (i.e. those not adjacent to the four sides of the town), are not designated as Migrash. In that case, only eight blocks out of the thirty-two are Migrash - exactly a quarter.

(b)Rav Ashi explains that the Beraisa is only concerned with the corners. What he is saying is - that of the sixteen blocks that make up the corners, one quarter (four blocks) are designated as Migrash. (According to Rashi's second explanation, it is only the corners that are designated for the Migrash.)

(c)How can Rav Ashi learn that the Beraisa is confined to the corners, asks Ravina, when it is referring to the Pasuk (not in fact mentioned in our Sugya) which explicitly writes "Saviv" - and the corners are not Saviv (according to Rashi's second explanation, the question is even stronger).

(d)"Saviv" does not necessarily mean 'completely surrounding' - It can also mean on the four corners, like we find by the sprinkling of the blood of (most of) the Korbanos, which was only sprinkled on two diagonally-opposite corners, which the Torah describes as "Saviv", because the blood then appears on a small section of each of the four sides.

2)

(a)The Gemara's Kashya 've'Ha Ika Mursha de'Karnesa' - refers to the thousand circular Amos which we learnt above (on the previous Amud) are designated as Migrash. But how can that be, asks the Gemara? We have already learnt that one squares a circular town, in order to reckon the Techum. In that case, the corners of the square will detract from the thousand Amos of the circular Migrash!?

(b)Even though we square the town in order to work out the Techum, answers the Gemara, however, that square is no more than an imaginary one; the circle remains intact, so that nothing is detracted from the circular Migrash that surrounds it.

3)

(a)When Chazal say that a square is a quarter more than a circle - it means a quarter of the total, which we would refer to as a third.

(b)The Gemara thinks that, if a square is a quarter (third) more than a circle, then the same will be true of the diagonal (the excess of the square over a circle). If that is so, then the diagonal of a circle whose diameter is two thousand Amos, ought to be six hundred and sixty seven Amos, and not eight hundred Amos, as the Gemara maintained on the previous Amud!?

(c)The Gemara answers that the previous contention is incorrect. The diagonal is not in fact, synonymous with the excess of the square over a circle, because its excess over the circle is even greater than that of the square.

4)

(a)Rebbi Meir learns from the Pasuk in Masei "mi'Kir ha'Ir va'Chutzah" - that one first adds on the Sh'iur of a Karpaf (seventy and two thirds Amos) before measuring the Techum of two thousand Amos.

(b)The Rabbanan hold that one only adds the Karpaf when there are two neighboring towns (i.e. one allows the space of a Karpaf between them, to still consider them as one town, but not to a single town.

(c)According to Rav Huna, when the Chachamim in the Mishnah said 'Lo Amru Karpaf' (implying one Karpaf, and not two), they meant the Din of a Karpaf - i.e. for two towns - two Karfifos.

(d)The Mishnah continues 'Im Yesh la'Zu Shiv'im Amah ve'Shirayim, ve'la'Zu Shiv'im Amah ve'Shirayim' ... which certainly seems to bear out Rav Huna.

5)

(a)When Rebbi Meir said in the Reisha that every town has a Karpaf - we might have thought that one Karpaf will suffice even for two towns. And had he taught us the Din of two Karfifos for two towns, we would have thought that there, two Karfifos do not separate the towns, because the demarcation line between two towns is an open unused space between them - and due to the many people who use the space, two Karfifos is not sufficient space to qualify for that. One town however, does not require a Karpaf at all, since it is anyway surrounded by an open space.

(b)The Gemara thinks that the three villages are actually in line, and that there is exactly one hundred and forty one and a third Amos in between the two outer villages. In that case, we can deduce that the three villages combine only because of the one in the middle. Otherwise, they would not combine - because of the two Karfifos in between them - not like Rav Huna.

(c)Rav answers that our Mishnah is speaking when there are far more than a hundred and forty one and a third Amos separating the two villages. And we are speaking here, not about when the third village is in line with the others, but when it forms a triangle with them. If, by placing the third village in line with the others, less than a hundred and forty one and a third Amos remain, then they are considered one village; otherwise, they remain three.

6)

(a)The middle village will only combine with the other two if it is not more than two thousand Amos away from the line that joins them.

(b)In the case of the town shaped like a bow, Abaye permitted walking the distance between the string and the bow even when it was more than two thousand Amos - because there were houses all along the bow, and would have been possible to walk to the string via the houses, which is not the case here.

(c)No! The distance between the outer villages make no difference at all. As long as the middle village would fill in all the space that is in excess of a hundred and forty one and a third Amos if it were in line with the others, the three combine.

7)

(a)Rav Huna rules, with regard to the city shaped like a bow, that if the distance between the two sides of the bow is more than four thousand Amos, they do not combine, but are considered to be two towns - because there we cannot say 'fill the space' (with the houses on the bow - see Tosfos DH 'Ela'); whereas here we say 'fill the space' (with the third village).

(b)Rava accounted for the fact that the inhabitants of Akistefun and Ardeshir considered themselves one town with regard to Eruvin, even though the River Diglas, which was wider than a hundred and forty one and a third Amos, divided between them - because there were still remains of walls visible in the river (which had the Din of Gedudi'os).

8)

(a)The rope used for measuring the Techum - had to be fifty Amos long, and had to be held next to the heart. The reason for this - is because Chazal fixed this arbitrarily, to avoid the scenario where one of the measurers holds the rope by his neck and the other one, by his feet (thereby subtracting from the two thousand Amos).

(b)If the measurers encountered ...

1. ... an acute 'valley' - they would (provided it was not more than fifty Amos across) absorb it in the two thousand Amos by measuring across it.

2. ... a steep pile of rubble or a steep hill- they would absorb it by going round the pile or the hill, measuring only in a parallel line to their previous measurements (i.e. the point between the two ends of the pile or the hill), before returning to the line where they had previously been measuring (as if the wall had not been there) and continuing from there.

(c)'u'Vilevad she'Lo Yetzei Chutz li'Techum' - means that, when they move away from the line of measurement (i.e. to the side, to avoid the valley, the rubble or the hill), they are not permitted to move outside the Techum to measure from there. Alternatively, they are not permitted to measure the valley etc. beyond the Techum whilst absorbing it (and then walk back the few Amos that they exceeded the Techum into the valley etc. (and deduct the excess from the measurement). This is because people who see them will think that the Techum reaches as far as they walked.

(d)If they are unable to 'absorb' the hill - they employ the method of measuring called 'Kidur' (Mekadrin) - which will be explained later.