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ERUVIN 57
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SUMMARY

1. There is an argument about whether the border of a city has an extra 70- plus Amos added to it.
 
2. The Chachamim agree that this 70-Amah measurement is used to extend a city to include another city.
 
3. There is a dispute about how this 70-Amah measurement is used according to the Chachamim.
 
4. The Gemara explains how one determines whether three cities that form a (rough) isosceles triangle are considered one city.
 
5. The Gemara explains how a Techum is measured.

A BIT MORE

1. Rebbi Meir says that it does, based on the verse, "from the wall of the city and outside of it," implying that a city includes a Chatzer (yard) outside the city which is deemed to be 70 and 2/3 Amos like the Chatzer of the Mishkan. The Chachamim say that a city does not receive this extra amount.
 
2. They agree that if a city is within 70-plus Amos of another city, both cities are considered to be within the same border on Shabbos (i.e. they are effectively one city).
 
3. Rav Huna: If there is a distance of more than two times 70-plus Amos (141.33 Amos) separating the two cities, they are not connected. Chiya bar Rav: If there is a distance of more than 70-plus Amos separating the two cities, they are not connected.
 
4. If the upper city is physically less than 2,000 Amos away from each of the other cities, and if -- when directly lowered into the space between the two cities -- it would be less than 141 Amos from each city, they are all considered one city with regard to Shabbos.
 
5. A rope that is exactly 50 Amos long must be used. The rope must be held next to the heart while measuring.

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