Eruv Between Two Balconies (Eruvin 79a)
The mishna on 78b says that two balconies can join in one eruv. Rashi says that the Mishna is teaching us that they can join even if they're far apart as long as you put a four tefach wide board to connect the two that people can comfortably walk across. Tosafos says that the case of the Mishna is that the two balconies are within four tefachim of each other they can combine because it's like a ditch less than four between them and they can easily get over it. So far so good.
Then Rava on 79a says that this is only true if they are less than three tefachim apart either horizontally or vertically. That means that they're not directly across from each other but if you would draw a straight line from the edge of one across to the other side it would be within three tefachim of the edge of the other one. Or the same thing vertically. That explanation probably wasn't great but if you don't get it then try to check one of the picture books. Anyway, if it's more than 3 tefachim then the two balconies can't combine. That's where I have a problem with Rashi and Tosafos.
Tosafos actually has a problem with Rashi. According to Rashi why should it matter that it's more than three tefachim away, there is a four tefach board going across between the two balconies and we said a few blatt ago that a person isn't afraid to walk on top of the wall if it's at least four tefachim across. The way I understood Rashi (and the way the Ran explains it) is that the reason this is worse is because the person is afraid to walk on a plank if it's on a steep slope or a sharp angle. My problem is that if that is true shouldn't we measure the angle and not the distance? In other words, if the two porches are 10 tefachim away from each other across and one is three tefachim higher than the other then you'd have a somewhat steep slope but if you push them to 20 tefachim apart from each other and keep one three tefachim higher than the other then the slope would be much, much less steep. So why shouldn't that be good? We should be looking at the slope!
I also have a problem with Tosafos' explanation. He said that there are four tefachim betwen the balconies and then Rava said that they're 3 tefachim apart which means that there is now actually a 5 tefach distance between the two. Why is that still good? We said that a person can only walk across four tefachim not five?