1) TWO BALCONIES THAT ARE NOT DIRECTLY OPPOSITE EACH OTHER
QUESTION: The Mishnah (78b) states that two balconies joined by a plank wider than four Tefachim may choose to make one Eruv together or to make two separate Eruvin. Rava says that two balconies that are not directly opposite each other and that are separated by more than three Tefachim cannot be joined to make a single Eruv, and each balcony must make its own separate Eruv. Placing a plank between them does not help.
RASHI explains that when Rava mentions two balconies that are "not directly opposite each other," he means that one juts out farther into Reshus ha'Rabim than the other. Rashi understands that the two balconies are on the same side of Reshus ha'Rabim, but one juts out more than the other.
(a) According to Rashi's explanation, why can the residents of the balconies not make a single Eruv together by simply placing a plank between the two balconies at the point where they are adjacent to each other (that is, where they begin to extend into Reshus ha'Rabim)?
(b) Moreover, why does Rashi not explain that when Rava mentions two balconies that are "not directly opposite each other," he means that they are on opposite, facing sides of Reshus ha'Rabim? (This is indeed how the RITVA and other Rishonim explain the Sugya.) (REBBI AKIVA EIGER, RASHASH)
ANSWERS:
(a) To answer the first question, the NACHAL ARAVIM (as cited by Perush Chai, 7:63) explains that Rashi means that the building from which the second balcony extends protrudes beyond the end of the other balcony. Therefore, it is not possible to place a plank from one balcony to the other. (See Graphic.)
(b) To answer the second question, we must first ask another question. TOSFOS (78b, DH v'Chen) asks that if there is a plank between the two balconies, then even when they are not directly opposite each other they should be considered connected by the plank! Why do they need to be directly opposite each other in order for the plank to connect them?
The RITVA and other Rishonim explain that a person usually will not walk on a plank between balconies, since there is a steep drop below him, and he is frightened to walk there. If the plank is not parallel to an edge of the balconies (and thus appears to offer less support) due to the fact that the balconies are not directly opposite each other, a person will not walk there at all.
Perhaps Rashi also understands that two balconies cannot be joined because the plank between them would have to be placed at an angle from the buildings. That is why he explains that the two balconies that are "not directly opposite each other" are on the same side of the Reshus ha'Rabim, but one juts out farther than the other and they have no overlapping width. A plank connecting them must be placed at an angle to the edges of the balconies. Had the Gemara meant that the balconies are on opposite sides of the Reshus ha'Rabim, the Gemara would have specified that they do not extend far enough such that their sides overlap at a certain point, for in such a case they would be able to be joined with a plank. (See Graphic.)

79b----------------------------------------79b

2) A HAYSTACK BETWEEN TWO CITIES
OPINIONS: The Beraisa states that when there is a pile of hay between the two Techumei Shabbos of two different cities, the residents of each city may feed their animals with hay from their respective side of the haystack. We are not concerned that the residents of one city will take hay from within the other city's Techum, even according to Rebbi Akiva who holds that the law of Techumin is mid'Oraisa. Even though one might transgress an Isur d'Oraisa by taking hay from within the other Techum into one's own Techum (RASHI DH Mahu d'Teima), the Rabanan were not concerned that this would happen and did not prohibit taking hay from the side of one's own Techum.
The MINCHAS CHINUCH (#24) wonders whether according to Rebbi Akiva, who holds that the law of Techumin is mid'Oraisa, the law of Techumei Kelim (i.e., that an object may not be moved out of the Techum of its owner even by another person) is also mid'Oraisa.
(a) The Minchas Chinuch points out that we may prove from the Gemara here that there is indeed a Techum d'Oraisa for objects. If the Techum for objects is not mid'Oraisa, then why does the Gemara say that we might have thought that Rebbi Akiva would prohibit using the hay lest one take hay out of its Techum? There would be no Isur d'Oraisa to take the hay out of its Techum, and thus no reason to make such a Gezeirah! It must be that the Techum of objects is indeed mid'Oraisa.
(b) It could be, however, that the Gemara here is not a proof that Techumei Kelim is mid'Oraisa. The Gemara says only that the hay is between two Techumim (i.e., between the Techumim of the residents of two cities). It does not say that the hay is at the end of its own Techum (that is, perhaps the hay's own Techum extends beyond this point towards the second city). However, if the hay is not at the end of its own Techum, then why may one not take hay from the other side of the haystack? The RITVA explains that the Gemara is concerned that the person feeding his animal will walk to the other side of the haystack to take hay, and by doing so he will be walking out of his own Techum. This is what Rashi means when he says that "one might take from a Techum that is not his." The Gemara is not discussing the Techum of objects at all.
(c) Although there is no definite proof from the Gemara here, the YAD BINYAMIN points out that the RAMBAN (17b) indeed states, as the Minchas Chinuch asserts, that the Techum of Kelim is mid'Oraisa. (See also BI'UR HALACHAH OC 340, DH l'Man d'Amar.)
3) A MINOR BEING "MEZAKEH" TO THE MEMBERS OF A MAVOY
QUESTION: The Mishnah describes how the residents of a Mavoy make a Shituf Mavo'os. The Mishnah says that one person may be Mezakeh the contents of a barrel to all of the members of the Mavoy. He may be Mezakeh it to them by having his grown children, or a Jewish slave or maidservant, make an acquisition on their behalf. One may not have his children who are still below the age of adulthood be Mezakeh it to them.
If a minor cannot make a Shituf Mavo'os because he does not have the ability to make an acquisition to others, why does the Mishnah say that a Jewish maidservant (Shifchah) may be Mezakeh the Shituf to others? A maidservant is, by definition, always a minor (because once she has signs of maturity, she goes free)!
ANSWER: TOSFOS (DH u'Mezakeh) explains that with regard to Shituf Mavo'os, which is only a d'Rabanan requirement, there is a unique leniency that allows even minors to be Mezakeh to others. When the Mishnah says that one's child who is a minor cannot be Mezakeh, it means that one's own child, who is dependent on his father's support, cannot be Mezakeh the Eruv. Such a minor is like an "extension" of his father and one cannot be Mezakeh his father's object to others just as one cannot be Mezakeh his own object to others (but he must have someone else be Mezakeh it to them on his behalf). The child of someone else, however, can be Mezakeh the food to others.

OTHER D.A.F. RESOURCES
ON THIS DAF