1) ADDING ROOM IN A HOUSE
QUESTION: The Mishnah teaches that a person who lives in a jointly-owned Chatzer may not make additions to his house, but he may build a room within his house or an attic atop his house. The Gemara explains that he may build the room only by dividing a pre-existing room but not by adding an additional room. The attic, or upper story ("Aliyah"), may be built with an "Apsa" (an apse). The RASHBAM explains that an Apsa refers to a small room on the side of a house with a roof lower than the roof of the rest of the house. His source is the Mishnah later (61a) which implies that an Apsa is a "Yatzi'a," a side-room. How, though, is this related to an upper story? The Rashbam explains that when the Mishnah says that one may build an upper story on his house, it refers back to the previous sentence which says that one may build an additional room by dividing a pre-existing room into two (with a vertical partition). The Mishnah means that after he divides a room into two, he may divide the additional room (that he has just made) with a horizontal partition, thus making a two-story Apsa.
Why does the Rashbam explain that the person divides only the back room? He should be permitted to make a second story with the entire house! The Rashbam apparently derives this from the Gemara which explains that the Aliyah is over the Apsa, but not over the entire house. The question, however, may be asked on the Gemara: why does the Gemara itself allow only a division over the Apsa? (MAHARSHA, RASHASH)
(a) The YISHUV DA'AS (of Rav Chaim Kanievsky shlit'a, in KOVETZ MEFARSHEI MAHARSHA) explains that it is true that the Halachah of the Mishnah applies even if the person divides the height of his entire house. However, a person does not normally lower the ceiling of his living quarters, because the ceiling was not built higher than necessary in the first place. A person divides only the ceiling of the extra room that he built for guests (which is considered temporary quarters) and which can be used even with a lower ceiling.
The ARUCH (Erech "Apsa") and the RASHBA explain that when the Gemara mentions "Apsa," it does refer to a second story (a normal Aliyah). This is also the meaning of the word "Apsa" as mentioned later (61a; see RABEINU GERSHOM there).
2) MOVING ONE'S WALL AWAY FROM "RESHUS HA'RABIM"
QUESTION: Rebbi Yochanan rules that if a person's wall was adjacent to Reshus ha'Rabim and he moved it away from Reshus ha'Rabim into his own property, he may not move it back to its original location. Rebbi Yochanan reasons that the public has already attained the right to walk through that area, and, consequently, it has become public property. However, he is allowed to extend protrusions ("Zizim") from his wall into the area on which the wall used to stand. The Gemara implies that even if he did not build these Zizim originally, he is allowed to add them even after the public has started walking over that area.
If the public already attained the right to the area by walking through it, why is the owner permitted to extend Zizim from the wall into the public property? (KOVETZ SHI'URIM)
ANSWER: The KOVETZ SHI'URIM answers that when a person withdraws his wall into his own property, his act is akin to making a declaration that the public may acquire only what he wants to offer to them. It is assumed that the person was offering the public only the right to walk in that area, but not the right to prevent him from extending his Zizim into that area. (It seems that one is permitted to add protrusions only above the height of a walking person, so that those who walk in that area will not be impeded by the Zizim.)