WHAT IS MEMA'ET?
Version #1 (Rashi) (Rav Nachman): If a ledge four by four sticks out of a wall, and one rested a ladder of any width on it, it is Mema'et;
This is only if the ladder rests on the ledge. If it rests [on the wall] next to the ledge, it is too far from the ledge, it is not Mema'et. (It is like a Mi'ut 'in the air.')
Version #2 (Rashba) (Rav Nachman): If a ledge four by four sticks out of a wall, and one rested a thin ladder on it, it is Mema'et. (It obstructs usage of the ledge. It is as if the ledge is less than four by four, so the ledge is not Mema'et);
This is only if the ladder rests on the ledge. If it rests [on the wall] next to the ledge, it offers easier access to the ledge. It is not Mema'et the ledge. (end of Version #2)
(Rav Nachman): If a wall is 19 Tefachim tall, one ledge permits it (if it is half-way up, it is within 10 Tefachim of the ground and within 10 of the top of the wall. Rashi requires a ladder going up to the ledge, but the Rashba does not.)
If it is 20 Tefachim tall, two ledges are needed. (One ledge cannot be within 10 of the ground and within 10 of the top.)
(Rav Chisda): Two ledges permit only if they are far enough apart [to erect a ladder from one to the other].
(Rav Huna): If a pillar in Reshus ha'Rabim is 10 tall and [exactly four by] four wide, and one inserted a peg of any thickness in the top, this diminishes [the usable surface from being four by four. It is not Reshus ha'Yachid.]
(Rav Ada bar Ahavah): This is only if the peg is at least three tall. (Then, its place is unusable);
(Abaye and Rava): This is even if it is less than three.
Question: What is the reason?
Answer: One cannot use its place.
(Rav Ashi): Even if it is three tall, it is not Mema'et.
Question: What is the reason?
Answer: One can hang things from it. (It is useful.)
Question (Rav Acha brei d'Rava): If one filled the entire top surface with pegs, what is the law?
Answer (Rav Ashi): We learn this from R. Yochanan's law!
(R. Yochanan): A pit and its Chulyah (a ring of dirt dug out from it) join with each other for the Shi'ur of 10 Tefachim tall [and four by four] to be Reshus ha'Yachid.
Question: Why do they join? One cannot use them together!
Answer: One can put a board or rock over the pit and use them together.
Summation of answer: Likewise, one can put a board over the pegs and use the area! (Therefore, it is not Mema'et.)
WHICH LADDERS ARE MEMA'ET?
(Shmuel): A ladder must be 14 Tefachim long to be Mema'et a wall 10 Tefachim tall. (Tosfos - we discuss a ladder at a 45 degree angle. It reaches as high on the wall as the distance from its bottom to the wall, about 7/10 of its length. The ladder is not four by four wide, therefore it must reach to [or near] the top of the wall. If it is 14 long, it reaches to the top);
(Rav Yosef): If it is any amount above 13 Tefachim long, it is Mema'et. (It reaches a height above nine, within one Tefach of the top);
(Abaye): Even if it is 11 Tefachim long, it is Mema'et. (It reaches a height above seven, within three of the top);
(Rav Huna brei d'Rav Yehoshua): If it is any amount above seven long, it is Mema'et. (It can be placed vertically. It reaches within three of the top.)
(Rav): I heard that a vertical ladder is Mema'et. I do not know why! (It is inconvenient to use.)
Shmuel: Surely, Rav should realize that it is Mema'et, just like a platform on top of a platform! (If less than three Tefachim separate them, they are like one. They are Mema'et, even though it is inconvenient to get to the top platform.)
(Rabah): [Detached] date trees in Bavel need not be fixed [in the ground. They are Mema'et in any case.]
Question: What is the reason?
Answer: Their weight fixes them. (They are not normally moved.)
(Rav Yosef): Ladders of Bavel need not be fixed.
Question: What is the reason?
Answer: Their weight fixes them.
Rav Yosef taught that ladders need not be fixed. All the more so he agrees that date trees need not be fixed;
Rabah taught that date trees need not be fixed, but he would say that ladders must be fixed.
COMPLETING THE SHI'UR
Question (Rav Yosef): If there are two ladders side by side with a gap in between, each is less than two Tefachim wide, and one made steps of straw in between (to complete the Shi'ur of four Tefachim), what is the law?
Answer (Rabah): One cannot walk on it [normally, i.e. stepping in the middle. Therefore, it is not Mema'et.]
Question (Rav Yosef): If a ladder is less than four wide, and one made extensions of straw on the sides (to complete the Shi'ur of four), what is the law?
Answer (Rabah): One can walk on it [normally, and hold onto the straw. Therefore, it is Mema'et.]
Question (Rav Yosef): [If one wants to carve steps into a wall (Rashi - to widen steps of a narrow ladder, to make them four wide; R. Tam - above a ladder that does not reach the top of the wall),] how much must one carve out to complete the Shi'ur?
Answer (Rabah): One must carve up to 10. (Rashi - he must widen the steps up to the height of 10 Tefachim. R. Tam - he must extend it to within 10 of the top.)
Question (Rav Yosef): If one wants to carve out the entire ladder in the wall, to what height must he carve out (Rashi - to be four wide)?
Answer (Rabah): He must do so up to the top of the wall.
Question: What is the difference between the cases?
Answer: When part is a proper ladder, it is easy to climb. (Therefore, it is easier to be considered an opening.) When it is totally in the wall, it is difficult.
Question #1 (Rav Yosef): If one made a tree (cut it to shape) to be a ladder, what is the law? We can ask according to both Rebbi and Chachamim [who argue about leaving Eruv Techumim in a tree]:
Rebbi permits regarding Eruv Techumim, because it suffices if he could take the food Bein ha'Shemashos, and Shevus (something forbidden mid'Rabanan on Shabbos, such as using a tree) does not apply Bein ha'Shemashos. However, an opening between Chatzeros must be usable for all of Shabbos!
Chachamim forbid regarding Eruv Techumim [because they forbid Shevus Bein ha'Shemashos, hence the food is inaccessible]. A tree is a proper opening between Chatzeros, even if one may not use it!
Question #2 (Rav Yosef): [Rashi - if you will say that a regular tree may be used,] if an Asherah (a tree planted or used for idolatry) was used for a ladder, what is the law? (It is not clear how to reconcile this with Rav Chisda (below), who forbids a tree and permits an Asherah. Others explain that he asks about a detached Asherah (Ritva) or dry Asherah (Tur), to which the Isur of an attached tree does not apply.)
We can ask according to Chachamim and R. Yehudah [who argue about leaving Eruv Techumim in a grave].
R. Yehudah permits leaving Eruv Techumim in Isurei Hana'ah, because [he permits Eruv Techumim only for the sake of a Mitzvah, which is not considered Hana'ah, and] once he acquired Shevisah, it does not benefit him. (He does not need the food. However, Eruv Chatzeros is not only for Mitzvos. It benefits him!)
Chachamim forbid there. (Since they permit Eruv Techumim even for Reshus, it benefits him.) However, a tree is a proper opening between Chatzeros, even if it is forbidden!
Answer #1 (to both questions - Rabah): A tree permits [to be Me'arev together], but an Asherah does not.
Objection (and Answer #2 - Rav Chisda): Just the contrary! It is unreasonable to permit a matter of Shabbos (transferring between Chatzeros) using something forbidden specifically on Shabbos. One can permit using an Asherah, whose Isur is unrelated to Shabbos! (Ritva - a Nochri can be Mevatel his Asherah, and permit it. A tree cannot become permitted on Shabbos.)
(Ravin): Anything forbidden due to Shabbos may not be used. Anything forbidden not due to Shabbos may be used.
Answer #3 (Rav Nachman bar Yitzchak): (The Tana'im argue here just like they argue about Eruv Techumim.) Rebbi and Chachamim argue about a tree, and Chachamim and R. Yehudah argue about an Asherah.
A DITCH BETWEEN TWO CHATZEROS
(Mishnah): If a ditch [along the entire border] between two Chatzeros is 10 deep and four wide, they may be Me'arev separately but not together, even if it is full of straw;
If it is full of dirt or pebbles, they may be Me'arev together, but not separately.
Version #1 (Rashba citing R. Tam): If one put a plank four wide [across the ditch, they may be Me'arev separately or together];
The same laws apply to two balconies opposite each other. If four Tefachim separate them, they may be Me'arev separately but not together. If less than four separate them, they may be Me'arev together but not separately.
Version #2 (Rashi): If one put a plank four wide across [the ditch]; or between two balconies opposite each other, they may be Me'arev together or separately;
If it is less than four, they may be Me'arev separately but not together. (end of Version #2)
(Gemara) Question: Elsewhere, we find that straw is a Chatzitzah!
(Mishnah): If a haystack [along the entire border] between two Chatzeros is 10 tall, they may be Me'arev separately, but not together.
Answer (Abaye): All agree that straw makes a Mechitzah [in any case]. It is a Chatzitzah only if he (the owner) was Mevatel it.