(Rav Nachman): If there are three houses [open to each other], between two Chatzeros [like the diagram in Rashi], and both Chatzeros put their Eruvin in the middle house, none of the three houses needs to be Me'arev:

The outer houses need not be Me'arev, for each is a Beis Sha'ar to the Chatzer. (They passed through to put their Eruv in the middle house.) The middle house need not be Me'arev, for the house in which the Eruv is placed need not contribute to the Eruv.

Question (Rachbah, to test Rabanan): If there are two houses between two Chatzeros, and each Chatzer passed through 'its' house (the one open to it) and put their Eruv in the other house, are the Eruvin valid?

Can each Chatzer consider 'its' house like a Beis Sha'ar, and the other house like a house [in which an Eruv can be placed]?

Answer (Rabanan): Either way you say, neither Eruv is valid [because both houses have the same status]:

If each house is considered a Beis Sha'ar, the Eruv cannot be placed in it;

(Mishnah): If one put an Eruv in a Beis Sha'ar, Achsadra or porch, it is invalid.

If each house is considered a house, the people of the Chatzer must pass through a house that was not Me'arev to get to their Eruv.

Question: How is this different from Rava's law?

(Rava): If Reuven and Shimon each told Levi 'make an Eruv (Rashi - Techumim; Tosfos - Chatzeros) for me', and Levi made Reuven's Eruv before Shabbos and Shimon's Eruv Bein ha'Shemashos, [even] if Reuven's Eruv was eaten Bein ha'Shemashos and Shimon's was eaten after dark, both of them are valid.

Answer: There, we are in doubt whether Bein ha'Shemashos is day or night. It is reasonable to be Machshir both Eruvin;

Here, if we consider one a house and the other a Beis Sha'ar [and vice-versa for the other Chatzer], Chachamim's words will be a mockery!

(Mishnah): If a window between two Chatzeros is four by four [Tefachim] and within 10 Tefachim of the ground, the Chatzeros can be Me'arev individually or together;

If it is less than four by four or higher than 10 Tefachim, the Chatzeros can be Me'arev individually, but not together.

(Gemara) Suggestion: Our Stam Mishnah is like R. Shimon ben Gamliel, who says that Lavud applies up to four Tefachim! (This is why the window must be four by four.)

Rejection: It is even like Chachamim. They argue only about Lavud, but all agree that an opening is important only if it is four Tefachim.

(Mishnah): If it is less than four by four...

Question: The Reisha taught that it must be four by four and within 10. Why must the Seifa disallow to be Me'arev together if it is less than four by four or higher than 10?

Answer: The repetition teaches that one cannot be Me'arev together only if the entire window is above 10 Tefachim. If part is within 10, they can be Me'arev individually or together.

Our Mishnah teaches like the following Beraisa;

(Beraisa): If the window is mostly above 10 Tefachim and partly within 10, or mostly within 10 and partly above, they can be Me'arev individually or together.

Question: If when it is mostly above 10 Tefachim and partly within 10 they can be Me'arev individually or together [even though it is inconvenient to use], we need not teach about when it is mostly within 10 and partly above!

Answer: Indeed, the Beraisa teaches that the first case is permitted, and all the more so the latter case!

(R. Yochanan): If a round window is between them, in order to be Me'arev together its circumference must be 24 Tefachim, and more than two Tefachim (Tosfos - of its height) must be within 10 Tefachim (for then it is four wide within 10).

Question: The diameter is a third of the circumference. It should suffice for the circumference to be 12 Tefachim [for the window to be four Tefachim wide]!

Answer: We require a square window of four Tefachim, therefore a larger circumference is required.

Question: The perimeter of a square around a circle exceeds the circumference by a quarter of the perimeter. Sixteen Tefachim suffice for a square [around a circle of circumference 12]!

Answer: True, the perimeter is a quarter more regarding a square around a circle. (However, here we require a circle around a square of side four and circumference 16.) The circumference of a circle around a square is greater, due to the corners. (The diameter of the circle must equal the diagonal of the square.)

Question: The diagonal of a square is two fifths longer than the side. If the side is four, the diagonal is five and three fifths, so the circumference of a circle around it is [only three times as much,] 16 and four fifths!

Answer: R. Yochanan holds like judges of Kisari, who say that a circle in a square is a quarter less than the square. A square in a circle is a half less. (See note 27 in Appendix.)

(Mishnah): If it is less than four by four [or higher than 10...]

(Rav Nachman): This refers only to a window between two Chatzeros, but a window between two houses allows to be Me'arev together, even if it is higher than 10.

Question: What is the reason?

Answer: We consider the house as if it was full (R. Yehonason - of boxes and cabinets, so it is convenient to transfer through the window. Rashi - it is as if the window is not 10 off the ground.)

Question (Rava - Beraisa): The same law applies to a window between two Chatzeros, houses, attics, roofs, or rooms. It must be four by four and within 10 [to permit an Eruv together].

Answer: This refers to a window between two Chatzeros.

Question: The Beraisa says that all of them have the same law!

Answer: For all of them the window must be four by four [but for a house it may be above 10].

Question (R. Aba): Does an opening in the floor of an attic require a permanent ladder nearby [to permit to be Me'arev together]?

Do we consider a house to be full only regarding [a window on] the side, but not regarding the middle?

Or, perhaps do we not distinguish?

Answer (Rav Nachman): It is not required.

Inference: A permanent ladder is not required, but a temporary ladder is!

Rejection (Rav Yosef bar Minyomi citing Rav Nachman): No ladder is required.

(Mishnah): If a wall between two Chatzeros is 10 Tefachim tall and four Tefachim thick, the Chatzeros can be Me'arev individually but not together;

If there are fruits on top of the wall, people from either Chatzer may alight on the wall and eat them, but they may not take them down.

If the wall was breached up to 10 Amos, the Chatzeros can be Me'arev individually or together, for it is like an opening;

If it was breached more than 10 Amos, the Chatzeros can be Me'arev together but not individually.

(Gemara) Question: If the wall is not four thick, what is the law [on top]?

Answer #1 (Rav): Since both have access to it [and it is too small to be a Reshus unto itself, it is Batel to both Chatzeros;] neither may carry there at all;

Answer #2: (R. Yochanan): People from either Chatzer may bring food up and eat it.