this outer house becomes a gatehouse to this courtyard, and that outer house becomes a gatehouse to that courtyard, and therefore the residents of the outer houses need not contribute to the eiruv. The middle house between them is the house in which the eiruv is placed, and therefore its residents need not contribute bread for the eiruv.

The Sage Raḥava tested the other Sages: If there were two courtyards and two houses between them, and a resident of this courtyard came through this house that opens to his courtyard and placed his eiruv in that house farther from his courtyard, and a resident of this other courtyard came through this house that opens to his courtyard and placed his eiruv in that house that opens to the other courtyard, did they acquire the eiruv or not, i.e., are the two eiruvin valid? Do you render it a house with regard to this courtyard, whose eiruv was placed there, and a gatehouse with regard to that one who passed through it in order to place his eiruv in the other house? And similarly, do you render the other house a gatehouse with regard to this one and a house with regard to that one?

The Sages said to Raḥava: Neither of them has acquired his eiruv. Whichever way you look at it, it is difficult: If you consider either house a gatehouse, the halakha with regard to one who places his eiruv in a gatehouse, a porch, or a balcony, is that it is not a valid eiruv. And if you consider either one a house, he would be carrying into a house for which he is not establishing an eiruv. Since the assumption that benefits one of them harms the other, and there is no way to establish firmly the status of these houses, the residents of both courtyards fail to acquire their eiruv.

Raḥava asked: What makes this case different from the ruling of Rava? As Rava said: In the case of two people who said to one person: Go and establish an eiruv of Shabbat limits for each of us, and he established an eiruv for one of them while it was still day, and he established an eiruv for the other one during twilight, and the eiruv of the one for whom he established an eiruv while it was still day was eaten during twilight, and the eiruv of the one for whom he established an eiruv during twilight was eaten after nightfall, both of them have acquired their eiruv. Twilight is of doubtful status as to whether it is considered day or night. If it is night, any eiruv established at that time is invalid, and if it is day, any eiruv eaten at that time is invalid. Rava nonetheless ruled leniently, despite the fact that two contradictory assumptions are involved, in keeping with the principle that in cases of doubt relating to an eiruv, the halakha is lenient. Consequently, with regard to the one whose eiruv was eaten during twilight, it is considered as though it was already night, and therefore his eiruv had already taken effect while it was still day before it was eaten. Conversely, with regard to the one whose eiruv was established during twilight, that period of time is viewed as day, and therefore his eiruv is valid as well.

The Sages respond: How can these cases be compared? There, where there is uncertainty whether it is day and uncertainty whether it is night, the matter is not noticeable, as no one sees exactly when each eiruv was established. But here, where the houses are clearly distinguishable, if with regard to this one, who placed his eiruv there, it is a house, then with regard to that one, who passed through it, it should also be regarded as a house. And if, with regard to this one, who passed through it, it is a gatehouse, then with regard to that one, who placed his eiruv there, it should also be considered a gatehouse. Therefore, neither of them acquires his eiruv.

MISHNA: If there is a window in a wall that separates between two courtyards, and the window measures four by four handbreadths and is within ten handbreadths of the ground, the inhabitants of the courtyards establish two eiruvin, one for each courtyard. And if they desire, they may establish one eiruv, thereby merging the two courtyards, as they may be considered as one due to the window.

However, if the window measures less than four by four handbreadths, or if it is above ten handbreadths from the ground, it is no longer considered a valid opening, and the two courtyards cannot be considered a single courtyard. Therefore, the residents establish two eiruvin, but they may not establish one eiruv.

GEMARA: With regard to the mishna’s determination that the size of the window must be four by four handbreadths, the Gemara asks: Let us say that we learned an unattributed mishna in accordance with the previously cited opinion of Rabban Shimon ben Gamliel, who said: Any gap less than four handbreadths is considered lavud, i.e., two objects are considered connected if the space between them is less than four handbreadths. That would explain why the window must be four handbreadths in size, as otherwise it would be considered as though it were sealed, based on the principle of lavud.

The Gemara rejects this suggestion: Even if you say that the mishna is in accordance with the opinion of the Rabbis that only gaps of less than three handbreadths are included in the principle of lavud, the Rabbis disagreed with Rabban Shimon ben Gamliel only with regard to the halakhot of lavud, i.e., what is considered connected. But with regard to an opening, even the Rabbis agree that if there is an opening of four by four handbreadths, it is significant, and if not, it is not significant.

It was taught in the mishna: If the window is less than four by four handbreadths, or above ten handbreadths from the ground, the residents of each courtyard must establish a separate eiruv. The Gemara objects: This is obvious. Since the mishna stated in the previous clause that if the window is four by four handbreadths and within ten handbreadths from the ground, they establish one eiruv, from this halakha itself I know that if the window is less than four by four handbreadths or above ten handbreadths, they may not establish one eiruv. Why was it necessary to teach this in the mishna?

The Gemara answers: It teaches us this matter: The reason is specifically that the entire window is above ten handbreadths; however, if part of it is within ten handbreadths of the ground, they establish two eiruvin, and if they desire, they may establish one eiruv.

The Gemara comments: According to this explanation, we already learned in the mishna that which the Sages taught in a baraita: If nearly all of the window is above ten handbreadths and only a small part of it is within ten handbreadths, or if nearly all of it is within ten handbreadths and only a small part of it is above ten handbreadths, they establish two eiruvin, and if they desire, they may establish one eiruv.

The essential meaning of this baraita is clear, but the Gemara raises a question with regard to its formulation: Now, if nearly all of it is above ten handbreadths and only a small part of it is within ten handbreadths, you said that they establish two eiruvin, and if they desire, they may establish one eiruv, i.e., the window has the status of an opening and therefore the two courtyards may establish a joint eiruv, then is it necessary to state the halakha governing the case where almost all of it is within ten and only a small part of it is above ten?

The Gemara answers that indeed, this baraita teaches employing the style: This, and it is unnecessary to say that, moving from the more difficult and novel case to the easier, more straightforward one.

Rabbi Yoḥanan said: A circular window must have a circumference of twenty-four handbreadths, with two and a bit of them within ten handbreadths of the ground, so that when he squares the window, i.e., if he forms the shape of a square inside it, it measures four by four handbreadths, and a bit of it is then within ten handbreadths of the ground.

The Gemara poses a question with regard to this calculation: Now, since there is a general principle that any circle with a circumference of three handbreadths is one handbreadth in diameter, then according to this formula, a window with a circumference of twelve handbreadths, meaning that it has a diameter of four handbreadths, should be sufficient to create a window of four by four.