הני מילי בעיגולא אבל בריבועא בעינן טפי

**This** measurement **applies** only **to a circle** and the ratio between its circumference and diameter, **but with regard to a square** that must fit entirely within that circle, **we require** a circle with a **larger** circumference. In order for a square of four by four handbreadths to be entirely contained within a circle, the circumference of the circle must measure more than twelve handbreadths

מכדי כמה מרובע יתר על העגול רביע בשיתסר סגיא

The Gemara asks: **Now, how much larger is a square than a circle?** It is larger by **one quarter.** If so, a circle **with** a circumference of **sixteen** handbreadths at most should **suffice.**

הני מילי עיגולא דנפיק מגו ריבועא אבל ריבועא דנפיק מגו עיגולא בעינן טפי מאי טעמא משום מורשא דקרנתא

The Gemara answers: **This** statement that a square is larger than a circle by a quarter **applies** only **to a circle circumscribed by a square, but** with regard to **a square circumscribed by a circle, we require more,** and the difference between the square and the circle is greater. **What is the reason** for this? It is **due to the projection of the corners** of the square, as the distance from the center of the square to its corners is greater than the distance from the center to its sides.

מכדי כל אמתא בריבוע אמתא ותרי חומשי באלכסונא בשיבסר נכי חומשא סגיא

The Gemara further objects: **Since every cubit in** the side of **a square** is **a cubit and two-fifths in the diagonal,** a square of four by four handbreadths has a diagonal of five and three-fifths handbreadths. And since the diameter of a circle equals the diagonal of the square that it encompasses, the circle circumscribing a square of four by four handbreadths has a diameter of five and three-fifths handbreadths. If that measure is multiplied by three to arrive at the circumference of that circle, the result is that a circle with a circumference of **seventeen handbreadths minus a fifth is sufficient** to circumscribe a square of four by four handbreadths. Why, then, does Rabbi Yoḥanan say that a circular window must have a circumference of twenty-four handbreadths?

רבי יוחנן אמר כי דייני דקיסרי ואמרי לה כרבנן דקיסרי דאמרי עיגולא מגו ריבועא ריבעא ריבועא מגו עיגולא פלגא:

The Gemara answers: **Rabbi Yoḥanan spoke in accordance with** the opinion of **the judges of Caesarea, and some say in accordance with** the opinion of **the Sages of Caesarea, who say: A circle** that is circumscribed **within a square** is smaller than it by **one quarter;** with regard to **a square** that is circumscribed **within a circle,** the difference between them is equal to **half** the square. According to this explanation, Rabbi Yoḥanan calculated as follows: Since a square of four by four handbreadths has a perimeter of sixteen handbreadths, the circumference of the circle that encompasses it must be fifty percent larger, or twenty-four handbreadths.

פחות מארבעה על ארבעה וכו׳: אמר רב נחמן לא שנו אלא חלון שבין שתי חצירות אבל חלון שבין שני בתים אפילו למעלה מעשרה נמי אם רצו לערב מערבין אחד מאי טעמא ביתא כמאן דמלי דמי

It was taught in the mishna: If a window is **less than four by four** handbreadths, or if it is above ten handbreadths from the ground, the residents of the two courtyards may not establish one joint *eiruv* but must instead establish two independent ones. **Rav Naḥman said: They taught** this *halakha* of a window within ten handbreadths of the ground **only** with regard to **a window between two courtyards. But** with regard to **a window between two houses, even** if it is **above ten** handbreadths **as well, if they wish to establish an eiruv, they establish one eiruv. What is the reason** for this

*halakha*? It is that

**a house is considered as though it**were

**filled,**and therefore there is no difference between below and above ten handbreadths with regard to a window in a house.

איתיביה רבא לרב נחמן אחד לי חלון שבין שתי חצירות ואחד לי חלון שבין שני בתים ואחד לי חלון שבין שתי עליות ואחד לי חלון שבין שני גגין ואחד לי חלון שבין שני חדרים כולן ארבעה על ארבעה בתוך עשרה

**Rava raised an objection to** the opinion of **Rav Naḥman** from that which was taught in a *baraita*: **A window between two courtyards, and a window between two houses, and a window between two attics, and a window between two roofs, and a window between two rooms are all one and the same to me; they all** must be **four by four** handbreadths and **within ten** handbreadths from the ground. This directly contradicts Rav Naḥman’s opinion.

תרגומא אחצירות והא אחד לי קתני תרגומא אארבעה על ארבעה

The Gemara answers: **Explain** that this *halakha* of ten handbreadths mentioned in the *baraita* is referring only to **courtyards.** The Gemara objects: **Doesn’t** the *baraita* **teach: Are all one and the same to me,** indicating that they are all equal in this regard? Rather, **explain** that they are all equal in that the window must be the size of **four by four** handbreadths, but not that all must be within ten handbreadths of the ground.

בעא מיניה רבי אבא מרב נחמן לול הפתוח מן בית לעלייה צריך סולם קבוע להתירו או אין צריך סולם קבוע להתירו

**Rabbi Abba raised a dilemma before Rav Naḥman:** With regard to **an aperture that opens from** the ceiling of **a house** occupied by one person **to an attic** occupied by another, **must a permanent ladder** be positioned in the opening **to render** carrying from one level to the other **permitted** by turning the two into a single residence? **Or, is a permanent ladder not necessary to render it permitted?**

כי אמרינן ביתא כמאן דמלי דמי הני מילי מן הצד אבל באמצע לא או דילמא לא שנא

The Gemara clarifies the two sides of the question: **When we say** that **a house is considered as though it** were **filled,** does **this apply** only to a window positioned **on the side, but not** to a window **in the middle?** In that case, the opening would not be viewed as near the full part of the house, and a permanent ladder would be required. **Or perhaps there is no difference,** and since the house is considered filled, no ladder is necessary.

אמר ליה אינו צריך סבור מינה סולם קבוע הוא דאינו צריך הא סולם עראי צריך איתמר אמר רב יוסף בר מניומי אמר רב נחמן אחד סולם קבוע ואחד סולם עראי אינו צריך:

Rav Naḥman **said to him: It is not necessary.** The Sages **understood from** this response that he meant that **a permanent ladder is not required, but a temporary ladder is required.** However, **it is stated** in this regard: **Rav Yosef bar Manyumi said** that **Rav Naḥman said: Neither a permanent ladder nor a temporary ladder is required,** as the fact that the opening is located within the house is sufficient to render it permitted to carry from the house to the attic.

**מתני׳** כותל שבין שתי חצירות גבוה עשרה ורוחב ארבעה מערבין שנים ואין מערבין אחד

**MISHNA:** If **a wall between two courtyards is ten** handbreadths **high and four** handbreadths **wide,** the residents of the courtyard **establish two eiruvin,** a separate one for each courtyard,

**but they**may

**not establish one**

*eiruv*.היו בראשו פירות אלו עולין מכאן ואוכלין ואלו עולין מכאן ואוכלין ובלבד שלא יורידו למטן

**If there was produce on top** of the wall, **these** residents of one courtyard **may ascend from this side and eat** from it, **and those** residents of the other courtyard **may ascend from that side and eat** from it, **provided that they do not lower** the produce **down** from on top of the wall to one of the courtyards.

נפרצה הכותל עד עשר אמות מערבין שנים ואם רצו מערבין אחד מפני שהוא כפתח יותר מכאן מערבין אחד ואין מערבין שנים:

**If the wall was breached,** the following distinction applies: If the breach was **up to ten cubits** wide, **they establish two eiruvin, and if they desire, they** may

**establish one**like any opening less than ten cubits wide. If the breach was

*eiruv*, as it is similar to an entrance,**more than this, they establish one**may

*eiruv*, and they**not establish two,**as a breach of this size nullifies the partition and joins the two courtyards into a single domain.

**גמ׳** אין בו ארבעה מאי אמר רב אויר שתי רשויות שולטת בו לא יזיז בו אפילו מלא נימא

**GEMARA:** The Gemara asks: If this wall **is not four** handbreadths in width, **what** is the *halakha*? **Rav said:** In this case, **the air of two domains controls it.** Since the wall is not broad enough to be regarded a domain of its own, the top of the wall is seen as belonging to both courtyards and is then prohibited to both of them. Accordingly, **one may not move** anything **on** top of the wall, **even** as much as **a hair’s breadth.**