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Eruvin 76b

עירובין ע״ו ע״ב

Learn Eruvin 76b step by step: Aramaic beside English, every question, answer and proof colour-coded.

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Topic

Round windows and the קיסרי measuring rule, רב נחמן on high windows and ceiling openings in houses, and the new משנה about a wall between two courtyards.

Overview

The amud opens by explaining רבי יוחנן's rule that a round חלון needs a circumference of 24 טפחים so that a 4×4 square fits inside it. The גמרא challenges this twice with geometry. The quarter rule suggests 16, and the diagonal rule (1 side gives 1⅖ diagonal) suggests 17 minus ⅕. It answers that רבי יוחנן followed the scholars of קיסרי: a circle around a square is bigger by half, so 16 plus 8 gives 24. Next, רב נחמן rules that the 10-טפחים height limit applies only to a window between courtyards. A window between houses works even when high, because a house is treated as full. רבא challenges him from a ברייתא, and the גמרא defends רב נחמן by saying the ברייתא's 'all the same' refers only to the 4×4 size. רב נחמן then rules that a ceiling opening from a house to an attic needs no ladder at all, neither permanent nor temporary. A new משנה follows about a wall between two courtyards: when it is intact, when it has produce on top, and when it is breached up to or beyond ten אמות. The גמרא begins by asking about a wall less than four טפחים wide. רב answers that both domains control it, so nothing may be moved on it.

Opening lines

הָנֵי מִילֵּי בְּעִיגּוּלָא,

These words (the 3-to-1 ratio giving 12) apply to a circle,

אֲבָל בְּרִיבּוּעָא בָּעִינַן טְפֵי.

but for a square (that must fit inside it), we require more.

מִכְּדֵי, כַּמָּה מְרוּבָּע יָתֵר עַל הֶעָגוֹל —

Now, by how much is a square larger than a circle?

רְבִיעַ, בְּשִׁיתְסַר סַגִּיא!

By a quarter. So with sixteen it should suffice!

The steps (20)

  1. ResolutionThe 12-handbreadth rule only describes a circle, not a square inside it
  2. ChallengeA square is only a quarter bigger than a circle, so 16 should be enough
  3. ResolutionThe quarter rule is for a circle inside a square, not a square inside a circle
  4. ChallengeUsing the diagonal, 17 minus a fifth should be enough
  5. Resolutionרבי יוחנן Followed the Scholars of קיסרי
  6. Statementרב נחמן: A High Window Between Houses Still Works
  7. Challengeרבא Challenges רב נחמן From a ברייתא
  8. ResolutionThe 10-טפחים Rule Refers Only to Courtyards
  9. ChallengeBut the ברייתא Says 'All the Same'
  10. Resolution'All the Same' Refers Only to the 4x4 Size
  11. Questionרבי אבא asks whether a ceiling opening needs a permanent ladder
  12. QuestionExplaining the two sides of the question
  13. Responseרב נחמן answers that no ladder is needed
  14. StatementSome understood that a temporary ladder is still needed
  15. RejectionCorrection: no ladder of any kind is needed
  16. StatementNew משנה: a wall between two courtyards
  17. StatementProduce on top of the dividing wall
  18. StatementA breach in the wall: up to ten אמות versus more
  19. QuestionWhat if the wall is less than four טפחים wide?
  20. Responseרב: both domains control it, so nothing may be moved there