Bava Basra 27a

בבא בתרא כ״ז ע״א

Bava Batra 27a

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Topic

Testing עולא's rule that a tree's roots draw from 16 אמות: the math of a בית סאה and challenges from the laws of ביכורים

Overview

עולא said a tree's roots draw nourishment from 16 אמות around it. The גמרא first tests this against a משנה about three trees in a בית סאה: dividing 2,500 square אמות among them gives each about 833⅓, but 16 אמות on every side makes a 32×32 square of 1,024. The גמרא answers that עולא rounded (לא דק), then objects that rounding is only accepted when it leads to strictness. It explains that the roots spread in a circle, not a square, which cuts the area to 768. Now עולא's 16 is about half an אמה short of the exact figure, so his rounding falls on the strict side and is accepted. The גמרא then brings two משניות about bringing and reciting over ביכורים: one about a buyer of a tree and its land, and one about a buyer of trees in someone else's field. Both seem to allow any amount of land. Each time it answers that the buyer owns 16 אמות. Finally it starts a third challenge from רבי עקיבא, who says any amount of land is obligated in פאה and ביכורים. That quote continues on the next amud.

Opening lines

The steps (11)

1. ChallengeThe math of three trees in a בית סאה doesn't match עולא
2. Resolutionעולא was not being exact
3. ChallengeRounding is only accepted when it leads to strictness
4. ResolutionThe roots spread in a circle, not a square
5. ChallengeEven with a circle, half an אמה is left over
6. Conclusionעולא rounded, and on the strict side
7. ChallengeChallenge from a buyer of a tree and its land
8. RejectionThe משנה means he bought 16 אמות
9. ChallengeChallenge from a buyer of three trees
10. RejectionHere too it means 16 אמות
11. ChallengeChallenge from רבי עקיבא: any amount of land