The Mishnah (3:5) discusses the laws of peah as they relate to partnerships. The first case is regarding brothers that share an inheritance. The Mishnah explains that if they divided the property, they would each need to leave peah for their own fields. If they then decided to combine and form a partnership, then only one peah needs to be left. The Mishnah continues that if two people bought a tree together in partnership, then only one peah needs to be left. If however one bought one side of the tree and the other bought the other, then each would need to leave peah.
The Mishnah Rishona explains that the novelty of the Mishnah is regarding the case where brothers divided and then joined together. When they initially divided, each brother took one side of the field. When they came together, one might view the case as similar to where two people purchased each side of a tree and each must still leave their own peah. Consequently, the Mishnah teaches that in the case of the brothers, only one peah needs to be left. The reason is, when they came together, they will now be sharing in each kernel, rather than dividing the produce by location.
The Mishnah Rishona however continues by citing the opinion of the Rosh that if brothers divided a single tree, then only peah needs to be left. The position is at first difficult to understand. The Mishnah appears to suggest that even a tree can be subdivided like a field. Consequently, if the brothers have divided the tree, then it would seem that they should each leave their own peah for their side of the tree. The Mishnah Rishona suggests that the Rosh understood this from the wording of the Mishnah. Since the Mishnah did not continuing by discussing a case of brothers dividing a tree, but rather two individuals purchasing a tree, it implies that the case of inheritance would not have the same law. The Mishnah Rishona however suggests that the case was not mentioned since normally a tree would not be worth dividing. How do we understand the position of the Rosh?
The R' Chaim Kanievsky shlita, (Derech Emuna, Biur Halacha, Peah 3:16) probes why if a field is owned by two different people one cannot leave peah from one field for the other. We find that for terumah one can separate from their own produce to satisfy the requirements for another. So why is peah different? He first cites the Rash who explains that each of them have the obligation to separate peah from "their field" ("sadcha"). This would seem that once the parts of the field have different owners, it is considered like the case where there are two species, and peah must be left for each.
The above understanding however does not fit with the explanation of the Rosh above. If the heirs divide the ownership of the tree, how can only one peah be left from that tree. It should be now considered like two distinct fields. Furthermore, we have learnt (2:8) that if one harvests half their field and then sells it to another, the purchaser must leave peah for the entire field. The Bartenura explains that the obligation to leave peah was created at the beginning of the harvest. It is therefore considered as if the sale did not include that section that needed to be left as peah. R' Chaim however asks, how can one leave peah for the section owned by the other? Granted that that the obligation started at the beginning of the harvest, he notes that according to the Yerushalmi the law would be the same, even if the owner sold half the field prior to harvest.
The R' Chaim therefore suggests that the Rash means, that since the Torah states "sadcha" each have an obligation to separate for their field and do not have an obligation for anyone else's. Consequently, each one should ideally separate from their own field. That is not to say that if one did separate for another's field it would not work. He notes that even though Rashi (Chulin) explains that it would not work, he suggests that this may only be on a rabbinic level. Consequently, in the case where the brothers are dividing a tree from an estate or one is selling half of his unharvested field, the Chachamim were lenient to allow one to separate peah from one's section of a field for another's.
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