Yerushalmi Bava Kamma 4:1 ירושלמי בבא קמא ד׳:א׳

MISHNAH: A bull which gored four or five bulls, one after the other¹A tame bull went on a goring spree before it could be declared notorious in court. The damage which it caused has to be liquidated by the rules of the tame bull; i. e., the bull has to be sold and from the proceeds half the damages have to be paid., should pay for the last of them²According to R. Meïr, a bull which gored becomes the property of its victim’s owner. The original owner has a claim to the excess of the sale price over the claim for restitution.
Assuming that the bull was worth a; it gored n bulls, worth a₁, a₂, … ,a_n. The owner of the last bull claims a_n/2 from the owner of the bull gored as the penultimate. If a - a_n/2 > 0, the owner of that bull satisfies himself up to the amount a_n-1/2. If a - a_n/2 - a_n-1/2 > 0, the preceding owner can satisfy himself up to a_n-2/2, and so on until all of the proceeds a are used up. In practically all cases, the owner of the attacking bull ends up with nothing. If there is anything left, it should revert to the penultimate. If then there is anything left, it should revert to the one before the penultimate. The later one is always advantaged, the words of Rebbi Meïr. Rebbi Simeon³He holds that the original owner and the owner of the victim become co-owners of the attacking bull. The last owner takes a/2; the owner of the penultimate victim then is a 50% owner of the remaining a/2, and so on. In this way, the owner of the j-th bull gored gets a/2^n-j+1; the owner of the attacking bull is left with the same amount as the one given to the owner of the first victim, a/2ⁿ.
If the values of the bulls are distinct, the last owner takes a_n/2, the one before him
min(a_n-1/2, a/2-a_n/4)
and so on. says, if a bull worth 200 gored a bull worth 200 and the carcass is not worth anything, each one takes a mina. If then it gored another bull worth 200, the last one takes 100 and the preceding each take 50. If then it gored another bull worth 200, the last one takes 100, the preceding one takes 50 zuz⁴Silver denars., and the two first ones each a gold denar⁵25 silver denars..

HALAKHAH: “A bull which gored four or five bulls,” etc. ⁶The basic explanation of this paragraph is given by Nachmanides, Milḥamot Hashem, to Mishnah 4:1. Rebbi Yannai said, Rebbi Meïr attacks him⁷The arguments given to the owner of the bull gored last against the owner of the bull gored as the penultimate. from two sides: As you take it, if it is yours⁸As explained in Note 2., give it to me. If it is not yours⁹But you are part owner as claimed by R. Simeon., hand it over to me that I may satisfy my claim. But did not Rebbi Eleazar say, the guarding of damages parallels the guarding of acquisitions¹⁰The property rights given by the Torah to the owner of the dead bull is one of ownership, not possession (cf. Qiddušin 1, Note 352). Therefore, the potential owner of the bull cannot be liable for the damages done by an animal not in his actual possession.? ¹¹In the Babli, 26b, this is labelled as R. Aqiba’s opinion. Rebbi Jehudah told him, it was delivered to him for his damages but it remains a pledge¹²Since he becomes owner for monetary gain, he is obligated for damages as if he were a paid trustee. The second argument attributed to R. Meïr really is valid only if the penultimate owner actually took possession of the offending bull..

What is between them? Rebbi Joḥanan said, dedication is between them. In Rebbi Jehudah’s opinion, the first [owner]¹³In this paragraph, one assumes that the bull gored only once. The first owner is the original one; the second is the the owner of the dead bull. may dedicate¹⁴The second owner is co-owner, but as long as he did not actually take possession of the bull, the first can pay him off as mortgage-holder and be both owner and in possession. Therefore, only he may dedicate since nobody can dedicate what is not in his possession (cf. Ketubot 5:5, Notes 105–106; Tosephta 5:1; Babli 33b).. In Rebbi Meïr’s opinion, [only] both together may dedicate it¹⁵While the bull is still in the possession of the first, ownership belongs to the second. They can only act together. The same reasoning applies to the following examples.. If it went up in price. In Rebbi Jehudah’s opinion, it increased for the first. In Rebbi Meïr’s opinion, it increased for the second. If it was rented out, in Rebbi Jehudah’s opinion, the rent belongs to the first. In Rebbi Meïr’s opinion, [the rent] belongs to both of them. If it improved¹⁶Cf. Chapter 3, Note 130., in Rebbi Jehudah’s opinion, the improvement belongs to the first. In Rebbi Meïr’s opinion, the improvement belongs to both of them.

Rebbi Joḥanan said, Rebbi Jehudah and Rebbi Simeon stated the same. Just as Rebbi Jehudah said, he acquired, so Rebbi Simeon said, he acquired¹⁷The owner of the injured animal becomes part owner with the owner of the attacker., only that Rebbi Jehudah says, he acquired the living and the dead¹⁸Chapter 3, Note 135; Tosephta 3:3. The owner of the attacker also becomes part owner of the carcass.; but Rebbi Simeon says he only acquired the (dead)¹⁹This certainly should read: the living. R. Simeon only discusses the case that the carcass be without value; this skirts the issue of ownership of an injured animal..

²⁰Mishnah Ketubot 10:4. The text and its relation to the corresponding one in Ketubot 10:4 is explained there in Notes 73–75. There, we have stated: “Similarly, if three who invested together lost or gained they would split in this manner.” Rebbi Abun said, the statement looks reasonable if they bought a precious stone because he can say to him, without my ten denars you could not have bought anything. But anything that usually is split {smaller units that can be bought with less capital} one adds together and splits {proportionally to the capital invested}. Rebbi Eleazar says, even things that usually are split [are divided evenly], because he can say to him, you have a lot of merchandise and you have difficulty selling it. I have little merchandise and turn it over rapidly and make as much as you do. So far if his merchandise was here. What if his merchandise was in Rome? He can say to him, by the time you went to Rome, I turn mine over rapidly here and make as much as you do.

It was stated: ²¹Tosephta Ketubot 10:4. Three who invested together and suffered theft, absorb [the loss] in the same way²²The distribution algorithm described in Ketubot 10:4 (Note 62).. But was it not stated: If those [precious] stones were stolen, half for each one²³Each of the investors absorbs the same amount of loss.. Rebbi Shammai said, tetradrachmas are large²⁴Probably one should interchange the positions of “large” and “easy”. Money can be divided easily and exactly; precious stones are a one or nothing affair as noted in the preceding paragraph. and it is possible to subdivide exactly but stones are easy²⁴Probably one should interchange the positions of “large” and “easy”. Money can be divided easily and exactly; precious stones are a one or nothing affair as noted in the preceding paragraph. and it is impossible to know which part in it belongs to whom. Because of the doubt, each one takes proportional to his investment. What did you see to say that we deal with theft, maybe one deals only with what is left²⁵Which is money and therefore easily distributed.? Rebbi Yose ben Rebbi Abun said, even if you say that we deal with theft, would not equity be hurt? Think of it, if one invested 50 and the other 150. If 50 was stolen, would not the one with 50 not lose anything²⁶This is difficult to understand. There are 150 left and the sum total of the claims is 200. By the method of Mishnah Ketubot 10:4, the first 50 are claimed by both investors, the remaining 100 only by the second. Therefore, the first gets 25, the second 125; each one loses 25. If the loss were distributed proportional to the investment, the first investor would take 37.5, the second 113.5. It is a matter of opinion which method be more equitable.?

²⁷Cf. Ketubot 10:4, Notes 76–79. There, we have stated: “If [the ox] gored an ox worth 200, the last one takes 100, the one before him 50, and the two first ones each a gold denar.” Rebbi Samuel in the name of Rebbi Ze‘ira: The same holds for earnings. Rebbi Yose said, the statement of Rebbi Ze‘ira disagrees with Rebbi Eleazar. Rebbi Mani said, I asked this before Rebbi Yudan. He said to me: does Rebbi Eleazar not agree if they contracted between themselves that each can take according to his contribution? Oxen are as if contracted. He turned around and said this before Rebbi Yose, who answered him, they disagree explicitly: Rebbi Eleazar said, if nothing was said, they split evenly; Rebbi Ze‘ira said, if nothing was said, each takes according to his contribution.