If one receives sheep at a fixed price from a non-Jew, its offspring are exempt from [the obligations of] the firstborn, but the second generation is obligated. If one offered the offspring as collateral for the mothers [should they die], then the second generation is exempt but the third generation is obligated. Rabban Shim'on ben Gamliel says: They are exempt even for ten generations, because the non-Jew has [residual] rights to them.
Bartenura on Mishnah Bekhorot
המקבל צאן ברזל מן הנכרי (he receives a guaranteed investment from the heathen – which is secure from any loss) – that the heathen placed his cattle to him (i.e., an Israelite) for fixed compensation and to give him those monies for up to ten years, whether they (i.e., the animals) died or lost value, and those offspring that they will have until that time will be [divided] between them.
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English Explanation of Mishnah Bekhorot
Introduction
Our mishnah discusses a Jew who receives a flock of sheep or goats from a non-Jew under “iron terms.” What this means is that all responsibility for the flock lies with the Jew, and he pays the non-Jew a fixed sum per year in return for use of the flock and the use of the offspring. Alternatively, instead of paying a fixed sum, the Jew and the non-Jew split the profits and the offspring.
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Bartenura on Mishnah Bekhorot
וולדות פטורין – from being firstling. Their offspring of those sheep when they grow and bear animals for the first time will be exempt from the law of firstlings. For if he does not give money to the heathen, he will seize the animal, and if he does not find the animal, he will seize the offspring, it is found that the heathen has a connection with the offspring. Therefore, the firstborn of these offspring is exempt from the law of firstlings, for all that the heathen has a hand in/connection to its mother is exempt from the [law of] firstlings. But when the offspring of the offspring bear animals for the first time , that is the fourth [generation] of the guaranteed investment, they shall be given to the Kohen, for all that much the heathen does not have a hand in/connection to seize the offspring of the offspring.
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English Explanation of Mishnah Bekhorot
If one receives flock from a non-Jew on “iron terms” their offspring are exempt [from the law of] the first born. In mishnah one we learned that the flock itself is exempt from the laws of the first born. Our mishnah teaches that if one of the offspring of the original flock gives birth, that offspring is also exempt from the law of the first born, meaning its first born is not holy. The reason for this exemption is that if the Jew reneges on his payment to the non-Jew, the non-Jew can take the offspring as part of his payment. This means that they are in some sense owned by the non-Jew and as we have learned, animals owned by non-Jews are not subject to the law of the first-born.
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Bartenura on Mishnah Bekhorot
העמיד ולדות תחת אמותיהן ולדי ולדות פטורין ולדי ולדי ולדות חייבים – if [the Israelite] stipulated that the offspring were in place of their mothers, when he (i.e., the Israelite) made an opening for the heathen for him to have power over the offspring and stated to him: “If the animals will die, you will take the offspring that reach my portion. Now, the power of the hand of the heathen is stronger and is connected to one generation more than of the first [alone]. Therefore, the offspring of the offspring of animals is a guaranteed investment, that when the animals gave birth for the first time, they are exempt from the [law relating] to firstborn animals, since the hand of the heathen belongs to/is attached to them. The offspring of the offspring of the offspring, when they first give birth, that is the fifth [generation] of guaranteed investment, should be given to the Kohen.
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English Explanation of Mishnah Bekhorot
But the offspring of their offspring are liable [to the law of the first born]. However, the offspring of the offspring are liable meaning that the first born offspring born of this offspring are holy and must be treated as such.
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English Explanation of Mishnah Bekhorot
If [the Israelite] put the offspring in the place of their mothers, then the offspring of the offspring are exempt, but the offspring of the offspring of the offspring are liable. If the Jew tells the non-Jew that he is going to pay him back not with the original flock but with its offspring, then the exemption is extended another generation, to the first born of the offspring of the offspring. (It might help you to use names here, Debbie, born of Charlene, born of Becca, born of Alice apologies to those with these names!). Again, since the non-Jew can claim these animals (Charlene), they are considered to be in his possession in order to exempt their offspring (Debbie).
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Bartenura on Mishnah Bekhorot
שאחריותן לנכרי -for always, everything that is found the Gentile grabs hold of. But the Halakha is not according to Rabban Shimon ben Gamaliel.
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English Explanation of Mishnah Bekhorot
Rabban Shimon ben Gamaliel says: even for ten generations the offspring are exempt [from the law of the first born] since they are pledged to the non-Jew. Rabban Shimon ben Gamaliel says that all subsequent offspring are pledged to the non-Jew, no matter how many generations removed. Therefore, they are all exempt from the laws of the first born (so Eunice is exempt, as if Freda, and Gladys and Harriet, and Iris would you like me to go to Z for Zoey, my daughter’s name?).