Gemara

(Rava): If one ate two k'Zeisim of Chelev in one Helam, and found out about one of them, and ate a third k'Zayis before finding out about the second:

If he brought a Korban [and said that it is] for the first, it atones for the first two, but not for the third.

If he brought a Korban for the third, it atones for the last two, but not for the first.

If he brought a Korban for the second, it atones for all three.

(Abaye): In any case, the Korban atones for all three.

Rava agrees to Greirah (a Korban for one Aveirah atones also for other Aveiros done in the same Helam), but not Greirah of Greirah. (What gets atonement through Greirah cannot be Gorer something else.)

Bava Metzi'a 96a - Question (Rami bar Chama): Is a man like a borrower of his wife's property, or a renter?

i. Suggestion: The case is, he rented a cow from a woman, and later married her.

Rejection: Whether he is a borrower or renter, the loan or rental b'Ba'alim (when the lender was working for him. The employer is always exempt in such cases) uproots the rental not b'Ba'alim!

98b - Question #1 (of R. Aba bar Mamal): If one borrowed a cow b'Ba'alim, and [before returning it] he rented it Lo b'Ba'alim (and it was lost or stolen), what is the law?

If the rental a separate matter, it is not b'Ba'alim, so he is liable;

Or, perhaps rental is a continuation of borrowing, for a borrower has the liability of a renter and more!

Question #2: If you will say that rental is a continuation of borrowing, if he rented b'Ba'alim and later borrowed it not b'Ba'alim, what is the law?

Surely, borrowing is not a continuation of renting, so he is liable;

Or, since it is a continuation regarding theft or loss, perhaps it a continuation for everything?

Question #3: If you will say that a partial continuation is not like a total continuation, if he borrowed b'Ba'alim, rented not b'Ba'alim, and borrowed it again, what is the law?

Does it revert to the original borrowing, which was b'Ba'alim?

Or, since he interrupted with a rental, it is a new borrowing not b'Ba'alim?

Question #4: If he rented b'Ba'alim, borrowed not b'Ba'alim, and rented it again, what is the law?

Does it revert to the original rental, which was b'Ba'alim?

Or, since he interrupted with borrowing, it is a new rental not b'Ba'alim?

This is not resolved.

Rishonim

Rambam (Hilchos She'elah 2:10): If one borrowed b'Ba'alim and rented Lo b'Ba'alim, he is exempt. The rental depends on the loan. However, if one rented b'Ba'alim and borrowed Lo b'Ba'alim, or borrowed b'Ba'alim, rented Lo b'Ba'alim, and borrowed Lo b'Ba'alim, or rented b'Ba'alim and borrowed Lo b'Ba'alim and rented [not] b'Ba'alim, all of these are a Safek Shemirah b'Ba'alim.

Rosh (Bava Metzi'a 8:11): The primary text of Questions 3 and 4 says 'if you will say that a partial continuation is like a total continuation, if he borrowed, rented, and borrowed again, is the rental an interruption? If he rented, borrowed, and rented again, is the loan an interruption? According to the Ge'onim who say that whenever the Gemara says 'if you will say...', the Halachah follows the premise, only the last two questions were not resolved. Since it is a Safek, we do not force one to pay.

Hagahos Ashri: If one rented b'Ba'alim and then borrowed Lo b'Ba'alim, and borrowed again Lo b'Ba'alim, we cannot say that the loan returns to its place, so he is surely liable. This is like the Ri, who exempts the first loan only due to its connection to the rental, but not due to itself. Therefore, it cannot exempt the rental after it, unless the latter returns to the initial rental. We do not say twice 'it is a continuation of...' However, perhaps we say so only that the middle loan does not exempt a rental afterwards, for this depends on two continuations, but if the second and third times were both rentals or both loans, both are a continuation of the previous. This requires investigation.

Tosfos (98b DH Sha'alah): The Gemara asked about She'elah b'Ba'alim followed by rental Lo b'Ba'alim. This implies that rental b'Ba'alim followed by rental Lo b'Ba'alim is obvious, i.e. the first rental continues. Above, we said that rental b'Ba'alim uproots a previous rental Lo b'Ba'alim, i.e. it is not a continuation! Rather, it is a Gezeras ha'Kasuv that whether the beginning or end is b'Ba'alim, he is exempt.

Poskim

Shulchan Aruch (CM 346:14): If one borrowed b'Ba'alim and rented Lo b'Ba'alim, he is exempt. The rental depends on the loan.

Beis Yosef (DH Mi): The Gemara asked whether rental is different, and even though he did Meshichah (took the animal to his Reshus, when he borrowed it) b'Ba'alim, and he did not do another Meshichah, he is liable. When he rented it, it was in his Reshus and did not require Meshichah. His Chatzer acquired through speech. It is a new Kinyan (acquisition) Lo b'Ba'alim. Or, perhaps we exempt, since rental does not add any obligations above borrowing, and initially he was exempt [since it was b'Ba'alim].

SMA (21): After the loan ended, it was still in his Chatzer, and he rented it for a time, and in that time it was lost or stolen.

Shulchan Aruch (ibid.): However, if one rented b'Ba'alim and borrowed Lo b'Ba'alim, or borrowed b'Ba'alim, rented Lo b'Ba'alim, and borrowed Lo b'Ba'alim, or rented b'Ba'alim and borrowed Lo b'Ba'alim and rented Lo b'Ba'alim, all of these are a Safek Shemirah b'Ba'alim.

Beis Yosef (DH Sachrah): Question #2 was if he rented b'Ba'alim, and before returning it borrowed Lo b'Ba'alim, and it died normally. Do we say that liability for Ones has no connection to rental, so it depends on the Kinyan Lo b'Ba'alim? Or, since liability for theft or loss applied to rental, we attribute everything to the initial Meshichah, even Onesim.

Beis Yosef (DH Sha'alah): In Question #3, he borrowed b'Ba'alim, rented not b'Ba'alim, and borrowed Lo b'Ba'alim. The Rosh says that the last two questions were not answered. Since it is a Safek, we do not force one to pay. The Tur says that if he seized the money, we take it from him. Surely this is a printing mistake. It should say 'if he seized the money, we do not take it from him.'

Shach (10): The Beis Yosef changed the text of the Tur to say 'we do not take it from him', like in Sa'if 11. I say that here the Tur means that we take it from him! The Rosh (Bava Kama 2:2) wrote that when the Gemara did not resolve the question, seizure does not help. The Tur himself wrote so in the name of the Rosh in Simanim 388 and 390. Sa'if 11 was not unresolved in the Gemara.

Beis Yosef (DH u'Mah she'Amar Rabeinu): The Rambam rules that only the first case is [Vadai] She'elah b'Ba'alim, and the others are Safek. It seems that his text says 'if you will say that' only in Question #2.

Beis Yosef (DH u'Mah she'Amar va'Doni): Why does the Tur say that the Rosh rules like the Rambam? Usually, the Rosh does not rule like the Ge'onim who rule like every 'if you will say...'! Here, he merely teaches what they would hold, but he disagrees and holds that all of the questions were not resolved! Also the Tur said so in his Kitzur Piskei ha'Rosh (11).

SMA (24): Rashi and the Rosh say that the latter questions depend on the first. If you will say that borrowing is a continuation of rental, since it applies partially, here since we must say so twice, i.e. rental after borrowing and borrowing after rental, we do not go so far to say so. Or, since initially he borrowed b'Ba'alim, this returns to its place.

Rema: Some say that if he rented b'Ba'alim and borrowed Lo b'Ba'alim, this is Shemirah b'Ba'alim.

SMA (24): This opinion holds that the text says 'if you will say...' in Question #3 and derives that the Halachah follows this, like the Ge'onim who say so. The Mechaber follows the Rambam, whose text did not say this.

Shulchan Aruch (15): Some say that if he rented b'Ba'alim and then rented Lo b'Ba'alim, the latter is b'Ba'alim, just like the first.

Aruch ha'Shulchan (20): Not only the second is attributed to the first. Rather, even the third or fourth, or any amount, when they are the same (all rentals or all loans). However, if he borrowed in Nisan b'Ba'alim, rented in Iyar Lo b'Ba'alim, and rented again in Sivan Lo b'Ba'alim, since rental interrupted between loans, the loan of Nisan does not exempt the rental of Sivan, even though it exempts the rental of Iyar. The rental of Iyar cannot be Gorer the rental of Sivan to exempt it, since Iyar itself is exempt only due to Greirah. We do not say Greirah of Greirah, like it says in Shabbos. When he borrowed again in Sivan, the Gemara did not settle this, since we need not attribute it to Iyar. If he seized, he need not return it (Tur). Even though Hagahos Ashri was unsure about this in the end, Rashi and Tosfos explicitly connote like I said.

Shulchan Aruch (ibid.): However, if the first was Lo b'Ba'alim and the latter was b'Ba'alim, the first is not Gorer the latter to make it Lo b'Ba'alim.

SMA (25): The beginning of the rental must be b'Ba'alim [to exempt]. If it was not, even if it was b'Ba'alim when it died, he is liable (Sa'if 5). One might have thought that here also it is like one rental, and initially it was Lo b'Ba'alim, so he is liable. This is not so. Since the first rental ended, it is like a new rental Lo b'Ba'alim, and he is exempt. Even though when the first rental was b'Ba'alim and the latter was not, we consider it like one rental to exempt, we are lenient about Shomerim. The Tur says so.