Gittin, Chapter 8, Mishnah 3. In the previous Mishnah we learned that if a man throws a get to his wife in a public domain: if the get is closer to her, she is divorced; if it is closer to him, she is not divorced; and if it landed halfway between them, she is divorced and not divorced, that is, a case of doubtful divorce. We also learned that the standard the Gemara set is the ability to guard the get: if she can guard it and he cannot, it is considered closer to her; if the reverse, it is closer to him; and if both can guard it, or neither of them can guard it, that is the middle case.
"Vechen le'inyan kiddushin" - And so too regarding kiddushin:
Our Mishnah rules that the very same law applies to kiddushin as well. If a man throws a ring or money to a woman for the purpose of kiddushin: closer to her, she is betrothed; closer to him, she is not betrothed; and if it landed in the middle, it is a case of doubt.
The reason for this comparison is the standing analogy between gittin and kiddushin, as the verse says: "Veyatz'ah mibeiso vehaysah le'ish acher" - "And she leaves his house and goes and becomes another man's wife." The woman leaves his house by means of the get, and then goes and marries another man. From here we derive an analogy between havayah (becoming) and yetziah (leaving): havayah, which is the term the Torah uses for kiddushin, is placed alongside yetziah, which is divorce, and therefore the laws of each are learned from the other.
"Vechen le'inyan chov" - And so too regarding a debt:
The Mishnah goes on to apply this law even to the repayment of a debt, and illustrates it: "Amar lo ba'al chovo zerok li chovi uzerako lo" - his creditor said to him, "Throw me the money you owe me," and he threw it to him. A lender standing in a public domain tells the borrower to throw him the money he owes, and the borrower throws it. These are the laws:
Closer to the lender - "zachah haloveh," the borrower has gained. Once the money landed within the lender's four amos, or in a place under his control, the borrower has gained, since the debt has been paid to his benefit.
Closer to the borrower - "haloveh chayav," the borrower is still liable. The money fell in his own domain, in a place where he can guard it, and therefore the loan has not yet been repaid and he is still obligated to pay it.
Halfway between them - "sheneihem yachloku," the two of them divide it, since it is a matter of doubt whether the debt was repaid or not.
The Gemara explains that this ruling applies in a specific case, where the lender said to the borrower: "Throw me the payment on the terms of gittin" - meaning that the matter should take effect in the same way that a get takes effect. But if he made no such stipulation, and simply said, "Throw me what you owe me," then it is the borrower's responsibility to make sure that the money actually reaches the lender's hands, and as long as it has not come into his genuine possession it is not considered repayment. For the lender's intent in saying "Throw it to me" is that the borrower remains responsible to safeguard the money until it literally reaches his hands, and if it was lost on the way, the debt has not been repaid.
Throwing a get onto a roof and from a roof:
"Haysah omedes al rosh hagag uzerako lah" - she was standing on top of the roof and he threw it to her. The woman is standing on a roof that belongs to her, and the husband throws her the get. "Keivan shehigia la'avir hagag harei zo megureshes" - once the get reached the airspace of the roof, she is divorced. That is, once it came within the three tefachim closest to the roof, which by the law of lavud are considered attached to the roof, it is as though it had actually come to rest, even though it has not yet landed. From that moment she is divorced, and even if something happened to the get afterward so that it never came to rest at all - it was burned or erased - the get is valid and the divorce takes effect.
"Hu milmalah vehi milmatah" - he is above and she is below. He is standing on his roof and she is in the courtyard below that belongs to her, and he throws her the get. "Keivan sheyatza mireshus hagag nimchak o nisraf harei zo megureshes" - once it left the domain of the roof, even if it was then erased or burned, she is divorced. Once the get left the airspace of the roof on which he is standing, even if it was afterward erased by water or burned, she is divorced, since it has already entered the airspace of the courtyard, which is her domain.
In summary: In this Mishnah we learned that the laws of throwing that were stated regarding a get apply to kiddushin as well, by force of the analogy between havayah and yetziah, and to the repayment of a debt as well: closer to the lender, the borrower has gained; closer to the borrower, he is still liable; and in the middle, they divide it, provided that the lender said he should throw it to him on the terms of gittin. We also learned that once the get reaches the airspace of the woman's domain, or once it leaves the domain of the roof on which the husband is standing, she is divorced, even if it was erased or burned afterward.