Arachin, Chapter 8, Mishnah 3. Our chapter is occupied with the public sale of a field that had been consecrated to the Beit Hamikdash, where the man who originally owned it bids against strangers for the right to buy it back. The last mishnah ended with a tie: if the owner names the very same sum a stranger names, the field is handed to the owner, because the Torah obligates him in a fifth beyond whatever he bids, so hekdesh takes in a larger amount from him. Our mishnah presses that logic further. Suppose the owner's figure falls below the stranger's figure, and yet, once his obligatory fifth is counted in, the treasury still comes out ahead with him. What then?
The owner bids twenty, the outsider bids twenty-one
The owner has named twenty sela'im. A second man now steps forward with the words "harei hi sheli", it is mine, "b'esrim v'echat", for twenty-one. The ruling is "hab'alim notnim esrim v'shesh": the field stays with the owner, and he lays out twenty-six sela'im.
Here is how that number is reached. The owner's twenty carries a chomesh with it, and a reminder is in place: wherever the Torah speaks of a chomesh, it means a fifth of the final sum, which works out to twenty-five percent of the original figure. Twenty sela'im plus its fifth comes to twenty-five, which is more than the outsider's twenty-one, so the owner's offer is the better one for the treasury and he keeps the field.
Still, he cannot walk away paying only twenty. The outsider's offer has publicly established that the field is worth twenty-one, and the treasury must receive at least the field's established value as principal. So the owner pays the twenty he bid, plus five sela'im for the chomesh, plus one more sela to bring the principal up to the twenty-one that was offered: twenty-six in all.
Notice the mechanism, because it governs the whole mishnah: the chomesh is figured only on the sum the owner himself named. The additional sela'im are simply added on afterward, as much as is needed to match the outsider's figure.
The rising bids
"B'esrim ushtayim": the outsider offers twenty-two. "Hab'alim notnim esrim v'sheva": the owner pays twenty-seven, namely his twenty, five for the chomesh, and two more to reach the twenty-two that was offered.
"B'esrim v'shalosh": someone offers twenty-three. "Hab'alim notnim esrim u'shmonah": twenty-eight, which is the twenty, the five of the chomesh, and three more to reach twenty-three.
"B'esrim v'arba": someone offers twenty-four. "Hab'alim notnim tish'a v'esrim": twenty-nine, which is the twenty, the five, and four more.
"Bachamisha v'esrim": someone offers twenty-five. "Hab'alim notnim sheloshim": thirty, which is the twenty, the five, and five more to reach twenty-five.
Across this whole series the owner's fifth never budges from five sela'im, however far his total climbs above twenty. The mishnah supplies the reason in two words, "she'ein mosifin chomesh", a fifth is not added, "al iluyo shel zeh", on account of the raise made by the other man. What the Torah imposes on the owner is a fifth of the figure he himself pronounced, and nothing past it. The surplus sela'im he lays down serve a single purpose, to bring the keren, the principal reaching the treasury, up to the worth the field has been shown to have; they carry no fifth of their own.
When the outsider's bid equals the owner's bid plus his fifth
When the outsider's bid equals the owner's bid plus his fifth
The next case: a stranger calls out "b'esrim v'shesh", twenty-six, exactly the sum that the owner's twenty yields once its fifth is included. Here the owner's offer no longer outstrips his rival's, and the mishnah awards him the field only on one condition, put as "im ratzu hab'alim", if the owner was prepared, "litein sheloshim v'echad v'dinar", to hand over thirty-one sela'im and a dinar, meaning that his own bid had been twenty-one from the start.
Let us break that down. There are four dinarim in a sela, so a fifth of twenty-one sela'im is five sela'im and one dinar: five for the twenty, and a quarter of a sela for the additional sela. An owner whose bid was twenty-one therefore owes twenty-one plus five and a dinar, a total of twenty-six sela'im and a dinar, one dinar more than the outsider's twenty-six. "Hab'alim kodmim," the owner takes precedence, and the field is awarded to him.
Once it is his, the same rule as before applies: his principal must be raised to match the outsider's figure of twenty-six, which means five more sela'im on top of his twenty-one. His final bill is thirty-one sela'im and a dinar. And note the sequence: even before that raise, his own bid with its chomesh already stood at twenty-six and a dinar, slightly above the competing offer, and that is precisely why the field went to him.
When the treasury loses nothing
"V'im lav": if the owner had not offered twenty-one but only twenty, and the outsider offered twenty-five, then "omrim higi'at'cha," the treasurer tells the outside bidder that the field has come to him. The owner's twenty with its fifth reaches exactly twenty-five, no more than what the outsider is offering. Since the treasury gains nothing by returning to the owner, there is no reason to press him to redeem his own field for a sum he never wished to pay.
One might object: had we forced the field on the owner, he would eventually have had to raise his principal to twenty-five, and the treasury would have collected thirty. But that added payment is only a consequence of the decision, not a factor in it. The comparison that decides the case is narrow: the outsider's bid against the owner's bid together with his chomesh. Whichever is higher wins the field. And when the two figures are equal, the field goes to the newcomer. We do not go back to the owner for a fresh offer when his bid plus the fifth merely ties the new bid. At that point the field is the outside bidder's, and it is his.