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1) [line 8] TENU CHELEK LI'PELONO BA'BOR - give a portion of [the water in] this pit to so-and-so

2) [line 8] SUMCHUS OMER: EIN PACHOS ME'REVI'A - Sumchus says: [the recipient is entitled] to no less than a quarter [of the water in the pit] (MAMON HA'MUTAL B'SAFEK CHOLKIN)
(a) Sumchus maintains that when the ownership of property is in doubt, it is divided among the claimants.
(b) According to the Rabanan who disagree with Sumchus, as long as one of the claimants has a Chazakah (i.e. evidence of prior ownership) over the property in dispute, he need not pay until his opponent brings a proof of his claim using witnesses. A Chazakah, with regard to this Halachah, can mean either Chezkas Mamon (the object is currently in his possession) or Chezkas Marei Kama (he has evidence that he was once the owner of the object, and nobody can show that it left his ownership since that time).
(c) The Rishonim argue whether we rule like Sumchus or like the Rabanan. The Rashbam here maintains that we rule like Sumchus. Tosfos rules like the Rabanan. According to Tosfos, the Gemara here quotes Sumchus merely because he explicitly ruled about the case that the Gemara is discussing. We can infer from Sumchus' ruling that the Rabanan argue and maintain "ha'Motzi me'Chaveiro Alav ha'Ra'ayah."

3a) [line 9] L'CHAVIS - [give a portion of the water in this pit to so-and-so] for his barrel (half of the water in a standard sized pit will fill a barrel; in our case, the doubt is whether the owner of the pit wanted to give a minimal amount of water to the recipient, or he wanted to give enough to fill up half ("Chelek") of the barrel)
b) [line 10] LI'KEDEIRAH - [give a portion of the water in this pit to so-and-so] for his pot (a third of the water in a standard sized pit will fill a pot; in our case, the doubt is whether the owner of the pit wanted to give a minimal amount of water to the recipient, or he wanted to give enough to fill up half ("Chelek") of the pot)
c) [line 10] LI'TAFI'ACH - [give a portion of the water in this pit to so-and-so] for his pitcher (a fourth of the water in a standard sized pit will fill a pitcher; in our case, the doubt is whether the owner of the pit wanted to give a minimal amount of water to the recipient, or he wanted to give enough to fill up half ("Chelek") of the pitcher)

4) [line 12] MA'ASER RISHON - see Background to Bava Basra 56:12

5) [line 16] EIN ADAM MAKNEH DAVAR SHE'LO BA LA'OLAM
There is a Machlokes Tana'im as to whether "Adam Makneh Davar she'Lo Ba l'Olam" - "a person can acquire a thing that has not yet emerged into the world," or not (Kedushin 63a). Some examples of things that have not yet emerged into the world are the fruits that will grow on a tree or the goods to be produced by one's wife. Here, the produce of Ma'aser Rishon that will grow, in the future, on the field, which the Levi stipulates will be given to him, is a "Davar she'Lo Ba la'Olam," since the produce has not yet come into the world.

6) [line 20] DIYUTA HA'ELYONAH - the upper story (this refers to a roof which has an enclosure around it which at least the height of ten Tefachim)

7) [line 2] ZIZIN - small wooden protrusions, or the ends of beams, that jut out from a wall, which people use for hanging things

8) [line 3] ALIYAH - an upper story (Rav Papa is referring to *rebuilding* an upper story that fell down after the house was sold; he is not referring to building a new upper story)

9) [line 8] MI'TEHOM AR'A V'AD RUM REKI'A - from the depth of the earth until the height of the sky

10) [line 9] UMKA V'RUMA BI'SETAMA LO KANI - the depth and the height (i.e. the rights to build beneath the foundation of the house, and the rights to the roof and airspace above the roof), when not specified, are not acquired by the buyer

11) [line 12] MECHILOS - underground rooms/caves/caverns

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