Explanation: It says so in the Beraisa of 49 Midos, and also in Eruvin. (This Beraisa was known to the Rishonim. It was lost from us (Daf Al ha'Daf). Presumably, Tosfos cites these sources to show one may rely on this approximation. It is known that this is only an approximation - PF.)

Explanation #1: When you surround Ula's tree (a circle inside a square of side 32) with a strip two thirds of an Amah wide, [the area] will be as big as the tree of the Mishnah, which exceeds [Ula's] by [the area of a rectangle] 65 and a third Amos [length], for a width of one Amah. (Ula's tree has area 768. The Mishnah's tree is 65 1/3 more, i.e. 833 1/3.)

If you surround a square of 32 by 32 Amos [with a strap two thirds of an Amah thick], you will need a length of 128 (next to the four sides), and for the four corners another eight thirds. This is a total of 130 and two thirds long, for a width of two thirds of an Amah.

Note: In each corner, we add a square of side two thirds of an Amah. If we put the four squares side by side, this forms a rectangle eight thirds long, for a width of two thirds of an Amah.

Deduct the quarter that a circle is less [than a square, from this 130 and two thirds], and 98 remains.

Similarly, if you cut 65 and a third Amos into three parts, lengthwise, it will be one strip 196 long a third wide. Cut it in half and put the halves side by side, and it will be a strip 98 long and two thirds of an Amah wide. (This shows that the above addition to Ula's tree makes it equal the tree of the Mishnah.)

Explanation #2: The Ri found in a Sefer, explicit in the margin, to surround Ula's tree (a circle of radius 16) with strings, until the width of the string[s] is two thirds of an Amah, [all] around.

Cut the strings and spread them out. The top (outermost) has length 100, for it surrounds [a circle of diameter] 33 and a third (for we added two thirds on each side), and for every Tefach of width (diameter), there are three Tefachim of circumference;

The bottom (innermost string) has length 96, for it surrounds [a circle of diameter] 32. The bottom [string] is two Amos shorter than the top on all (i.e. both) sides.

Cut off the excess [what the other strings extend past the bottom string] on one side, and (flip it over, and) bring it to the other side, so the long strings will complete the [deficiency of] the short strings, and now there will be a strip [of width two thirds, and its length is uniformly] 98. This is the same [area] as 65 and a third [length, and a width of one Amah].

Explanation #3: A square of side 33 and a third has area 1111 and a ninth [square] Amos;

Deduct the quarter [that a circle is less than a square], and 833 and a third remain. This shows that the tree of the Mishnah is 33 and a third by 33 and a third.

Explanation #4: Or, similar to this, a third of a [Beis] Se'ah is 16 and two thirds by 50 (since an entire Beis Se'ah is 50 by 50). Cut it in half and put the halves side by side, and it will be 25 long and 33 and a third wide.

Explanation #5: A Beis Se'ah is 100 by 25. Take a third for one tree. This is 33 and a third by 25;

This equals a circle of 33 and a third by 33 and a third, since a square is an additional outer quarter over the circle inside, which is an inner third. (An outer quarter means that the excess is a quarter of the bigger amount (the square). It equals an inner third, i.e. a third of the smaller amount (the circle).) This excess is eight and a third wide, and 33 and a third long;

Together, this is a square 33 and a third by 33 and a third. Make it round, so it will lack the quarter that you added, and it will be a circle 33 and a third by 33 and a third.

Explanation #6: According to texts that say "half an Amah remains", we can explain that Ula counts 16 in every direction, aside from the place of the tree. The place of the tree is a third by a third;

It turns out that Ula's tree is 32 and a third by 32 and a third. When you surround it on every side by a half Amah, it will be 33 and a third by 33 and a third. Make it round, so it will lack the quarter that you added, and it will be a circle 33 and a third by 33 and a third.

Explanation #7 (R. Meshulam): Ula does not count the place of the tree. The place of the tree is an Amah by an Amah. It turns out that Ula's tree is 33 by 33;

If it were square, it would be 1089: Deduct a quarter (because it is a circle), and 816 and three quarters remain. The text does not say "768 remain";

It turns out that the [area of the] tree of the Mishnah (833 and a third) exceeds Ula's tree by 16 Amos, a third and a quarter.

Explanation: "And half an Amah" refers to a Beis Se'ah, which is 50 by 50. When you remove half an Amah on the length and width, the lack is 50 [square] Amos less a quarter (49 and three quarters);

This is for three trees. For one tree it is 16 Amos and a third (a third of 49) and a quarter (a third of three quarters), and what remains is like a tree of Ula.

Question: This is also a leniency, for he brings Bikurim, and uproots them from Terumah and Ma'aser, like it says below (81b)!

Answer: Ula discusses only that he does not bring within 16. Outside 16, sometimes he brings, and sometimes he does not bring.

Implied question: According to how we establish this with 16 Amos, we must explain what is the Chidush!

Answer (Rashba): It comes to teach and infer that had he bought a tree Stam, he would not bring and recite;

If he bought two [trees], even Stam, he brings and recites, for he bought land, and this is like R. Meir, who says that one who acquired two trees, he acquired land.

Implied question: We could have asked from the Seifa! In Maseches Bikurim, the Seifa of [the Mishnah] brought here explicitly teaches that one who buys three trees in another's property, he brings and recites!

Answer: It is the style of the Gemara in several places, that it derives what it can from the Reisha [even if it is explicit in the Seifa].

Question: We say below (82a) that [one who buys] three [trees,] he acquired land. How much? Under them, between them and outside them, the amount for the harvester and his basket.

Answer: That is when the tree's branches are very big, and extend past 16 Amos.

Question: One who buys one tree, why doesn't he bring and recite, according to the opinion that Kinyan Peros (the right to eats the produce) k'Kinyan ha'Guf (is like permanent ownership of the property itself)?

Why is it different than one who sells his field for Peros? [The buyer] brings and recites, according to that opinion, like we say in Gitin (47b)!

Suggestion: This Tana holds that Kinyan Peros Lav k'Kinyan ha'Guf.

Rejection: R. Meir holds that it is like Kinyan ha'Guf, in Gitin (48a) and Bava Kama (90a), and he holds that one who buys one tree, he brings and does not recite!

Answer #1: There is different, for the land is acquired to him until a fixed time. Here, if the tree will dry up right away, he has no rights in the land.

Answer #2: There, the land is acquired to him for anything, to spread out Peros or seed it with beets and vegetables. Regarding a tree, he has rights only for nurturing.

Explanation (Rashi): The text does not say Viduy, for it is not written in Viduy Ma'aser Sheni "me'Artzecha", and not "Adamah Asher Nasata Li."

Implied question: It says [in Viduy Ma'aser] "u'Varech Es Amecha Es Yisrael v'Es ha'Adamah Asher Nasatah Lanu"!

Answer: This does not mean that he has a share [in the land]. Rather, [Hash-m gave it] to all of Yisrael.

Objection: You are forced to say that there is no Viduy without land, for in the Yerushalmi, [a Beraisa explaining our Mishnah] taught "also Viduy" [applies to any amount of land]!

Observation: In any case, the text of our Mishnah does not mention it. Since [Viduy] was taught about our Mishnah in the Yerushalmi, this shows that it is not in the Mishnah itself.

Explanation: However, one may not write a Pruzbul on Metaltelim, because one can eradicate them (and the lender will be unable to collect), and this is an uncommon loan;

Implied question: One can eradicate a flowerpot with a hole. Why may one write a Pruzbul on it?

Answer: Rabanan did not distinguish among [matters that are considered] land.

Implied question: Why may one write a Pruzbul on any amount of land? (This is an uncommon loan, for the lender is assured of collecting only a small amount!)

Answer #1 (Rashbam, in Gitin 37a): Ona'ah (overcharging) does not apply to land. [Since one could sell the land for any amount,] it is as if he has collateral for the entire loan.

Rebuttal: Granted, the law of Ona'ah (if one was overcharged a sixth regarding Metaltelim, the sale stands and he gets back what he overpaid) does not apply to land, but Bitul Mekach applies [if what he overpaid is] above half [the price. Therefore, one cannot sell land for more than twice its value!]

Answer #2: Rather, it is because one can collect [the land for part of the debt, sell it back,] and collect it again, like the episode with the plot of Abaye (Kesuvos 91b). Through this, one could collect his entire debt.

Support: We find like this regarding one who lends money to a Kohen, [Levi or Oni, on condition that he will keep tithes that the borrower is entitled to receive, and deduct their value from the loan]. If [the borrower died and] left land the size of a needle [point], the lender may collect (keep tithes worth) land the size of an axe (far more. See also Tosfos in Gitin 37a, Kidushin 26b).

Implied question: Wheat nurtures three Tefachim, like is proven in Shabbos (85a)!

Suggestion: Perhaps when the Mishnah cited here says "any amount", it is not precise.

Rejection: In Kidushin (26a), we bring this in the Sugya of whether or not we require [Metaltelim acquired Agav, i.e. along with land to be] gathered [on the land];

We ask [if they must be on the land], what can one acquire Agav any amount?, and answer that a needle was inserted in the land. The Gemara asks "did the Tana elaborate to teach [how one can acquire] a needle?!", and answers that a gem hangs from it.

Inference: We truly discuss Mashehu of land!

Answer: Granted, it nurtures three Tefachim. In any case, its primary nurturing is right where it is;

Also a tree nurtures for 25 [Amos], but in any case, its primary nurturing is within 16 [Amos].

Reference: In Bava Metzi'a (107a) Rav and Shmuel argue about a tree that leans over the border;

Rav says that what leans on this side is like this side, and what leans on this side is like this side. Shmuel says, they divide.

Rashi explained there that we discuss where the roots lean. Therefore, our Sugya here is like Rav, that it depends on the roots.

The Rashba explained differently there. (Tosfos there says that we discuss a tree on the border. Its roots are half in Reuven's property, and half in Shimon's, but most of the foliage is on Reuven's side.)

Reference: In Bava Kama (82a) the Gemara asks why this is not listed among the 10 stipulations Yehoshua made, and it answers. (An Amora, R. Yehoshua ben Levi, taught that Yehoshua made 10 enactments. R. Yochanan argues with him.)

Explanation (R. Chananel): "Chaluli" denotes fear. They make a wooden form that looks like a man, and a bird cannot stay there.

The Beraisa teaches that this does not suffice. Even though the bird flees, sometimes it leaves flesh of a Mes that it brings in its mouth, and it remains on the branch;

Therefore, the only solution is to cut all the branches.