Shalom R' Pesach,

I think you are correct that if Rashi meant that the hive reaches a width of six Tefachim only at some point in the middle of its height, your question would arise. However, I do not think that this is what Rashi means by "b'Emtza'isah."

The entire discussion in Rashi is about the geometry of a round hive. A Reshus ha'Yachid requires an area of four by four Tefachim, and in order to fit a four-by-four square inside a circle, the diameter of the circle must contain the diagonal of that square. This is why Rashi immediately invokes the rule that the diagonal of a square is one and two-fifths times its side, arriving at five and three-fifths Tefachim, which Abaye rounds to six.

I therefore think that "b'Emtza'isah" means the width measured across the middle of the circular hive, i.e. its diameter. In fact, the word "b'Emtza'isah" is quite appropriate here: the relevant measurement is the line that crosses the circle through its center, which must be large enough to contain the diagonal of the required four-by-four square.

As you pointed out from Tosfos and Rabeinu Chananel, this is also the basic discussion of the Rishonim on the Sugya. Rashi, Tosfos, Rabeinu Chananel, and the other Rishonim are all dealing with the same basic calculation: how large the diameter of a round hive must be in order to contain the required area of four by four. The discussion between them concerns, among other things, whether the thickness of the walls is included in that calculation. Rabeinu Chananel understands Abaye's six Tefachim precisely and uses the additional two-fifths for the walls, whereas Tosfos rejects this and follows Rashi that Abaye's figure of six is not exact.

I think this also answers your first two points. Rashi does not say "Chalalah" because he is not simply telling us how wide the empty space is. He is describing the particular measurement that matters in a circular object: its width through the center. And the fact that Rashi immediately proceeds to discuss the diagonal and then whether Abaye's six is precise strongly supports this reading of "b'Emtza'isah."

Regarding your third point about the thickness of the bottom and the ten-Tefach height, I think this is a separate issue. Rashi here is explaining the particular Chidush in Abaye's distinction between a hive that is six Tefachim wide and one that is less than six. That is why he goes into detail about the calculation that produces the six-Tefach measurement. I do not think his silence here about how the ten-Tefach height is measured tells us how to interpret "b'Emtza'isah."

I think your basic Diyuk is a good one, but it actually helps clarify Rashi. "B'Emtza'isah" does not mean that the hive bulges out halfway up its height. It refers to measuring the round hive across its center, which is precisely the measurement needed for the diagonal calculation that occupies Rashi and the other Rishonim here.

I hope this helps,

Aharon Steiner