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The Gemara asks:
Now,
by
how much is
the area of
a square greater than the
area of a
circle
with a diameter the length of the side of that square? It is greater by
one-quarter
of the area of the circle. If so,
768
square cubits, three-quarters of 1,024,
remain
for each tree, but
there still remains half a cubit
more based on the mishna’s calculation. In other words, the measurement would be more accurate if a tree is considered to draw nourishment from a distance of sixteen and a half cubits on each side…
Bava Batra 27a:4
Rabbi Yoḥanan said: A circular window must have a circumference of twenty-four handbreadths, with two and a bit of them within ten
handbreadths of the ground,
so that when he squares
the window, i.e., if he forms the shape of a square inside it, it measures four by four handbreadths, and
a bit
of it
is then within ten
handbreadths of the ground. The Gemara poses a question with regard to this calculation:
Now, since
there is a general principle that
any
circle
with a circumference of three handbreadths is one handbreadth in diameter…
Eruvin 76a:16-76b:5
The mishna continues: If the cross beam is
round, one considers it as though it were square.
The Gemara asks:
Why do I need this
clause
as well?
Similar cases were already taught in the mishna. The Gemara answers:
It was necessary
to teach
the last clause
of this section, i.e., the principle that
any
circle
with a circumference of three handbreadths is a handbreadth in diameter.
The Gemara asks:
From where are these matters,
this ratio between circumference and diameter…
Eruvin 14a:18-14b:4
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