Eruvin 76b (עו:) — the Talmud in English

For

that statement

that a circumference of three has a width of one tefach applies

to a circle.

But to a square,

if one comes to circumscribe the square with a circle, until one finds within the circle a square whose side is four tefachim long,

we require

a circumference

greater [

according to Rashi, Sukkah 8a].

The initial assumption was that it would be sufficient for the circumference of the round window to equal the circumference of a four-by-four window [Meiri].

Therefore we ask: In a square window of four by four, there is an internal circle whose width at its midpoint [its diameter] is four tefachim, equal to the width at the midpoint of the square.

To draw this circle, one must multiply its diameter by three [as we say: Anything whose circumference is three has a width of one tefach],

since

indeed

how much greater is the circumference of the outer

circle than the circumference of the inner

square

than the circumference of the inner

greater than the circumference

of

circle?

inside it by

One quarter “from the outside” [that is, an addition of one third to the circumference of the circle].

Since a circle whose diameter is four requires a circumference of twelve tefachim, as we said, if one must circumscribe the outer square—which is four by four, one must add one third to twelve, and

sixteen—

the circumference of a round window—

is sufficient,

since with this circumference it would be possible to circumscribe a four-by-four window. See Tosafot, Sukkah 8a?! And we answered:

That statement—

that it is sufficient to add one quarter from the outside—applies to

a circle emerging from within

[that emerges from]

a square.

That is, if one comes to calculate the circumference of the outer square from the circumference of an inner circle, and one knows the circumference of the inner circle, one must add one quarter, and one thereby obtains the circumference of an outer square.

But

here this is not sufficient. Rather, we need a complete four-by-four square in the window’s opening, circumscribed by a circle, contrary to what we had assumed until now.

This is

a square emerging from within a circle,

and one comes to determine the circumference of the outer circle when the given measurement is the circumference of the inner square [which in our case is sixteen tefachim];

we require

adding to it

more

than one quarter.

What is the reason?

Because of the projection of the corners [the addition represented by the diagonal of the square, running from corner to corner]. That is, the width of the circle wherever it is measured is equal to the width of the square’s diagonal. In the inner square, however, its width is not equal to this width, except from one corner [angle] of the square to another corner; therefore, the circumference of the outer circle requires an addition greater than one quarter over the circumference of the inner square.

And we ask: Ultimately, we do not require all this, since we need only to triple the length of the square’s diagonal—which is the width and diameter of the circle—according to the calculation that “anything whose circumference is three has a width of one tefach.”

Let us examine this:

Since, every square amma

has an amma and two fifths on its diagonal [every square amma: its diagonal is one amma and two fifths], and in a four-by-four window its diagonal, according to this calculation, is five amot and three fifths.

If so, if the circumference of the round window is

If so, if the circumference of the round window is

of

the length

of seventeen and five tenths [seventeen amot less five fifths]

[seventeen cubits less one-fifth of a cubit],

is also sufficient,

since that is the result of tripling five amot and three fifths. Why do I need twenty-four tefachim?!

And we answered:

Rabbi Yohanan,

the master of this statement concerning the round window,

said [

held]

in accordance with the judges of Caesarea [

a place].

And some say, in accordance with the Rabbis of Caesarea, who say:

A circle from within a square

is one quarter: the circumference of the inner circle within every square is smaller by one quarter than the outer square [as we said: By how much is a square greater than a circle? One quarter]. And

a square from within a circle

is one half.

That is, the circumference of the inner square within the circle is smaller than the outer circle by half the circumference of the inner square, namely, by one third of the outer circle; thus, the circumference of the square is two thirds of the circumference of the circle.

The reason is that, according to their view, every square amma has two amot on its diagonal [Tosafot]. Thus, in order to circumscribe a square of one by one amma with a circle, one must triple two amot, which is a circumference of six amot. Since the circumference of the square is four amot, this gives two thirds of the circle’s circumference. And in order to circumscribe a square window of four by four tefachim, whose diagonal according to this calculation is eight tefachim, the circumference of the circle is found to be twenty-four tefachim—which is Rabbi Yohanan’s statement! In the Gemara, tractate Sukkah, folio 8b, they said concerning the words of the judges of Caesarea: “That is not so, for we see that it is not so much” [we see that it is not as great as they said].

We learned in the Mishna:

Less than four by four,

or higher than ten, permits establishing two eruvin but does not permit establishing one.

Rav Naḥman said: They taught this only

that the window must have part of it within ten tefachim

with regard to a window between two courtyards.

But with regard to a window between two houses, even if

the window was

higher than ten

tefachim above the house’s ground,

nevertheless, if they wish to establish an eruv

together,

they may establish one.

What is the reason?

A house

is considered as though it is filled. Since the house is roofed, it is considered full, and it is as though the window is not ten tefachim high, since the entire house is filled [Mishna Berura; see also Gaon Yaakov. See there the view of Rabbeinu Yehonatan].

Rava raised an objection to Rav Naḥman

from what we learned in a beraita:

The same applies to me for a window between two courtyards,

and the same applies to me for a window between two houses.

And the same applies to me for a window between two upper stories,

and the same applies to me for a window between two roofs [for according to the Sages below, folio 89a, it is prohibited to take an object from one person’s roof to another’s until they establish an eruv between them—Rashi. See also Gaon Yaakov].

And the same applies to me for a window between two rooms—

in

all of them

the window must be

four

tefachim

by four

tefachim, and the window must be

within ten!

We see that even a window between two houses must be within ten. This is difficult for Rav Naḥman?!

And we answered:

Interpret it:

establish the statement of the beraita that the window must be within ten as referring to

a

window between two

courtyards

alone, and not to a window between two houses.

And we ask:

But it says, “The same applies to me”!

This indicates that all the cases are equal in their law.

And we answered:

Interpret it:

the meaning of “the same applies to me,” which indicates that all the cases are equal, applies only with regard to the first law,

a

window

four by four.

It does not apply to the second law, that the window must be within ten.

We have established that a staircase is considered an “opening.” If there is a staircase between two courtyards with a partition between them, then, if they wish, they may establish one eruv.

Rabbi Abba asked Rav Naḥman: A skylight,

a round opening,

open from the house to the upper story,

where the house belonged to one person and the upper story to another, and they wished to establish one eruv together—

Do we say that since the skylight is higher than ten tefachim above the house’s ground, they cannot establish one eruv through it [as with a window higher than ten, through which one may not establish an eruv], but rather

it is necessary

to install a

staircase

of steps,

fixed,

in order

to permit it

through the skylight?

Or

perhaps we say: A house is considered as though it is filled. Therefore, the skylight is not considered ten high, and they may establish an eruv between them through the skylight,

and there is no need for a fixed staircase to permit it.

Rabbi Abba explains his uncertainty: Is it that

when we say

“a house is considered as though it is filled,”

that statement

applies with regard to a window

at the side

of the wall,

but in the middle,

at the height of the house’s roof,

we do not

say that the house is filled there as well?

Or perhaps -

it makes no difference

whether the side of the house is from its midpoint?

He said to him

Rav Naḥman said to Rabbi Abba:

It does not require

a ladder. For the house is considered as though it were filled, even with regard to a skylight in the middle of the roof!

They thought to infer:

specifically,

it is a fixed ladder that does not require

being there so that they can establish an eruv through the skylight.

But a temporary ladder -

is required

to be there.

But

it was stated:

Rav Yosef bar Minyomi said that Rav Naḥman said: Both a fixed ladder and a temporary ladder -

do not require one.

Mishna:

A wall between two courtyards, ten

handbreadths

high and four

handbreadths

wide -

the courtyards may establish

two

separate eruvin, one eruv for each;

but they may not establish one

in order to carry from one to the other through the small openings between them.

If there were

on top of this wall, which was four handbreadths wide,

produce -

the people

of the one

courtyard

go up from this side and eat

on top of the wall.

And

the people

of the other

courtyard

go up from this side and eat.

See illustration

Provided that they do not lower

the produce

downward [

below -

later, 92a].

For the wall is jointly owned by both of them, and it is prohibited to take something out from a jointly owned courtyard into an individual’s courtyard, [as will be explained further in the Gemara].

But if the wall was less than four handbreadths wide and is not an independent domain, the Gemara below immediately discusses what its status is.

(If it was breached) [

If it was breached -

Rif, variants of the text]

the wall

between them, if the breach was

up to ten cubits [

including ten] and the wall was not breached across its entire width,

they may establish -

if they wish -

two

separate eruvin, and each courtyard is permitted on its own, but they may not carry from one to the other.

And if they wish, they may establish

one

eruv

and they are permitted even to carry from one to the other.

The reason that, if they wish, they may establish two eruvin, and one courtyard does not prohibit the other, is

because it is [

the breach between them]

like a doorway.

For this is the measure of a doorway everywhere, and the courtyards are not breached into one another in a manner that would cause one to prohibit the other; rather, a partition—with a doorway in it—separates them!

If the breach was

wider than this [

ten cubits], it is a “breach,” since it is in the partition separating them, and not a “doorway” [and likewise if the courtyard was breached across its entire width and no projecting remnants of the wall remained], the residents of the two courtyards are considered as though they all live in one courtyard [Rashi].

Therefore:

they may establish one

eruv and everyone may carry throughout both courtyards;

but they may not establish two

even in order to permit carrying within each courtyard separately, since this is like residents of one courtyard who divided their eruv: they have accomplished nothing, and each group prohibits the other.

Gemara:

Introduction:

We learned below, on page 89a, and it was cited above, on page 74a:

Rabbi Shimon says: Roofs, courtyards, and enclosed fields are all one domain with regard to vessels that had rested in them, but not with regard to vessels that had rested inside the house.

It is permitted to carry from one person’s courtyard to another person’s courtyard vessels that had rested in the courtyard, because the courtyards are not considered separate domains merely because their ownership differs, in a manner that would prohibit carrying from one courtyard to another as though these were two domains.

Only houses themselves are considered separate domains, because they are fixed dwelling places - Rashi below, 91a].

But vessels that had rested inside the house and were taken out into the courtyard, even by means of a permitted act, may not be carried from one courtyard to another.

And we read below, on page 91a, and likewise cite it above, on page 74a:

Rav said: The halakha is in accordance with Rabbi Shimon [that the courtyards are one domain with regard to vessels that had rested in them], provided that they did not establish an eruv [the residents of one of the courtyards - Ritva].

But if they established an eruv, they may not [carry from one courtyard to the other even vessels that had rested in the courtyard]. For we issue a decree prohibiting the carrying of courtyard vessels, since it is common for vessels that had rested inside the house to be present in the courtyard, having been taken out there through the eruv they established; and perhaps one will come to take vessels belonging to the houses out into the courtyard.

But Shmuel and Rabbi Yoḥanan disagreed with him there, and ruled in accordance with Rabbi Shimon, whether they established an eruv or whether they did not establish an eruv. In their view, no decree was issued against courtyard vessels even when house vessels are now present in the courtyard.

And in the Gemara below, on page 92a, we prove from the anonymous Mishna here, which teaches: “provided that they do not lower them downward,” that it is prohibited to take something from one courtyard to another even when it is a vessel that had rested inside it [i.e., the produce], in a place where they established an eruv, and this is in accordance with Rav.

For you are compelled to say that the reason it is prohibited to lower the produce from the wall into the courtyard [which is like carrying from one courtyard to another] is that the Mishna is speaking of a case where they established an eruv, and carrying from one to the other was prohibited by decree, lest one bring vessels from the courtyard that had rested in the house up onto the wall [Rabbenu Yehonatan. See there]; and this supports Rav.

And according to the one who does not issue this decree, we reject this proof there, explaining that what is meant by “downward” is “downward into the houses.” That is, in truth, carrying from the wall to the courtyard is permitted; only bringing something into the houses is prohibited.

If it does not have

the wall between two courtyards a width of

four

handbreadths -

what

is its status with regard to carrying from the courtyards onto it and carrying on top of it?

Rav said: The airspace of the two

domains

on its two sides

controls it.

Therefore:

one may not move on it

produce that had rested on top of it,

even

as much as

a hair’s breadth [

like a strand of hair].

And Rashi explained: Since it is not significant enough to be considered a domain [as it does not have the measure of a domain that could stand independently], it is subordinate to both of them, and the domains of the two courtyards control it and prohibit one another; and it is prohibited to carry even on top of it.