Ask A Question about the Daf

Previous daf

Eruvin 78

1) THE LENGTH OF A LADDER NEEDED TO REACH THE TOP OF A WALL

OPINIONS: The Gemara (77b) says that a ladder placed against a wall serves to lower the height of the wall so that it is no longer 10 Tefachim high (and the top of the wall may be used by the Chatzer). The Gemara records several opinions as to how long the ladder must be:

(1) Rav Yehudah in the name of Shmuel says that a wall that is 10 Tefachim high needs a ladder which is 14 Tefachim long.
(2) Rav Yosef says that the ladder must be 13 Tefachim and a bit.
(3) Abaye says that the ladder can be 11 Tefachim and a bit.
(4) Rav Huna brei d'Rav Yehoshua says that the ladder can even be seven Tefachim and a bit.

What is the reason for these measurements, and what are the Amora'im arguing about?

(a) RASHI says that the Amora'im are arguing about how close to the top of the wall the ladder has to reach.

1. Rav Yehudah maintains that the ladder must reach the top of the wall. According to Rav Yehudah, the ladder must be 14 Tefachim, because not only is it necessary for the ladder to reach the top of the wall (for which a 10-Tefach ladder would have sufficed), it is also necessary for the ladder to be placed at an angle so that one can climb up easily. The the foot of the ladder must be on the ground four Tefachim away from the wall in order to achieve an ascendable slope, and thus the length of the ladder must be 14 Tefachim (10 for the height of the wall, and 4 for the distance from the wall to the foot of the ladder).

2. Rav Yosef requires the ladder to reach within a Tefach of the top of the wall, since a Tefach is a negligible distance. He agrees that the foot of the ladder must be 4 Tefachim away from the wall.

3. Abaye requires the ladder to reach within 3 Tefachim of the wall, because within 3 Tefachim, Lavud works to make it as if the ladder is at the top of the wall. Abaye, too, agrees that the foot of the ladder must be 4 Tefachim away from the wall.

4. Rav Huna brei d'Rav Yehoshua agrees with Abaye, that the ladder need only reach within 3 Tefachim of the top of the wall. He maintains, however, that it suffices to place the ladder vertically against the wall, and it does not have to be placed 4 Tefachim away.

TOSFOS (DH Tzarich) points out an error in the mathematical calculations of Rashi's explanation. Rashi says that the ladder must be 14 Tefachim long, according to Rav Yehudah, because it must reach the top of the wall which is 10 Tefachim high, and its foot must be 4 Tefachim away from the wall. Such a ladder, though, would be considerably less than 14 Tefachim high -- it would only need to be the diagonal of a rectangle which is 10 X 4, or approximately 10.8 Tefachim long! The foot of a 14-Tefach long ladder, when its top is placed at the top of the wall, would reach *10*, and not 4, Tefachim away (since 14 is the diagonal of a square which is 10 X 10). How could Rashi make such a blatant error?

It seems that Rashi is consistent with his opinion elsewhere (Shabbos 85a, Eruvin 5a, 76b, 94b). Rashi seems to maintain that the Rabanan established a Halachic definition whereby when any distance-based Halachah is obtained by measuring the diagonal of a rectangle or square, the diagonal is obtained by *adding the two sides* that create the diagonal, which is simpler than calculating the diagonal itself (see Insights to Eruvin 5:2, 76:2:c).

(b) TOSFOS (DH Rav Yosef) disagrees with Rashi's explanation Rather, Tosfos cites the RI who explains that the Amora'im are not only arguing how high on the wall the ladder must reach, but they are also arguing how far the foot of the ladder must be placed away from the wall. The all, agree, though, that the ladder must be distanced from the wall the *same distance* as the *height* that the ladder must reach. (That is, the ladder forms the hypotenuse of an isosceles triangle.) When each Amora gave a measurement for the length of the ladder, he were not giving the exact length of the ladder; rather, he was giving a number which would serve as a reminder to know how close to the top of the wall (and how far away from the wall) the ladder must be.

1. Rav Yehudah requires the ladder to reach the top of the wall, a height of 10 Tefachim. Therefore, he requires that the foot of the ladder be 10 Tefachim away from the wall. The length of the ladder, then, comes to 14 Tefachim.

2. Rav Yosef requires the ladder to reach within a Tefach of the top of the wall, and therefore the foot of the ladder must also be just over 9 Tefachim away from the wall. The diagonal of those dimensions comes to 12.6. Thus, Rav Yosef requires a ladder whose length is a bit plus 12.6.

3. Abaye requires the ladder to reach within 3 Tefachim of the top of the wall, and therefore the foot of the ladder must also be just over 7 Tefachim away from the wall. The diagonal of a 7x7 square comes to 9.8 (using Chazal's calculation of 1.4xS), and thus Abaye requires the ladder to be a bit more than 9.8.

(As far as why Rav Yosef says 13 and a bit when the ladder needs to be only 12.6 and a bit, and Abaye said 11 and a bit when the ladder needs to be only 9.8 and a bit, the MAHARSHA explains that they were expressing the length of the ladder in terms of the height of the wall which the ladder must reach (as a "Siman b'Alma"). That is, Rav Yosef says that the ladder must reach just less than a Tefach from the top of the wall, and thus 14 (the length of Rav Yehudah's ladder) minus a little less than a Tefach is 13 and a bit. Abaye, too, says that the ladder must reach just less than 3 Tefachim from the top of the wall, and 14 minus just less than 3 equals 11 and a bit.)

4. Tosfos explains Rav Huna brei d'Rav Yehoshua's opinion like Rashi; the ladder need only reach within 3 Tefachim of the top of the wall, and may be placed vertically against the wall.

QUESTION: We see from the various opinions in the Gemara (see previous Insight) that the ladder must reach the top of the wall (or within 3 Tefachim of the top) in order to permit using the top of the wall and to permit the two Chatzeros on either side of the wall to make one Eruv together.

Why is that? The Gemara earlier (77b) discussed diminishing the 10-Tefach height of the wall by placing a platform (Itzteva) on the ground next to the wall. The platform certainly did not have to reach to the top of the wall! Similarly, the Gemara earlier on this Amud said that a ledge (Ziz) protruding from a wall can also decrease the 10-Tefach height of a wall. Why, then, does a ladder have to reach to the *top* of the wall?

ANSWERS:

(a) TOSFOS (77b, DH Im) says that the platform or ledge must be four *by four* Tefachim -- that is, it must be four Tefachim in both length and width. Such a ledge diminishes the height of the wall even when it is not near the top of the wall, but ten Tefachim below the top. A ladder, though, is only four Tefachim in one dimension, and it is not both four Tefachim wide and long. Therefore it must reach the top of the wall.

(b) RASHI does not seem to accept this reasoning as he allows a ledge to diminish the height of a wall even if it is 4 Tefachim in only one dimension (77b DH she'Shelivosav). He must have had another answer to this question. The MAHARAM M'ROTENBURG (who follows Rashi's ruling), quoted by the ROSH, answers that the Gemara earlier was discussing how to decrease the height of the wall so that the Chatzer on the side of the wall where its height has been diminished may be considered the sole user of the wall. That is, that Chatzer is considered to have easy access and use of the wall, as opposed to the Chatzer on the other side of the wall. To accomplish that, diminishing the height by placing a platform or a ledge along the wall will suffice.

Here, though, the Gemara is discussing making a Pesach, an entranceway, in the wall, so that the Chatzeros adjoining the wall on either side may make one Eruv Chatzeros together. In order to be considered a "Pesach," the ladders must reach to the *top* of the wall, and not just diminish its height to less than 10 Tefachim.

78b