The Mishna (76b) taught that a solid ten-tefah (handbreadth) high wall dividing two courtyards will negate the possibility that the two hatzeirot (courtyards) will be able to join and make a single eiruv. Nevertheless, the Gemara (77b) teaches that if solid ladders are placed on either side of the wall, allowing free access between the courtyards, then the hatzeirot can be considered as one.
On our daf the Gemara discusses how long a ladder is needed in order for the courtyards to be considered connected. Several opinions are brought by the Gemara, each of which offers a different ruling on how high the ladder needs to be to permit the courtyards on either side of a ten-tefah high wall to share an eiruv.
Rav Yehuda said that Shmuel said: If a wall is ten handbreadths high, it requires a ladder fourteen handbreadths high, so that one can place the ladder at a diagonal against the wall. The ladder then functions as a passageway and thereby renders the use of the wall permitted. Rav Yosef said: Even a ladder with a height of thirteen handbreadths and a bit is enough, as it is sufficient if the ladder reaches within one handbreadth of the top of the wall.
Abaye said: Even a ladder that is only eleven handbreadths and a bit suffices, as the ladder will still reach a height of over seven handbreadths, i.e., within three handbreadths of the top of the wall.
Rav Huna, son of Rav Yehoshua, said: Even if the ladder is only seven handbreadths and a bit it is sufficient, as he can stand the ladder upright against the wall. Since it will reach within three handbreadths of the top of the wall, the principle of lavud applies. Therefore, even a ladder placed in this manner is considered a valid passageway between the two courtyards.
The simplest way to explain these opinions is according to Tosafot, who argue that the ladder must allow easy access from one courtyard to the next. Therefore, it is reasonable to assume that the ladder is placed at a 45-degree angle, so that the distance on the ground from the wall to the beginning of the steps is the same as the height of the wall that the ladder reaches. The ladder is, in effect, the hypotenuse of a right triangle. This makes particular sense if the “ladder” being discussed looks more like steps than like the ladders with rungs that we are familiar with today.
Here is how these opinions would appear according to Tosafot:
A ladder that is 14 tefahim high will reach to the top edge of the ten-tefah wall – which is the requirement according to Rav Yehuda quoting Shmuel.
A ladder that is 13 tefahim high reaches above nine tefahim, fulfilling the requirement according to Rav Yosef, who allows the ladder to reach within one tefah of the top.
A ladder of 11 tefahim reaches above seven tefahim on the wall, which works according to Abaye, who rules that within three tefahim of the top suffices by virtue of the rule of lavud – that a gap of less than three tefahim is considered closed.
Rav Huna also makes use of lavud, but he believes that even a ladder placed directly against the wall will suffice.