May 23, 2013
The sixth chapter of Massekhet Eiruvin
dealt with situations where two courtyards joined together and became one unit for the rules of eiruv
and carrying on Shabbat
The seventh perek (chapter), which begins on our daf (page), opens by discussing cases where hatzeirot (courtyards) that are next to one another either
- cannot join each other,
- are obligated to join each other,
- or are permitted to do so.
The first Mishnah
deals with courtyards that are divided by a wall which has a window in it. If the window is within ten tefahim
(handbreadths) of the ground and is minimally four tefahim
square in size, then the courtyards can choose whether or not to join as one. If the window is higher than ten tefahim
or smaller than four by four, the hatzeirot
are considered separate and need to make their own eiruvin
in the Gemara
introduces the possibility of a round window, arguing that it would need to be 24 tefahim
in circumference in order to ensure that a square inscribed in that window would be at least four by four. In the ensuing discussion about the relationship between circles and squares, the Gemara explains that Rabbi Yohanan’s position is based on the rule taught by the judges of Caesarea
that “a square inscribed within a circle is half of the square.”
Later on in the Gemara, Rabbi Yohanan’s position is rejected in its entirety as being based on an error. Rabbi Ya’akov Kahane
in his Ge’on Ya’akov
argues that Rabbi Yohanan knew that his figures were not accurate, but chose to present a larger than necessary rule so that, in case of a mistake, there would be well over the minimum four by four, leaving room for error. Nevertheless, many attempts have been made to try and explain the mathematical positions presented by these Sages.
By drawing lines that bisect the outer square, the circle and the inner square, it becomes clear that the inner square is half the size of the outer one. The inner square is made up of four triangles, each of which is half of the four smaller squares that together make up the outer square.
This essay is based upon the insights and chidushim of Rabbi Steinsaltz, as published in the English version of the Koren Talmud Bavli with Commentary by Rabbi Adin Steinsaltz, and edited and adapted by Rabbi Shalom Berger. To learn more about the Steinsaltz Daf Yomi initiative, click here.
To dedicate future editions of Steinsaltz Daf Yomi, perhaps in honor of a special occasion or