י"ז תשרי תשפ“אMon, Oct 5 2020 

OVERVIEW of the Daf Distinctive INSIGHT 1) The Levite cities (cont.) Measurements of Chazal דאמר מר כל אמתא בריבוע אמתא ותרי חומשא באלכסוא The last two explanations that explain how the open area surrounding the Levite cites represents one-fourth the total area As the master stated: Every amah of a square makes a diagonal that are presented. is one and two-fifths. R’ Ashi explains that although for techum purposes we treat points out that the Gemara’s ( ד"ה כל אמתא) a round city as though it were square the Levite cities remain T osafos round and the circular strip of open space around them remains calculation that the diagonal of a square is one and two-fifths complete. the length of its side is inaccurate. The actual length of the R’ Ashi also explains how the residents of a round city gain diagonal is slightly larger, approximately 1.414. The Tashbatz eight-hundred amos in the corner of the squared techum area. writes that although this and other (שו"ת תשב"ץ סי' קס"ה) 2) : The Mishnah discusses the size and the circum- measurements of Chazal are slightly imprecise, we nonethe- stances when an open area is granted to a city before the two- thousand amah techum is measured. less treat them as though they are completely accurate. This which states that ( ע' לעיל ג: ) The source for providing a city with open space is based upon the rule (3 4) Clarifying the opinion of Chachamim measurements are part of Halachah L’Moshe MiSinai. In a R’ Huna and Chiya bar disagree regarding the opinion of similar fashion, Tosafos HaRosh explains why the Gemara ( quoted a pasuk to demonstrate that the circumference of ( יד. Chachamim. According to R’ Huna a karpaf of space (70 2/3 amos) is granted each one of the two cities whereas according to a circle is three times its diameter. Even though the measure- Chiya bar Rav one karpaf is shared by the two cities. ment is not exact, the pasuk teaches that for purposes of hala- The Gemara unsuccessfully attempts to prove one of the two chah, the ratio of three to one is sufficient. writes that the ( מצוה רח ) opinions correct. The Sefer HaChinuch In the course of the Gemara’s discussion R’ Chanina is quot- measurements of Chazal are imprecise and therefore should ed as explaining that the case in the Mishnah of three cities refers not be relied upon for exact measurements. The reason to a configuration where the cities are not in a row but rather Chazal utilized these imprecise measurements rather than shaped like a triangle. The novelty of the ruling is that we can being more accurate was that they erred on the side of strin- look at the middle city as if it were in a row with the other two to gency. Our Gemara is an example. Using precise measure- be able to consider them one large city. ments the size of the techum is slightly larger than what a cal- rules that the above ruling applies only if the middle city is not more than two-thousand amos from the outer cities to culation using one and two-fifths will yield. Nonetheless, they the middle. chose to round down as a precaution. If, however, one is Abaye further rules that there is no limit as to how far the measuring a friend’s field he should not use the ratio of 1:1.4 outer two cities are from one another. because that would violate the prohibition against measuring An example of two cities merged because an interval of great- inaccurately. er than seventy and two-thirds amos did not exist is presented. The Mishnah Berurah rules (Sha’ar HaTziyun 372:#18) 5) MISHNAH: The procedure for measuring the techum is de- that even though these measurements are not precise, one scribed.  may nonetheless rely upon them for calculations because of the difficulty in measuring more accurately. One may certain- ly be lenient for issues that are only rabbinic . The Chazon REVIEW and Remember Ish maintains that even regarding Biblical issues these meas- urements may be used, because this manner of evaluation is ? סביב What are the two translations of the word .1 included in the rule that measurements are Halachah 2. How is the techum measured when two cities are not sepa- L’Moshe MiSinai.  rated by more than 141 and 1/3 amos? Today’s Daf Digest is dedicated לע" מרת יהודית בת הרב שמואל אלחן, ע"ה קירשבוים Why does Abaye differentiate between the arc-shaped city .3 and the three cities configured like a triangle? Today’s Daf Digest is dedicated 4. Is the slope of a hill or valley included when measuring the By Mr. and Mrs. Alan Matten techum of a city? In memory of their mother מרת חי' מאשה בת ר' דוד, ע"ה עירובין  ז“ —Number 275 HALACHAH Highlight Daf DIAGRAM שלשה כפרים המשולשים — אם Assuring that one’s tefillin are square יש בין שים כל אמתא בריבוע חיצוים וכו ‘ When the length of the side of a square is one amah

T he Gemara relates that the diagonal of a square that is one f there are 141 1 I amah by one amah is 1.4 amos. Tosafos notes that this number 1/3 amos be- is not precise and cites a proof to his assertion. Shulchan Aruch 2 tween the two rules that the diagonal of one’s tefillin should match the ratio outer towns, the that Chazal established that the diagonal of a square that is one third town which amah by one amah is 1.4 amos. This is the method that one is offset serves to should adopt when measuring the square of the batim as well as combine the the stitching. Sefer Orchos Rabbeinu 3 relates that someone visit- outermost villages ed the Chazon Ish and asked him if his tefillin were square. Cha- into one residen- zon Ish looked at them and replied that according to his eyes they tial entity, and are square. The questioner suggested to Chazon Ish that perhaps they are as one. he should use a measuring instrument to confirm that they are This is provided that the village which is offset is within 2000 precisely square. Chazon Ish responded that he already declared amos of the two towns which are aligned.  that they are square and these meet the requirement to be square that was given to Moshe on Har Sinai. This is consistent with his must be that one’s tefillin are considered even l’chatchilah square approach to many issues in which he ruled that halachah follows as long as they are square according to this ratio even though it is the way it appears to one’s eyes and did not require one to use not precisely square. After establishing this principle he goes on measuring instruments. to express surprise at the report of a Gadol who insisted that his Rav Moshe Feinstein 4 also did not require the use of a micro- tefillin should be measured with a microscope to assure that they scope to confirm that one’s tefillin are exactly square and suggest- are square.  .1 תוס' ד"ה כל אמתא. ed the following proof to his position. Shulchan Aruch mentions .2 שו"ע או"ח סי' ל"ב סע' ל"ט. that one’s tefillin should be square in accordance with Chazal’s .3 אורחות רביו ח"א עמ' שע"ה. ratio that the diagonal of a square that is one amah by one amah .4 שו"ת אג"מ יו"ד ח"ב סי' קמ"ו.  is 1.4 amos. Since we know mathematically that this is not true it

Yad Malachi: forbade, if the second rabbi is greater in Distinctive INSIGHT 1. This principle only applies if it is wisdom and age than the first rabbi he clear that the first Beis Din would not may reverse the first rabbi's ruling (Klalei Greater in wisdom and age have consented. However, if circumstances HaDinim, Ches §232). have changed to the extent that it is clear Igros Moshe, Yoreh Deah 1:127 cites ואור"ת דהלכה כרב הוא דאמר קרפף לזו that the first Beis Din would have consent- Chasam Sofer, Yoreh Deah §13, who וקרפף לזו דגדול היה בחכמה ובמין מחייא בר ed to rule differently, the second Beis Din רב דזוטר מייה טובא כדמוכח בסוף פרק יש may nullify the first one's ruling (§65). maintains that a rabbi in his city has the בערכין (דף טז) שהיה רב הוא מוכיחו — -same status as a Beis Din, and that there תוספות עירובין דף ז/א 2. This principle only applies to a nul- Rabbeinu Tam rules in accordance with Rav lification of the prior enactment. A second fore another rabbi cannot nullify the first Huna, because he was greater in wisdom and Beis Din may, however, add to the first rabbi's enactments unless he is greater in age than Chiya bar Rav. This principle, laid Beis Din's enactment (§66). [Elsewhere, wisdom and age than the first rabbi. Igros down in Avodah Zarah 7a, is similar to the however, Malachi seems to contradict Moshe clarifies that this is only in the case principle that a second Beis Din cannot nullify himself (Klalei HaDinim, Aleph §73).] of enactments. However, if the first rabbi the prior enactment of another Beis Din unless 3. A second Beis Din can nullify the had only consented to the congregation's first Beis Din's enactment temporarily it is greater than the first one in wisdom and in enactments, or had only issued advice, at times and in places where ,(הוראת שעה) numbers (Eduyos 1:5; see Ra'avad ad loc. for then the second rabbi may nullify the first the age factor). special exigencies exist (§67). Although a second rabbi cannot per- rabbi's ruling even if he is not greater than S ome parameters of this principle from mit that which another rabbi previously him in wisdom and age. 

Daf Digest is published by the Chicago Center, under the leadership of HaRav Yehoshua Eichenstein, shlit”a HaRav Pinchas Eichenstein, Nasi; HaRav Zalmen L. Eichenstein, Rosh Kollel; Rabbi Tzvi Bider, Executive Director, edited by Rabbi Ben-Zion Rand. Daf Yomi Digest has been made possible through the generosity of Mr. & Mrs. Dennis Ruben.