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Based on the Rashi's comment on Bereshis 18:1,

AND THE LORD APPEARED UNTO HIM to visit the sick man. R. Hama the son of Hanina said: it was the third day after his circumcision and the Holy One, blessed be He, came and enquired after the state of his health (Bava Metzia 86b)

Rabbi Eliyahu Mizrachi makes a long comment where he makes the following two suggestions:

  • According to Rabbonan the milla occured on Erev Pesach, the 14th of Nissan, and then in the afternoon Hashem and the angels visited Avraham Avinu, so that it can also be considered 15th of Nissan.
  • According to R. Chama bar Chanina, the milla was also made on the 14th of Nissan, but the visit of the angels occurred on the 17th of Nissan.

The commentary Nachalas Yaakov by Rabbi Yaakov Lorberbaum (missing in Sefaria) but quoted in Sifsei Chakhomim reviews a number of other conflicting aggados and suggests that according to all opinions the milla took place on the 12th of Nissan. We can easily see that Nachalas Yaakov corrects the R. Mizrachi's explanation of the opinion of R. Chama bar Chanina, but not quite his understanding of the opinion of the Rabbonan.

There is also a midrash Pirkei D'Rabbi Eliezer 29, which states:

Rabban Gamaliel said: Abraham sent and called for Shem, the son of Noah, and he circumcised the flesh of the foreskin of our father Abraham, and the flesh of the foreskin of Ishmael his son, as it is said, "In the selfsame day was Abraham circumcised, and Ishmael his son" (Gen. 17:26). "In the selfsame day" (means) in the might of the sun at midday. Not only that, but (it indicates) the tenth day of the month, the Day of Atonement. It is written in connection with the Day of Atonement, "Ye shall do no manner of work on that selfsame day, for it is a day of atonement" (Lev. 23:28); and in the present instance the text says, "In the selfsame day was Abraham circumcised" (Gen. 17:26). Know then that on the Day of Atonement (Yom Kippurim) Abraham our father was circumcised. Every year the Holy One, blessed be He, sees the blood of our father Abraham's circumcision, and He forgives all the sins of Israel, as it is said, "For on this day shall atonement be made for you, to cleanse you" (Lev. 16:30). In that place where Abraham was circumcised and his blood remained, there the altar was built, and therefore, "And all the blood thereof shall he pour out at the base of the altar" (Lev. 4:30). (It says also), "I said unto thee, In thy blood, live; yea, I said unto thee, In thy blood, live" (Ezek. 16:6).

We thus have 3 opinions about the date of Avraham Avinu's bris milla:

  1. Rabbi Chama bar Chanina according to Nachalas Yaakov says that it was done on the 12th of Nissan
  2. Rabbonan according to R. Eliyahu Mizrachi say that it was don on erev Pesach the 14th of Nissan (if not towards the evening of the beginning of the 15th of Nissan).
  3. Pirkei d'Rabbi Eliezer says it was done on the 10th of Tishrei - Yom haKippurim.

We have 2 questions:

A. Both according to Rabbi Eliezer (Rosh Hashanah 10b) and Rabbi Yehoshua (Rosh Hashanah 11a) Yitzchak avinu was born on 15th of Nissan, the day (or the next day) when the angel made a mark on a wall (Rashi on Bereshis 21:2). Can we use the suggestion of Nachalas Yaakov to explain how according to all opinions the Avraham's milla occured on 12th of Nissan, including the Pirkei d'R. Eliezer's?

B. Alternatively, if these are 3 different opinions based on different calculations what would be the calculations of Pirkei d'R. Eliezer, assuming that he knew the aggados mentioned by R. Mizrachi and Nachalas Yaakov?

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  • The Daas Zekeinim (Bereishis 18:14) adds at least one more opinion, but I don’t understand it clearly. But if the milah occurred on 14 Nissan, shouldn’t the third day be 16 Nissan as opposed to 17? (If the angels came on the 16th, it would explain Rashi (ibid) לאותו מועד המיוחד שקבעתי לך אתמול - “yesterday” being the 14th which can be considered the first day of Pesach.)
    – Yø-c Ro
    Commented Oct 6 at 19:52
  • @Yø-cRo Thank you for your comment! The opinion of Daas Zekeinim is exactly the opinion of rabbonan: 14th turning into 15th of Nissan. This is why I seprated it into the 2nd opinion. As far as your calculation about 16th - that is only possible if one is calculating a portion of the 14th day is like a whole day. But here they mean 3 times 24 hour periods i.e. 72 hours or 3 full days.
    – Y DJ
    Commented Oct 7 at 2:46
  • I’m quite sure shlishi l’milah is not counted מעת לעת. See e.g. Aruch Hashulchan Yoreh De’ah 262:2 דכשנתרפא ביום חמישי, לבלי למולו, מפני שיהיה שלישי למילה בשבת
    – Yø-c Ro
    Commented Oct 7 at 8:55
  • @Yø-cRo There are 2 points: 1. That would be only the case if Avraham could arrange the millah on Thursday on his own volition, so that the 3rd day would start on Shabbos. But Avraham performed the millah on the day he was commanded. I am not sure if the rules of techum Shabbos would even apply to visitting non-Jewish guests or angels on the 3rd day.
    – Y DJ
    Commented Oct 7 at 15:06
  • @Yø-cRo 2. Also, the same paragraph is about the circumcized children (2nd day is more dangerous than 3rd day), because for kids the wound heals quickly. Nachals Yaakov is really stressing the point, that for adults it's the opposite: as bodily moisture gathers at the bottom, the 3rd day after millah is by far more dangerous than the 2nd.
    – Y DJ
    Commented Oct 7 at 15:09

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