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A Besulah who is pregnant is permitted to a Kohen Gadol. (1)
There are various opinions regarding the distance between the upper and lower waters. (2)
Upon seeing the angel in charge of writing the merits of Yisrael sitting as he wrote, Acher went off the proper path. (3)
Each person has a share both in Gan Eden and in Gehinom. A Tzadik merits his own and his friend's portion in Gan Eden, while a Rasha is punished with his own and his friend's portion in Gehinom.
Torah is difficult to acquire like gold utensils and easy to lose like glass utensils.
When Acher died, he was not judged because he had learned Torah, and he did not go to Olam ha'Ba because he had sinned. (4)
A person should learn Torah only from a Rav who is similar to an angel of Hashem. (5)
A Torah sage is compared to a nut. Just as a nut that became dirty remains clean inside, the Torah of a Talmid Chacham who sinned remains pure.
Hashem is pained when the blood of Resha'im is spilled, and all the more so when the blood of Tzadikim is spilled.
Do'eg and Achitofel asked 300 inquiries regarding the Halachos of a flying container, and yet they are included among the three kings and four ordinary people who have no share in the World to Come.
The reason why Acher became a heretic was because he always sang Greek songs, and when he stood up in the Beis Midrash, heretical books would slip off his lap.
A BIT MORE
1. Even though a Kohen Gadol may marry only a Besulah, we assume that she is still a Besulah and that she conceived [from Shichvas Zera that was present] in a bathtub in which she bathed.
2. One opinion is that they were separated by three-fingerbreadths. Another opinion is that they were separated by the width of a thread. A third opinion is that they were separated by the distance between two planks in a bridge. A fourth opinion is the distance between two garments that are lying on each other. A fifth opinion is the distance between two cups that are placed on each other inverted.
3. There is a tradition that there is no sitting, competition, backside, or fatigue in Shamayim. Therefore, when Acher saw the angel sitting, it led him to heretical thoughts.
4. Rebbi Meir said, "It is better that he should be judged and punished and [eventually] go to Olam ha'Ba. When I will die, I will ensure that smoke will rise from his grave." When Rebbi Meir died, smoke arose from the grave of Acher.
5. A Gadol ba'Torah may learn from a teacher even though the teacher is not similar to an angel of Hashem.
The Gemara says that the source of the heresy of Acher was his incessant singing of Greek songs. Rashi says that such songs are forbidden after the destruction of the Beis ha'Mikdash. The Maharsha asks that if the problem was that he was singing following the Churban, what is the difference if he was singing Greek songs or Jewish songs? Moreover, the prohibition against singing after the destruction of the Beis ha'Mikdash is not so severe that it should be the source of his heresy. Therefore, the Maharsha understands that the problem was that the songs were Greek and contained heretical content. Those heretical songs eventually led him to heresy.
One should not learn from a teacher who is not following the proper path, even though he is a great scholar and the entire nation needs his scholarship. Only when he returns to the proper path may one learn from him. (Shulchan Aruch YD 246:8)
Although the Gemara says that a Gadol ba'Torah may learn from a person who is not similar to an angel of Hashem, the Shulchan Aruch does not permit it because nowadays no one has the status of a Gadol ba'Torah in this regard. (Shach)
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