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שָׁלשׁ גְּרָנוֹת לְמַעְשַׂר בְּהֵמָה, בִּפְרוֹס הַפֶּסַח, בִּפְרוֹס הָעֲצֶרֶת, בִּפְרוֹס הֶחָג, דִּבְרֵי רַבִּי עֲקִיבָא. בֶּן עַזַּאי אוֹמֵר, בְּעֶשְׂרִים וְתִשְׁעָה בַּאֲדָר, בְּאֶחָד בְּסִיוָן, בְּעֶשְׂרִים וְתִשְׁעָה בְאָב. רַבִּי אֱלִיעֶזֶר וְרַבִּי שִׁמְעוֹן אוֹמְרִים, בְּאֶחָד בְּנִיסָן, בְּאֶחָד בְּסִיוָן, בְּעֶשְׂרִים וְתִשְׁעָה בֶאֱלוּל. וְלָמָּה אָמְרוּ בְּעֶשְׂרִים וְתִשְׁעָה בֶאֱלוּל וְלֹא אָמְרוּ בְּאֶחָד בְּתִשְׁרֵי, מִפְּנֵי שֶׁהוּא יוֹם טוֹב, וְאִי אֶפְשָׁר לְעַשֵּׂר בְּיוֹם טוֹב, לְפִיכָךְ הִקְדִּימוּהוּ בְּעֶשְׂרִים וְתִשְׁעָה בֶאֱלוּל. רַבִּי מֵאִיר אוֹמֵר, בְּאֶחָד בֶּאֱלוּל רֹאשׁ הַשָּׁנָה לְמַעְשַׂר בְּהֵמָה. בֶּן עַזַּאי אוֹמֵר, הָאֱלוּלִיִּין מִתְעַשְּׂרִין בִּפְנֵי עַצְמָן:

Существует три гранота [дата окончания сезона отела, после которой запрещается продавать или убивать до десятины животных, рожденных в этот период] для десятины животных: до Песаха, до Шавуота и до Суккот, [это] слова равви Акивы. Бен Аззай говорит: двадцать девятого Адара, первого Сивана и двадцать девятого Ав. Рабби Элазар и Рабби Шимон говорят: о первом из Нисана, о первом из Сивана и о двадцать девятом из Элула. И почему они сказали двадцать девятый из Элул, а не первый из Тишрей? Потому что это святой день, а в святой день нельзя платить десятину. Поэтому они перенесли его до двадцать девятого Элула. Раввин Меир говорит: первый день Элул - Новый год для десятины животных. Бен Аззай говорит: те, кто родился в Элуле, платят десятину сами.

Bartenura on Mishnah Bekhorot

שלש גרנות למעשר בהמה (three harvesting seasons/threshing floors for tithing of cattle) – in three periods during the year, the cattle are tithed. And the language of גרנות/harvesting seasons/threshing floors, like the grain of the threshing floor which is subject to sacred gifts/forbidden as eatables forbidden pending the separation of sacred gifts and we don’t consume from them until they are tithed, so in these three periods of the year we don’t eat from the cattle nor do we sell them until we tithe them.
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English Explanation of Mishnah Bekhorot

Introduction Our mishnah deals with when a person is supposed to tithe his animals. The concept is that one tithes one out of every ten animals born in a given year, not one out of every ten animals. Therefore, our mishnah and tomorrow’s mishnah must determine when this year begins.
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Bartenura on Mishnah Bekhorot

פרוס הפסח – fifteen days prior to Passover, that is the last day of [the month of] Adar. And the language [usage of] פרוס, is one-half, one-half of the time that we ask [questions] about the laws of Passover, as it is taught in a Baraita (Talmud Megillah 32a): We ask questions about the laws of Passover thirty days prior to Passover. And similarly, [the phrase] פרוס עצרת/half-a-month before Atzeret/Shavuot, 15 days prior. And similarly [the phrase] פרוס החג/fifteen days prior to the Festival/Sukkot, that is the last day of Elul. And they (i.e., the Rabbis) established these three times that they would establish for the tithing of cattle, in order that the cattle would be available/found for those making Pilgrimage [to the Temple in Jerusalem], and even though it is taught [towards the conclusion] in our Mishnah that until the time of the threshing floor/harvesting seasons, it is permitted to sell and to slaughter, that the harvesting season/threshing floor is what establishes the tithing [of cattle], nevertheless, people did not slaughter until they tithed, for it was satisfactory for people to fulfill the Mitzvah with his money for a matter in which he is not lacking anything, as for example the tithing of cattle in which he himself offers up the tithe and eats it as a peace offering, but if they didn’t tithe at these three periods [of the year] there would be many prevented from selling because they didn’t tithe, and there would not be cattle readily found for those making Pilgrimage [to the Temple].
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English Explanation of Mishnah Bekhorot

There are three periods [lit. threshing floors] for the tithe of cattle: in the peras of Pesah, in the peras of Atzeret ( and in the peras of the Feast [of Sukkot], the words of Rabbi Akiva. “Peras” means “before” and it is interpreted in the Talmud as being fifteen days. According to Rabbi Akiva, a few weeks before all three of the pilgrimage holidays it becomes forbidden to eat any of the animals that were born since the previous holiday until he first separates any necessary animal tithes. These periods are referred to as “threshing floors” which is the end of the processing of grain. At the threshing floor produce becomes liable for tithing. The language is borrowed from that context.
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Bartenura on Mishnah Bekhorot

בן עזאי אומר בתשעה ועשרים באדר – that is fifteen days prior to Passover. But that Rabbi Akiva holds that the Adar that is closest to Nisan (i.e., the month in which Purim falls – the Second Adar in a leap year) is sometimes defective/short – i.e., 29 days and sometimes full – i.e., 30 days) and fifteen days prior to Passover, sometimes we begin on the twenty-ninth of Adar and sometimes on the thirtieth [day] of Adar, therefore, they did not establish for it [an exact] time. But Ben-Azzai holds that the Adar nearest Nisan (i.e., Second Adar in a leap year) is always defective/short, and the beginning of the fifteen-day period prior to Passover is always on the twenty-ninth [day of] Adar.
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English Explanation of Mishnah Bekhorot

Ben Azzai says: on the twenty-ninth of Adar, on the first of Sivan and on the twenty-ninth of Av. Ben Azzai lists the three dates in a slightly different manner. The twenty-ninth of Adar is about two weeks before Pesah, the first of Sivan is less than a week before Shavuot, and the twenty-ninth of Av is one month before Rosh Hashanah.
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Bartenura on Mishnah Bekhorot

באחד בסיון – because of the paucity of cattle that give birth from Nisan until Atzeret/Shavuot (see Talmud Bekhorot 58a), if one advances it fifteen days prior to Atzeret, all of them will be consumed prior to Atzeret, and there won’t be cattle found for those making Pilgrimage [to the Temple in Jerusalem].
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English Explanation of Mishnah Bekhorot

Rabbi Elazar and Rabbi Shimon say: on the first of Nisan, on the first of Sivan and on the twenty-ninth of Elul. Rabbi Elazar and Rabbi Shimon also provide slightly different dates the first of Nissan (the month with Pesah), the first of Sivan (the month with Shavuot) and the twenty-ninth of Elul, the day before Rosh Hashanah. One needs to tithe before Rosh Hashanah because Rosh Hashanah is, according to these two rabbis, the new year for animal tithes. We shall learn more about this in mishnah six (see also Rosh Hashanah 1:1).
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Bartenura on Mishnah Bekhorot

בעשרים ותשעה באב – Ben Azzai, according to his reasoning, who stated further on [in our Mishnah], [The cattle born] in Elul are tithed by themselves and they are not combined with those that were born prior to Elul, for perhaps, on the first of Elul is the New Year for the Tithing of Cattle (see Tractate Rosh Hashanah, Chapter 1, Mishnah 1) and there would be new and old, and it is doubtful to him when is Rosh Hashanah – either Elul or Tishrei, therefore he did not set a time for their “threshing floor” of the summer on the twenty-ninth of Elul so that they don’t come to combine those born in Elul with them.
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English Explanation of Mishnah Bekhorot

And why did they say the twenty-ninth of Elul and not the first of Tishrei? Because it is a Yom Tov and you cannot tithe on a Yom Tov. Consequently they moved it up to the twenty-ninth of Elul. One cannot tithe on Rosh Hashanah because it is a festival (Yom Tov). Therefore, they moved the day up to the last day of the preceding month, Elul.
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Bartenura on Mishnah Bekhorot

באחד בניסן – they (i.e., Rabbi Eleazar and Rabbi Shimon) hold like Rabban Shimon ben Gamaliel who stated that we ask questions about the laws of Passover two weeks prior to Passover, that is, also regarding the laws of Passover that we tithe for cattle in order that they are not appropriate on the Festival/Yom Tov.
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English Explanation of Mishnah Bekhorot

Rabbi Meir says: the first of Elul is the New Year for the tithe of cattle. Rabbi Meir disagrees with Rabbi Elazar and Rabbi Shimon with regard to the date for the new year for animal tithes. While they hold that it is on the first day of Tishrei, he holds that it is on the first of Elul. The anonymous opinion in the first mishnah of Rosh Hashanah accords with Rabbi Meir.
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Bartenura on Mishnah Bekhorot

באחד בסיון – as we stated the reason of Ben Azzai, because of the small number of cattle that are born from Nisan until Atzeret.
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English Explanation of Mishnah Bekhorot

Ben Azzai says: those born in Elul are tithed by themselves. Ben Azzai doubts whether the halakhah is according to Rabbi Elazar and Rabbi Shimon or Rabbi Meir. The result of this doubt is that animals born in Elul are tithed on their own, because we don’t know if they should be tithed with those born before them (Rabbi Elazar and Rabbi Shimon’s opinion) or those born after them (Rabbi Meir’s opinion).
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Bartenura on Mishnah Bekhorot

מפני שהוא יום טוב – he said one thing and more. First – because we need recognition of that which is new and old, that the first of Tishrei is Rosh Hashanah for the tithing of cattle, for even though he did not come to combine them with those of Tishrei, for not a single lamb had been born today, and if it had been born, it was not old enough. Even so, we don’t tithe that of today, because we need to establish recognition between new and old, so that people would know to not combine the new with the old. Nd furthermore, because it is Yom Tov, because of the required marking with red paint (see Talmud Bekhorot 58a) that one paints on each tenth in order that it would be recognized, but it is forbidden to pain on Yom Tov/the holy day.
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Bartenura on Mishnah Bekhorot

האלוליין מתעשרין בפני עצמן – as we explained above, that it is doubtful to him whether the New Year for the tithing of cattle is on the first [day] of Elul or on the first [day] of Tishrei, therefore, we don’t tithe those of Elul with those [animals] born from Tishrei and onwards, because one doesn’t combine old with the new.
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