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Mishnah Horayot 3:1

If an anointed priest transgressed and afterwards relinquished his high priesthood, and similarly if a ruler transgressed and afterwards relinquished his reign, the anointed priest brings a bullock, and the ruler brings a he-goat.

כֹּהֵן מָשִׁיחַ שֶׁחָטָא וְאַחַר כָּךְ עָבַר מִמְּשִׁיחוּתוֹ, וְכֵן נָשִׂיא שֶׁחָטָא וְאַחַר כָּךְ עָבַר מִגְּדֻלָּתוֹ, כֹּהֵן מָשִׁיחַ מֵבִיא פַר, וְהַנָּשִׂיא מֵבִיא שָׂעִיר:

Jerusalem Talmud, Halakhah 3:1 (on Mishnah 3:1–2)

Mishnah Horayot 3:2

If the anointed priest relinquished his high priesthood and afterwards transgressed, and similarly if a ruler relinquished his reign and afterwards transgressed, the anointed priest brings a bull while the ruler is like a regular person.

כֹּהֵן מָשִׁיחַ שֶׁעָבַר מִמְּשִׁיחוּתוֹ וְאַחַר כָּךְ חָטָא, וְכֵן הַנָּשִׂיא שֶׁעָבַר מִגְּדֻלָּתוֹ וְאַחַר כָּךְ חָטָא, כֹּהֵן מָשִׁיחַ מֵבִיא פַר, וְהַנָּשִׂיא כְהֶדְיוֹט:

The Jerusalem Talmud discusses this mishnah with 3:1 above.

Mishnah Horayot 3:3

If they transgressed before they were appointed, and afterwards they were appointed, they are regarded as regular people. Rabbi Shimon said: if their sin came to their knowledge before they were appointed they are liable, but if after they were appointed they are exempt. Who is meant by a ruler? A king; for it says, “Any of all the commandments of the Lord his God” (Leviticus 4:22), a ruler (king) who has none above him save the Lord his God.

חָטְאוּ עַד שֶׁלֹּא נִתְמַנּוּ וְאַחַר כָּךְ נִתְמַנּוּ, הֲרֵי אֵלּוּ כְהֶדְיוֹט. רַבִּי שִׁמְעוֹן אוֹמֵר, אִם נוֹדַע לָהֶם עַד שֶׁלֹּא נִתְמַנּוּ, חַיָּבִין. וּמִשֶּׁנִּתְמַנּוּ, פְּטוּרִין. וְאֵיזֶהוּ הַנָּשִׂיא, זֶה הַמֶּלֶךְ, שֶׁנֶּאֱמַר (ויקרא ד) וְעָשָׂה אַחַת מִכָּל מִצְוֹת ה' אֱלֹהָיו, נָשִׂיא שֶׁאֵין עַל גַּבָּיו אֶלָּא ה' אֱלֹהָיו:

Jerusalem Talmud, Halakhah 3:2 (on Mishnah 3:3–4)

Mishnah Horayot 3:4

And who is the anointed priest? He who was anointed with the anointing oil and not he that has more garments. The only difference between a high priest who is anointed with the anointing oil and one who has more garments is the bull that is offered for [the unwitting transgression of] any of the commandments. And the only difference between the acting (high) priest and the former (high) priest is the bull on the Day of Atonement and the tenth part of the ephah. They are both equal in the service of the Day of Atonement, and both are commanded to marry a virgin and are forbidden to marry a widow; they are both forbidden to become impure for their relatives; they do not let their hair grow long, nor do they rend their clothes; and they return the (accidental) killer (from the city of refuge).

וְאֵיזֶהוּ הַמָּשִׁיחַ, הַמָּשׁוּחַ בְּשֶׁמֶן הַמִּשְׁחָה, לֹא הַמְרֻבֶּה בִבְגָדִים. אֵין בֵּין כֹּהֵן הַמָּשׁוּחַ בְּשֶׁמֶן הַמִּשְׁחָה לִמְרֻבֶּה בְגָדִים אֶלָּא פַר הַבָּא עַל כָּל הַמִּצְוֹת. וְאֵין בֵּין כֹּהֵן מְשַׁמֵּשׁ לְכֹהֵן שֶׁעָבַר, אֶלָּא פַר יוֹם הַכִּפּוּרִים וַעֲשִׂירִית הָאֵיפָה. זֶה וָזֶה שָׁוִין בַּעֲבוֹדַת יוֹם הַכִּפּוּרִים, וּמְצֻוִּין עַל הַבְּתוּלָה, וַאֲסוּרִין עַל הָאַלְמָנָה, וְאֵינָן מִטַּמְּאִין בִּקְרוֹבֵיהֶן, וְלֹא פוֹרְעִין, וְלֹא פוֹרְמִין, וּמַחֲזִירִין אֶת הָרוֹצֵחַ:

The Jerusalem Talmud discusses this mishnah with 3:3 above.

Mishnah Horayot 3:5

A high priest rends [his clothes] from below and an ordinary priest from above. A high priest offers sacrifices while an onen but does not eat them and an ordinary priest neither offers sacrifices nor eats them.

כֹּהֵן גָּדוֹל פּוֹרֵם מִלְּמַטָּה, וְהַהֶדְיוֹט מִלְמַעְלָה. כֹּהֵן גָּדוֹל מַקְרִיב אוֹנֵן וְלֹא אוֹכֵל, וְהַהֶדְיוֹט לֹא מַקְרִיב וְלֹא אוֹכֵל:

Jerusalem Talmud, Halakhah 3:3

Mishnah Horayot 3:6

Whatever is more frequent than another takes precedence over that other; And whatever is more sacred than another takes precedence over that other. If the bull of the anointed priest and the bull of the congregation are standing [to be sacrificed], the bull of the anointed priest precedes that of the congregation in all its details.

כָּל הַתָּדִיר מֵחֲבֵרוֹ, קוֹדֵם אֶת חֲבֵרוֹ. וְכָל הַמְקֻדָּשׁ מֵחֲבֵרוֹ, קוֹדֵם אֶת חֲבֵרוֹ. פַּר הַמָּשִׁיחַ וּפַר הָעֵדָה עוֹמְדִים, פַּר הַמָּשִׁיחַ קוֹדֵם לְפַר הָעֵדָה בְּכָל מַעֲשָׂיו:

Jerusalem Talmud, Halakhah 3:4 (on Mishnah 3:6–7)

Mishnah Horayot 3:7

A man takes precedence over a woman in matters concerning the saving of life and the restoration of lost property, and a woman takes precedence over a man in respect of clothing and ransom from captivity. When both are exposed to degradation in their captivity the man takes precedence over the woman.

הָאִישׁ קוֹדֵם לָאִשָּׁה לְהַחֲיוֹת וּלְהָשִׁיב אֲבֵדָה. וְהָאִשָּׁה קוֹדֶמֶת לָאִישׁ לִכְסוּת, וּלְהוֹצִיאָהּ מִבֵּית הַשֶּׁבִי. בִּזְמַן שֶׁשְּׁנֵיהֶם עוֹמְדִים לְקַלְקָלָה, הָאִישׁ קוֹדֵם לָאִשָּׁה:

The Jerusalem Talmud discusses this mishnah with 3:6 above.

Mishnah Horayot 3:8

A priest takes precedence over a levite, a levite over an israelite, an israelite over a mamzer, a mamzer over a natin, a natin over a convert, and a convert over a freed slave. When is this so? When all these were in other respects equal. However, if the mamzer was a scholar and the high priest an ignoramus, the scholar mamzer takes precedence over the ignorant high priest.

כֹּהֵן קוֹדֵם לְלֵוִי, לֵוִי לְיִשְׂרָאֵל, יִשְׂרָאֵל לְמַמְזֵר, וּמַמְזֵר לְנָתִין, וְנָתִין לְגֵר, וְגֵר לְעֶבֶד מְשֻׁחְרָר. אֵימָתַי, בִּזְמַן שֶׁכֻּלָּן שָׁוִין. אֲבָל אִם הָיָה מַמְזֵר תַּלְמִיד חָכָם וְכֹהֵן גָּדוֹל עַם הָאָרֶץ, מַמְזֵר תַּלְמִיד חָכָם קוֹדֵם לְכֹהֵן גָּדוֹל עַם הָאָרֶץ:

Jerusalem Talmud, Halakhah 3:5

The Mishnah: English translation: Joshua Kulp, Mishnah Yomit (Conservative Yeshiva), via Sefaria, licensed CC BY; changes made (line breaks, spacing, a typo, and Kulp's study notes removed from five mishnayot). Hebrew: Torat Emet 357, public domain; Bikkurim chapter 4 from Dan Be'eri's edition of the Kaufmann manuscript, public domain.

The Jerusalem Talmud: English translation and Hebrew/Aramaic text: Heinrich W. Guggenheimer, The Jerusalem Talmud: Edition, Translation, and Commentary (Berlin: De Gruyter, 1999-2015), via Sefaria, licensed CC BY 4.0; changes made (his footnotes and the page markers removed).