The commandment of the additional sacrifice on the eighth day of Sukkot, which is called Shemini Atseret: To sacrifice the additional sacrifice on the eighth day of the holiday of Sukkot — and that is the additional [sacrifice] of Shemini Atseret — as it is stated (Leviticus 23:27), “and you shall sacrifice a fire-offering to the Lord; it is an atseret (convocation), etc.” And in the Order of Pinchas (Numbers 29:36-38), it is explained at length. And in the explanation, they, may their memory be blessed, said (Yoma 2b) that it is a festival on its own. And therefore, we should count this additional sacrifice as a commandment on its own.
מִצְוַת קָרְבַּן מוּסָף בְּיוֹם שְׁמִינִי שֶׁל סֻכּוֹת שֶׁהוּא נִקְרָא שְׁמִינִי עֲצֶרֶת – לְהַקְרִיב קָרְבַּן מוּסָף בַּיּוֹם הַשְּׁמִינִי מֵחַג הַסֻּכּוֹת, וְזֶהוּ מוּסַף שְׁמִינִי עֲצֶרֶת, שֶׁנֶּאֱמַר (ויקרא כג לו) וְהִקְרַבְתֶּם אִשֶּׁה לַיְיָ עֲצֶרֶת הִיא וְגוֹ', וּבְסֵדֶר פִּנְחָס (במדבר כט לג לח) מְפָרֵשׁ אוֹתוֹ בַּאֲרֻכָּה. וּבְבֵאוּר אָמְרוּ זִכְרוֹנָם לִבְרָכָה (יומא ב, ב), שֶׁהוּא רֶגֶל בִּפְנֵי עַצְמוֹ וְקָרְבַּן בִּפְנֵי עַצְמוֹ, וְעַל כֵּן, יֵשׁ לָנוּ לִמְנוֹת מוּסָף זֶה, מִצְוָה בִּפְנֵי עַצְמָהּ.
The commandment of the additional sacrifice on the eighth day of Sukkot, which is called Shemini Atseret: To sacrifice the additional sacrifice on the eighth day of the holiday of Sukkot — and that is the additional [sacrifice] of Shemini Atseret — as it is stated (Leviticus 23:27), “and you shall sacrifice a fire-offering to the Lord; it is an atseret (convocation), etc.” And in the Order of Pinchas (Numbers 29:36-38), it is explained at length. And in the explanation, they, may their memory be blessed, said (Yoma 2b) that it is a festival on its own. And therefore, we should count this additional sacrifice as a commandment on its own.
מִשָּׁרְשֵׁי מִצְוַת מוּסָף וּמִכָּל עִנְיָנָהּ, כָּתַבְתִּי הַרְבֵּה פְּעָמִים לְמַעְלָה, מָה שֶׁהִשִּׂיגָה יָדִי.
I have already written what my hand has reached from the roots of this commandment and its content many times above.