Sifrei Devarim Paragraph 142
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(דברים טז טו) שִׁבְעַת יָמִים תָּחֹג לַה׳ אֱלֹהֶיךָ בַּמָּקוֹם אֲשֶׁר יִבְחַר ה׳, וַהֲלֹא כְּבָר נֶאֱמַר (ויקרא כג לד) ״חַג הַסֻּכּוֹת שִׁבְעַת יָמִים לַה׳״? מַה תַּלְמוּד לוֹמַר שִׁבְעַת יָמִים? מְלַמֵּד שֶׁכָּל הָרֶגֶל תַּשְׁלוּמִים לָרִאשׁוֹן.
(Devarim 16:15) "Seven days shall you celebrate before the L-rd your G-d": I might think that he sacrifices the festive offering (chagigah) all seven days; it is, therefore, written (Vayikra 43:41) "And you shall celebrate it" (the first day), and not all seven days.
[יָכוֹל יִטְעוֹן חֲגִיגָה כָּל שִׁבְעָה? תַּלְמוּד לוֹמַר: (ויקרא כג מא) ״אוֹתוֹ״,] אִם כֵּן לָמָּה נֶאֱמַר שִׁבְעַת יָמִים? תַּשְׁלוּמִים כָּל שִׁבְעָה.
If so, how is "seven days" to be understood? As referring to compensation (i.e., if he did not offer the chagigah on the first day, he can do so all seven days.
כִּי יְבָרֶכְךָ ה׳ אֱלֹהֶיךָ, יָכוֹל בּוֹ בַּמִּין? תַּלְמוּד לוֹמַר: בְּכָל תְּבוּאָתְךָ וּבְכֹל מַעֲשֵׂה יָדֶיךָ.
"For the L-rd your G-d will bless you": I might think, only in that species (which he sacrifices); it is, therefore, written "in all of your produce and in all to which you put your hand."
וְהָיִיתָ אַךְ שָׂמֵחַ, לְרַבּוֹת לֵילֵי יוֹם טוֹב הָרִאשׁוֹן לְשִׂמְחָה.
"and you shall be only happy": to include the night of the last day of the festival for rejoicing.
יָכוֹל שֶׁאֲנִי מְרַבֶּה לֵילֵי יוֹם טוֹב הָאַחֲרוֹן לְשִׂמְחָה? תַּלְמוּד לוֹמַר: אַךְ.
I might think also to include the night of the first day of the festival; it is, therefore, written "only" (to exclude this).
מִכָּן אָמְרוּ: (חגיגה א, ד) יִשְׂרָאֵל יוֹצְאִים יְדֵי חוֹבָתָם בִּנְדָרִים וּבִנְדָבוֹת. יָכוֹל אַף בְּעוֹפוֹת וּבִמְנָחוֹת? תַּלְמוּד לוֹמַר: אַךְ.
From here it was taught: One may fulfill his obligation [of rejoicing] with meat of voluntary sacrifices. I might have thought [that one can likewise fulfill his obligation] with fowl and meal-offerings? Therefore it states "Only..." [to exclude this].