אמר רב אשי הכי נמי מסתברא דאי לא תימא הכי הא מתניתא מאן קתני לה בן תימא בן תימא הא פסלה לה בלינה ש"מ
An objection is raised: 'And thou shalt be altogether' [ak] joyful:' this is to include the night of the last day of the Festival for rejoicing. You say, to include the light of the last day of the Festival; yet perhaps it is not so, but it is to include the night of the first day of the Festival? Therefore 'ak' is stated, dividing it. Now what is the reason? Is it not because he has no light wherewith to rejoice! - No: [it is] as it was taught. Why do you prefer to include the night of the last day of the Festival and to exclude the night of the first day of the Festival? I include the night of the last day of the Festival, because there is rejoicing before it; while I exclude the night of the first day of the Festival, because there is no rejoicing before it.
Sefer HaChinukh
To not leave over from the festive (chagigah) sacrifice to the third day: To not leave over anything from the festive sacrifice of the fourteenth day until the third day - and that is the sacrifice that comes with the Pesach [sacrifice] to increase the joy - but rather to eat it all within two days, which are are the fourteenth and fifteenth. And about this is it stated (Deuteronomy 16:4), "and none of the meat of what you slaughter on the evening of the first day shall be left to the morning." And the received (traditional) understanding came upon this (Pesachim 71a) that the verse is speaking about the festive [sacrifice] that comes with the Pesach, [to say] that the time of its eating is up to two days. And about this festive [sacrifice], Scripture stated (Deuteronomy 16:2), "And you shall slaughter the Pesach to the Lord, your God, flock and cattle" - meaning to say, that with the Pesach, he bring another sacrifice; meaning to increase the joy.
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