Midrash sur Les Nombres 28:17

(Exodus 12:2) "It is the first": What is the intent of this? It is written (Devarim 16:1) "Observe the month of Aviv (spring) and offer the Pesach to the L rd your G d, etc." Observe Pesach for Aviv, and Aviv for Pesach, that Aviv fall out in its proper time. How so? Intercalate Adar, so that Aviv fall out in its proper time. If they intercalated Adar and Aviv did not fall out in its proper time, I might think that they should intercalate the New Moon of Nissan. R. Yishmael says: If you say this, you make Nissan twice; but the Torah has said: "It is the first (i.e., one) to you" (and not two). R. Nathan says "Observe the month of Aviv" — Observe the month which is closest to Aviv. And which is that? Adar. But we have not heard how many (days) are to be intercalated. From "Observe the month (of Aviv"), we infer that a month (of days, i.e., thirty) are to be intercalated. And this follows, viz.: A month is intercalated and a year is intercalated. Just as a month, (with) one of its units (i.e., days), so, a year, with one of its units (i.e., months). __ But perhaps, just as (with a) month — one thirtieth of it, so, (with) a year, one thirtieth of it? It is, therefore, written "Observe the month." (A month is intercalated and not one thirtieth of it. __ But perhaps, just as a year, one twelfth of it, so, a month, one twelfth of it? It is, therefore, written (Numbers 28:17) "And on the fifteenth day of this month" — You intercalate a day for a month, and not one twelfth of it. R. Yitzchak said: If you said this, the moon would already be in the middle of the sky (in the beginning of the month)! You must perforce revert, then, to the first formulation, viz.: A month is intercalated and a year is intercalated. Just as a month is added to only at its end, so, a year is added to only at its end. R. Yirmiyah says: Just as uncleanliness constrains (the offering of the Pesach [viz. Numbers 9:10] and (the advent of) spring constrains, then just as the (constraint in) the first is not less than thirty days, so, (that in) the second must be no less than thirty days. __ But perhaps (an intercalation is to be made backwards] even if spring arrives prematurely? It is, therefore, written (Exodus 13:10) "and you shall keep this statute (of Pesach) in its time" — You add to its time, but you do not subtract from it.