126 Beitzah 2/1-4

(1) When a festival falls on the eve of Shabbat, one should not, at the outset, cook for Shabbat on the festival, but one may cook for the festival, and if he has [food] left over, it is left over for [and its use is permissible on] Shabbat. And one may prepare a cooked dish on the eve of a festival [which falls on the eve of Shabbat] and rely on it [to permit cooking on the holiday] for Shabbat. Beit Shammai say: two cooked dishes [are required in order to rely on this leniency]. Beit Hillel say: one cooked dish [is sufficient]. And they are in agreement regarding a fish with an egg on top of it, that those [together] are considered two cooked dishes. If it [the food set aside] was eaten or lost, one may not, at the outset, cook [on the holiday for Shabbat by relying] upon it. But if any amount of it remains, one may rely upon it [to cook on the holiday] for Shabbat.

(2) If it [a festival] falls [on the day] after Shabbat, Beit Shammai say: everything [requiring ritual immersion] should be immersed before Shabbat. And Beit Hillel say: vessels [must be immersed] before Shabbat, but people [may immerse even] on Shabbat.

(3) And they [Beit Shammai and Beit Hillel] are in agreement that [on festivals] one may touch [impure] waters [to the mikvah waters] using a stone vessel [containing the impure waters, which cannot itself be rendered impure] in order to purify them [the impure waters], but one may not immerse [an impure vessel containing impure waters, as that would purify the vessel as well, which may not be done on a holiday]. And [they are also in agreement] that one may immerse [vessels on a festival] from one level to another [i.e. to raise the purity level of something that is already pure, such as immersing something that was already pure for terumah so that is will be pure for sanctified foods as well], and [that, on a festival, one may immerse vessels] from one group to another group [i.e. for the Pascal offering, which must be brought and eaten with a designated group, if one immersed vessels to be used for the offering of one group, and then he switched to another group, he may immerse them again, on the festival, for use for the offering of the second group, such as if the second group requires a higher level of purity].

(4) Beit Shammai say: Shelamim [offerings whose various parts are consumed by their owners, by the priests, and by the fire on the altar] may be brought [on a festival], and one does not lean upon them [as one normally does when bringing a sacrifice], but not olot [offerings that are entirely burnt on the alter]. And Beit Hillel say: shelamim and olot may be brought [on a holiday], and one does lean upon them.