. The two he-goats of Yom Kippur are essential to [the validity of] each other. The two lambs of Shavuos are essential to [the validity of] each other. The two loaves are essential to [the validity of] each other. The two arrangements are essential to [the validity of] each other. The two spoonfuls [of frankincense] are essential to [the validity of] each other. The arrangements and the spoonfuls [of frankincense] are essential to [the validity of] each other. The two kinds [of breads] of the nazir, the three [ingredients added to] the [red] cow, the four [kinds of bread] of the todah-offering, the four [species] of the lulav, and the four [ingredients] of the metzora’s purification are essential to [the validity of] one another. The seven sprinklings of the [red] cow are essential to [the validity of] one another. The seven sprinklings between the poles, and on the Curtain, and on the Golden Altar are essential to [the validity of] one another.

The seven branches of the menorah are essential to [the validity of] one another. Its seven lamps are essential to [the validity of] one another. The two [Scriptural] passages which are in a mezuzah are essential to [the validity of] each other, and even the writing of one [letter] is essential to them. The four passages which are in tefillin are essential to [the validity of] one another, and even the writing of one [letter] is essential to them. The four fringes of the tzitzis are essential to the validity of one another, as they are all four one mitzvah. R’ Yishmael says: The four of them are four mitzvos.

The blue thread is not essential to [the validity of] the white thread, and the white is not essential to [the validity of] the blue. The tefillah of the hand is not essential to [the validity of] that of the head, and that of the head is not essential to [the validity of] that of the hand. The flour and the oil are not essential to the wine, nor is the wine essential to them. The blood applications on the outer Altar are not essential to [the validity of] one another.

The bulls, the rams, and the lambs are not essential to one another’s [validity]. R’ Shimon says: If they had many bulls but no libations, they should bring one bull with its libations rather than offering all of them without libations.

The bull, the rams, the lambs, and the goat are not essential to the [validity of the] bread, nor is the bread essential to their [validity]. The bread is essential to the [validity of the] lambs, but the lambs are not essential to the [validity of the] bread; [these are] the words of R’ Akiva. Said Shimon ben Nannas: Not so; rather the lambs are essential to the [validity of the] bread while the bread is not essential to the [validity of the] lambs. For we find that when Israel was in the Wilderness for forty years, the lambs were offered without bread; therefore, now too the lambs can be offered without bread. Said R’ Shimon: The halachah follows the words of Ben Nannas, but not for his reason. For whatever is mentioned in the Book of Numbers was offered in the Wilderness, and whatever is mentioned in Leviticus was not offered in the Wilderness; once they came to the Land [of Israel], both these and those were offered. Why [then] do I say that lambs may be offered without bread? Because the lambs render themselves permissible without bread, [but the] bread without the lambs has nothing to render it permissible.

The tamid-offerings are not essential to the [validity of the] mussaf-offerings; nor are the mussaf-offerings essential to the [validity of the] tamid-offerings; nor are the mussaf-offerings essential to each other’s [validity]. [If] they did not offer a lamb in the morning, they should [nonetheless] offer [one] in the afternoon. Said R’ Shimon: When? When they acted under constraint or unwittingly. However, if they [acted] intentionally and did not offer the lamb in the morning, they may not offer [one] in the afternoon. [If] they did not burn the incense in the morning, they burn [it] in the afternoon. Said R’ Shimon: All of it was offered in the afternoon. For the Golden Altar was dedicated only with the [burning of the] incense; and the Olah Altar only with the tamid of the morning; and the shulchan only with the lechem hapanim on the Sabbath; and the menorah only with its seven lamps in the afternoon.

The chavitin of the Kohen Gadol were not brought by halves; rather, he brings a full issaron and divides it, and offers half in the morning and half in the afternoon. [If] a Kohen offered half in the morning and died, and they appointed another Kohen in his place, he should not bring half an issaron of his own, nor the half of the first one’s issaron; rather, he brings a full issaron and divides it in half, and he offers half, and half is destroyed. Thus, two halves are offered and two halves are destroyed. [If] they did not appoint another Kohen, from whom was it brought? R’ Shimon says: From the public. R’ Yehudah says: From the heirs. And it was offered whole.

All minchah-offerings are brought as matzah except for the leavened [bread] of the todah-offering and the shtei halechem, which are brought leavened. R’ Meir says: He abstracts sourdough for them from within themselves and leavens them. R’ Yehudah says: This, too, is not preferred. Rather, he brings sourdough, places it within the measure, and then fills the measure. They said to him: This, too, would be deficient or excessive.