[If] he intended piggul with the kometz but not with the frankincense; [or] with the frankincense but not with the kometz — R’ Meir says: It is piggul and one is liable to kares over it; but the Sages say: There is no kares for it unless he intends piggul with all that renders it permissible. The Sages concur with R’ Meir concerning the sinner’s minchah-offering and the jealousy minchahoffering, that if he intended piggul with the kometz, it is piggul and one is liable to kares over it, since the kometz is that which renders it permissible. [If] he slaughtered one of the lambs [intending] to eat [the] two loaves tomorrow, [or] he burnt one of the spoonfuls [of frankincense intending] to eat [the] two arrangements tomorrow — R’ Meir says: It is piggul and one is liable to kares over it; but the Sages say: There is no piggul unless he intends piggul with all that renders it permissible. [If] he slaughtered one of the lambs [intending] to eat from it tomorrow, it is piggul but its companion is valid. [However, if he intended] to eat from its companion tomorrow, they are both valid.

[If] one performs kemitzah on a minchahoffering [intending] to eat something which is not meant to be eaten, [or] to burn [upon the Altar] something which is not meant to be burnt — it is valid. R’ Eliezer invalidates [it]. [If his intent was] to eat something which is meant to be eaten, [or] to burn [upon the Altar] something which is meant to be burnt — but less than an olive’s volume — it is valid. [If his intent was] to eat something half an olive’s volume and to burn half an olive’s volume — it is valid, for eating and Altar-burning are not combined.

[If] he did not pour, [or] he did not mix, [or] he did not break [it] into pieces; [or] he did not salt, [or] he did not wave, [or] he did not bring [it] near; or [if] he broke them into large pieces, or he did not anoint them — they are valid. [If] its kometz mixed with the kometz of another, [or] with the minchah-offering of Kohanim, [or] with the minchah-offering of the Anointed Kohen, [or] with the minchah-offering of the libations — it is valid. R’ Yehudah says: In the case of the minchah-offering of the Anointed Kohen and the minchahoffering of libations it is invalid, because this [one’s] mixture is thicker, and this one’s mixture is thinner, and they absorb from each other.

[If] two minchah-offerings in which kemitzah had not been performed mixed together — if it is possible to perform kemitzah in each by itself, they are valid; if not, they are invalid. [If] a kometz mixed with a minchah-offering in which kemitzah had not been performed, it is not burnt [on the Altar]. But if he burnt [it], the one in which kemitzah had been performed is credited to the owner, and the one in which kemitzah had not been performed is not credited to the owner. [If] its kometz mixed with its remainder, or with the remainder of another [minchah-offering], he should not burn [it on the Altar]; but if he did burn [it], it is credited to the owner. [If] the kometz became tamei and he offered it, the tzitz effects acceptance; [if] it went out and he offered it, the tzitz does not effect acceptance; for the tzitz effects acceptance for that which is tamei, but not for that which went out.

If its remainder became tamei, burnt, or lost — according to the rule of R’ Eliezer, it is valid; but according to the rule of R’ Yehoshua, it is invalid. [If it was] not [placed] in a sacred vessel, it is invalid. R’ Shimon validates [it]. [If] he burnt its kometz twice, it is valid.

The kometz — its smaller part is essential to [the validity of] its larger part. [For] the issaron — its smaller part is essential to [the validity of] its larger part. [For] wine — its smaller part is essential to [the validity of] its larger part. [For] oil — its smaller part is essential to [the validity of] its larger part. The flour and the oil are essential to [the validity of] each other. The kometz and the frankincense are essential to [the validity of] each other.

. 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.