In a case of the blood of an offering that is to be placed on the altar with one placement that was mixed with the blood of another offering that is to be placed on the altar with one placement, e.g., the blood of a firstborn offering with the blood of another firstborn offering or the blood of an animal tithe offering, the blood shall be placed with one placement. In a case of the blood of an offering that is to be placed on the altar with four placements that was mixed with the blood of another offering that is to be placed on the altar with four placements, e.g., the blood of a sin offering with that of another sin offering, or the blood of a burnt offering with that of a peace offering, the blood shall be placed with four placements.

If the blood of an offering that is to be placed on the altar with four placements was mixed with the blood of an offering that is to be placed on the altar with one placement, Rabbi Eliezer says: The blood shall be placed with four placements. Rabbi Yehoshua says: The blood shall be placed with one placement, as the priest fulfills the requirement with one placement after the fact.

Rabbi Eliezer said to Rabbi Yehoshua: According to your opinion, the priest violates the prohibition of: Do not diminish, as it is written: “All these matters that I command you, that you shall observe to do; you shall not add thereto, nor diminish from it” (Deuteronomy 13:1). One may not diminish the number of required placements from four to one. Rabbi Yehoshua said to Rabbi Eliezer: According to your opinion, the priest violates the prohibition of: Do not add, derived from the same verse. One may not add to the one required placement and place four.

Rabbi Eliezer said to Rabbi Yehoshua: The prohibition of: Do not add, is stated only in a case where the blood is by itself, not when it is part of a mixture. Rabbi Yehoshua said to Rabbi Eliezer: Likewise, the prohibition of: Do not diminish, is stated only in a case where the blood is by itself. And Rabbi Yehoshua also said: When you placed four placements, you transgressed the prohibition of: Do not add, and you performed a direct action. When you did not place four placements but only one, although you transgressed the prohibition of: Do not diminish, you did not perform a direct action. An active transgression is more severe than a passive one.

GEMARA: The mishna teaches that according to the opinion of Rabbi Eliezer, if a cup containing the blood of blemished animals became intermingled with cups holding the blood of fit offerings, and the blood in one of the cups was sacrificed, all the remaining cups are fit. Rabbi Elazar says: Rabbi Eliezer permitted the rest of the cups only if they were sacrificed two by two, as at least one of them is certainly permitted; but he did not permit them to be sacrificed one by one, as he may be found to have presented the blood of the prohibited cup by itself.

Rav Dimi raises an objection from the mishna: And the Rabbis say that even if the blood in all the cups was sacrificed except for the blood in one of them, the blood shall be poured into the Temple courtyard drain. This indicates that even in this case, where only one cup remains, Rabbi Eliezer disagrees with the Rabbis and permits the blood in the cup to be presented. Rabbi Ya’akov said to Rabbi Yirmeya bar Taḥlifa: I will explain it to you: What does the mishna mean when it states: Except for the blood in one of them? It means except for one pair, i.e., two cups, as even Rabbi Eliezer did not permit the presentation of the cups one by one.

§ The dispute between Rabbi Eliezer and the Rabbis was also stated above with regard to a mixture of limbs from fit and unfit offerings. The Gemara notes: And it is necessary for the mishna to teach this dispute with regard to both cases, as, if it were stated only with regard to that case of the limbs, one would have said that it is in that case alone that Rabbi Eliezer says that the rest of the limbs are sacrificed, because the offering’s atonement, i.e., the presenting of the blood, has already been performed, as the limbs are sacrificed after the blood has been presented. But in this case of the blood in the cups, say that Rabbi Eliezer concedes to the Rabbis that the rest of the blood is unfit to be presented.

And conversely, if the dispute were stated only with regard to this case of the cups, one would have said that it is in this case alone that the Rabbis say that the blood in the rest of the cups is unfit, but in that case of the limbs, say that the Rabbis concede to Rabbi Eliezer that the rest of the limbs are fit to be sacrificed, as the blood has already been presented. Therefore, it is necessary for the mishna to state that the dispute applies in both cases.

§ The Gemara continues its discussion of the dispute between Rabbi Eliezer and the Rabbis. We learned in a mishna there (Para 9:1): With regard to a flask containing water of purification into which any amount of regular water fell, Rabbi Eliezer says: The priest should sprinkle two sprinklings on the ritually impure person, as in this manner he ensures that he will be sprinkled with some of the water of purification; but the Rabbis disqualify the mixture for purification.

The Gemara clarifies: Granted, one can understand why the Rabbis disqualify the mixture, as they hold three opinions: They hold that there is mixing, i.e., when two substances are mixed together each drop is assumed to contain a bit of each of them. And they hold that an act of sprinkling of the water of purification requires a minimum measure of water of purification, and in this case each sprinkling contained some of the regular water. And they hold that it is of no help to sprinkle the water twice, as one cannot combine sprinklings, i.e., two acts of sprinkling the water of purification do not combine to render one pure. Therefore, the person is not purified.

But what does Rabbi Eliezer hold? If he holds that there is no mixing, i.e., when two substances are mixed together each drop is not assumed to contain a bit of each of them, then even if one sprinkles two sprinklings, what of it? Perhaps on both occasions he sprinkles regular water. Rather, one must say that Rabbi Eliezer holds that there is mixing. If he holds that the act of sprinkling does not require a minimum measure, why do I need two sprinklings? One act of sprinkling would be enough. Rather, you must say that Rabbi Eliezer holds that the act of sprinkling requires a minimum measure. And if Rabbi Eliezer holds that one cannot combine sprinklings, then even if one sprinkles two sprinklings, what of it? And alternatively, if he holds that one combines sprinklings, who says that the two sprinklings will amount to the minimum measure? Perhaps most of the water he sprinkled was regular water.

Reish Lakish says: Actually, Rabbi Eliezer holds that there is mixing, and sprinkling requires a minimum measure. And here we are dealing with a case where the two types of water were mixed together in a ratio of one to one, and therefore by performing two sprinklings the priest ensures that he has sprinkled the minimum measure of one sprinkling of water of purification.

Rava says: Actually, Rabbi Eliezer maintains that there is mixing, and sprinkling does not require a minimum measure. Consequently, it should suffice for the priest to perform one sprinkling. And the requirement to sprinkle twice is a penalty that the Sages imposed, so that one who mixes regular water with the water of purification would not benefit from this act by diluting the valuable water of purification.

Rav Ashi states a different explanation: Rabbi Eliezer holds that there is no mixing, and therefore if the priest sprinkles only once there is a concern that he might not have sprinkled any water of purification at all, and therefore he sprinkles two sprinklings.

The Gemara raises an objection from a baraita against Reish Lakish’s opinion that Rabbi Eliezer holds that sprinkling requires a minimum measure. Rabbi Yehuda HaNasi says: According to the statement of Rabbi Eliezer that if the priest performs two sprinklings the purification ritual is valid, a sprinkling of any amount renders the impure person ritually pure, as sprinkling does not require a minimum measure, and even a sprinkling that contains half fit water and half unfit water renders the individual ritually pure.