Just as here, in the case of first fruits, it is the priest who takes the basket in his hand and waves it, so too there, in the case of the peace offering, a priest performs the waving. Just as there, with regard to a peace offering, it is the owner who performs the waving, as it is written: “He who offers…his hands shall bring it,” so too here, the owner waves the first fruits. How so; how can the waving be performed by both the priest and the owner? The priest places his hands beneath the hands of the owner and waves the first fruits together with the owner.

The Gemara asks: And let the mishna also say that the halakha that first fruits require waving is in accordance with the statement of Rabbi Yehuda, as it is taught in a baraita: Rabbi Yehuda says with regard to the verse written in the portion of first fruits: “And you shall place it before the Lord your God” (Deuteronomy 26:10), the reference is not to the placement of the fruits alongside the altar. Rather, this is a reference to waving the first fruits. Do you say that this is a reference to waving, or perhaps it is a reference only to actual placement of the first fruits?

He explains: When it states earlier: “And the priest shall take the basket from your hand, and place it before the altar of the Lord your God” (Deuteronomy 26:4), placement alongside the altar is already stated; how do I realize the meaning of: “And you shall place it”? This is a reference to waving. It is therefore clear that Rabbi Eliezer ben Ya’akov is not the only tanna who holds that there is a requirement of waving the first fruits, as indicated by the mishna; Rabbi Yehuda also maintains this opinion.

Rava says: The tanna of the mishna could have said that this halakha is in accordance with the opinion of Rabbi Yehuda. He preferred to ascribe this opinion to Rabbi Eliezer ben Ya’akov, since the verse opened first with the phrase cited by Rabbi Eliezer ben Ya’akov as the source for the requirement of waving the first fruits, as Rabbi Eliezer ben Ya’akov derives this halakha from the verse: “And the priest shall take the basket from your hand” (Deuteronomy 26:4); whereas Rabbi Yehuda derives it from the later verse: “And you shall place it before the Lord your God” (Deuteronomy 26:10). Rav Naḥman bar Yitzḥak says: The tanna preferred to cite this halakha in the name of Rabbi Eliezer ben Ya’akov since his strength in Torah is great, as the halakha is invariably in accordance with his opinion.

§ The mishna teaches: And the sacrificial portions of the peace offerings of an individual, which are consumed on the altar, and their breast and thigh, which are eaten by the priests, require waving. This requirement applies to peace offerings belonging both to men and to women, by male Jews and not by others. The Gemara asks: What is the mishna saying? This statement is apparently self-contradictory, as the mishna first states that offerings brought by women require waving, and then it indicates that the offerings of others, including women, do not require waving.

Rav Yehuda said that this is what the tanna of the mishna is saying: Both with regard to men and with regard to women, their offerings require waving, but the waving itself is performed only by male Jews, i.e., if the owner is a male he waves the offering together with a priest. But in the case of offerings brought by women, the female owner does not participate in the waving, as the priest alone performs the mitzva.

§ The Sages taught in a baraita: With regard to peace offerings, the verse states: “Speak to the children of Israel, saying: He who offers his sacrifice of peace offerings to the Lord shall bring his offering out of his sacrifice of peace offerings. His own hands shall bring the offerings of the Lord made by fire. The fat with the breast he shall bring, that the breast may be waved for a wave offering before the Lord” (Leviticus 7:29–30). From the phrase: “The children of [benei] Israel,” it may be derived that the Jewish people wave their offerings, but gentiles who bring their offerings do not wave them. Furthermore, as the term “benei” can also mean: Sons of, it may be derived that only sons of Israel, i.e., males, wave their offerings, but that women do not wave their offerings.

Rabbi Yosei says: We have found that the Torah differentiates between the offering of a Jew and the offering of gentiles and also between the offering of men and the offering of women, with regard to the obligation of placing hands. Placing hands is performed only on offerings of male Jews, not on those brought by gentiles and women. Therefore, one might have thought that a similar distinction should apply to the halakha of waving. Can we therefore differentiate between these different offerings also with regard to waving, and conclude that this requirement also applies only to offerings of male Jews, not those brought by gentiles or women?

Rabbi Yosei explains: No; this conclusion is incorrect, since what is the reason that the Torah differentiates between males Jews on the one hand and gentiles and women on the other hand, with regard to placing hands? The reason is that the case of placing hands is unique, as it is performed only by the owner of the offerings; he cannot appoint an agent to perform this ceremony on his behalf. Therefore, since gentiles and women may not perform this ceremony themselves, it is logical that their offerings are excluded from this requirement.

By contrast, can we differentiate between males Jews on the one hand and gentiles and women on the other hand, with regard to waving as well? Since waving is also performed by priests, there is no reason to distinguish between offerings of male Jews and offerings brought by others, as the priests can wave those on behalf of their owners. If so, what is the meaning when the verse states: “The children of [benei] Israel”? It means that only the Jewish people wave their offerings, but gentiles who bring their offerings do not wave them. Only sons of [benei] Israel, i.e., males, wave their offerings, but women do not wave their offerings.

It is taught in another baraita: With regard to the phrase: “The children of Israel,” I have derived only that the requirement of waving applies to the children of Israel, i.e., those who were born Jewish. From where is it derived that the same applies to converts and to emancipated Canaanite slaves? The verse states, immediately after that phrase: “He who offers [hammakriv] his sacrifice of peace offerings” (Leviticus 7:29), which indicates that the halakha of waving applies to anyone who brings his offering to the Temple, including converts and emancipated slaves.

The baraita challenges: Or perhaps this term does not serve to include converts and emancipated Canaanite slaves, but rather this is referring to the priest who sacrifices [hammakriv] the sacrificial portions on the altar? The baraita answers: This term cannot be referring to the priest, as when it states: “His own hands shall bring the offerings of the Lord made by fire. The fat with the breast he shall bring, that the breast may be waved for a wave offering before the Lord” (Leviticus 7:30), the requirement of waving by the owner is stated. Since the obligation of the owner to wave is stated in this verse, and the obligation of the priest is derived from the verbal analogy from the term “hand” written with regard to a peace offering, evidently both the owner and the priest must wave the offering. The Gemara asks: How so? The Gemara answers: The priest places his hands beneath the hands of the owner and waves the offering together with the owner.