If the agent subtracted ten from the denominator and separated one-fortieth or added ten to the denominator and separated one-sixtieth, thereby giving more or less than the owner intended, his teruma is teruma. From where do we derive that one can appoint an agent to separate teruma? And if you would say that it is derived from divorce, one could argue: What is an aspect unique to divorce is that it is considered a non-sacred matter in relation to teruma and will have different halakhot, so one cannot learn from divorce that one can appoint an agent to separate teruma. The Gemara answers: The verse states with regard to teruma: “So you also shall set apart a gift unto the Lord of all your tithes” (Numbers 18:28). Once the verse states “you,” the addition of the word “also” in the term “you also” serves to include an agent.

The Gemara asks: And let the Merciful One write in the passage concerning teruma that one can appoint an agent, and the halakha that one can appoint an agent to act on his behalf in these other matters, i.e., divorce and betrothal, can come and be derived from it. The Gemara answers: Agency in these matters cannot be derived in this manner because the derivation can be refuted: Separating teruma is different, in that it is able to be separated by mere thought. It is enough for one to decide that a certain portion of his produce shall be teruma to have that status take effect. Just as there is this leniency unique to separating teruma, perhaps the leniency that enables one to appoint an agent is also unique to separating teruma.

The Gemara further clarifies the source for agency: Generally, the Paschal offering was brought by a group of people together. But there is that which we learned in a mishna (Pesaḥim 98b): In the case of a group whose Paschal offering was lost before it was sacrificed, and they said to one member of the group: Go and search for our Paschal offering, and when you find it, slaughter it on our behalf; and this person went and found the lost animal and slaughtered it on behalf of the entire group, but meanwhile, despairing of his return, they took a different animal and slaughtered it as a Paschal offering, the halakha is as follows: If his Paschal offering was slaughtered first, he eats from his offering, and they eat and drink with him. This demonstrates that one can act as an agent to slaughter the Paschal offering.

From where do we derive this halakha, that one can appoint an agent to slaughter an offering? And if you would say that it is derived from these other instances of agency, i.e., divorce and teruma, one could refute this derivation by saying: What is unique about these is that they are considered non-sacred matters relative to offerings, and perhaps offerings have their own set of halakhot.

The Gemara answers: He derives it from that which Rabbi Yehoshua ben Korḥa says, as Rabbi Yehoshua ben Korḥa says: From where is it derived that the legal status of a person’s agent is like that of himself? As it is stated with regard to the Paschal offering: “And the whole assembly of the congregation of Israel shall slaughter it in the afternoon” (Exodus 12:6). Is it so that the whole assembly slaughters the offering? But only one person from each group slaughters it. Rather, it can be derived from here that the legal status of a person’s agent is like that of himself.

In light of that exposition, the Gemara asks: Let the Merciful One write in the Torah the halakha of an agent with regard to offerings, and these, i.e., agency in the cases of betrothal, divorce, and teruma, can come and be derived from it. The Gemara answers: Agency in these matters cannot be derived in this manner because the derivation can be refuted: What is unique about offerings is that the majority of their actions are performed by means of an agent. Since most of the sacrificial service is performed by priests, who serve as the agents of those bringing the offerings, the general halakha of agency cannot be derived from there.

The Gemara continues to ask: For the reasons stated, the halakha of agency cannot be derived for any one of these from any other one of them. Still, derive one of these from the other two. The Gemara clarifies: Which of them will be derived from the others?

If you say: Let the Merciful One not write the halakha of agency with regard to offerings and derive agency with regard to offerings from these, i.e., divorce and teruma, that derivation can be refuted: What is unique about these is that they are considered non-sacred matters relative to offerings, as even teruma is not sacred compared to offerings, and sacred procedures such as offerings may have their own halakhot. If you say: Let the Merciful One not write the halakha of agency with regard to divorce, and derive agency with regard to divorce from these, i.e., teruma and offerings, this too can be refuted: What is unique about these is they can be designated by means of thought, and therefore may be easier to effect than divorce.

Rather, it is the third derivation that is possible: Let the Merciful One not write the halakha of agency with regard to teruma, and derive agency from these, i.e., offerings and divorce. Although teruma is sacred, offerings are more sacred, and yet the halakha of agency applies to them. Although the separating of teruma can be accomplished by means of thought, as opposed to divorce, offerings can also be designated by means of thought. The Gemara answers: It is indeed so; this is the derivation for the applicability of agency to teruma.

The Gemara asks: But then why do I need the derivation that once the verse states “you,” the addition of the word “also” in the term “you also” serves to include an agent? The Gemara answers: It is necessary to function as the source of the statement of Rabbi Yannai, as Rabbi Yannai says that from the term “you also,” the following is derived: Just as you, those who appoint agents, are members of the covenant, i.e., Jews, so too, your agents must be members of the covenant. A gentile cannot separate teruma even if appointed as an agent by a Jew.

The Gemara asks: Why do I need a verse to teach this halakha? It is derived from that which Rabbi Ḥiyya bar Abba says that Rabbi Yoḥanan says, as Rabbi Ḥiyya bar Abba says that Rabbi Yoḥanan says: A slave cannot become an agent to receive a bill of divorce from the hand of a woman’s husband on her behalf because he is not included in the laws of bills of divorce and betrothal. This indicates that there is a principle that if certain matters do not apply to a person, he cannot act as an agent with regard to those matters. Therefore, since gentiles are not commanded to separate teruma, they cannot be agents for its separation.

The Gemara answers: It was nevertheless necessary to derive this halakha for the case of teruma, because it cannot be derived from the statement of Rabbi Yoḥanan. This is as it might enter your mind to say: It is a slave who cannot serve as an agent to receive a bill of divorce, since he cannot release a woman by divorce at all; but a gentile, since he is included in his own teruma, as we learned in a mishna (Terumot 3:9): A gentile or a Samaritan who separated teruma from their own produce, their teruma is considered teruma, despite the fact that they are not obligated to do so, I will say that he can also be appointed as an agent. To counter this argument, the term “you also” teaches us that only members of the covenant can act as agents for separating teruma; gentiles cannot.

The Gemara asks: But according to Rabbi Shimon, who exempts one from paying an additional penalty for the teruma of a gentile, this explanation cannot be stated. As we learned in a mishna (Terumot 3:9): If the teruma of a gentile gets mixed with regular produce, it is considered to be a mixture of teruma and non-sacred produce, and if a non-priest eats this mixture unwittingly he is liable to pay for it an additional one-fifth beyond its value, just as is the halakha with regard to one who unwittingly eats teruma. But Rabbi Shimon exempts him from paying the additional one-fifth, as he holds that the teruma of a gentile possesses no sanctity and is considered a mere gift to a priest. If so, if there is no need to learn the additional halakha that a gentile cannot act as an agent with regard to the separating of teruma, why do I need the derivation from “you” and “you also”?

The Gemara answers: It was necessary to state this additional term, as it might enter your mind to say: Since the Master says that the word “you” is interpreted as a limitation, it means that “you,” but not sharecroppers, can separate teruma, as a sharecropper cannot separate teruma from the produce of the owner of the field; “you” can separate teruma but not partners from shared property without the consent of the other; “you” can separate teruma but not a steward [apotropos] from the estate that he is administering; and “you” can separate teruma but not one who separates teruma from produce that is not his, you might also say: “You” can separate teruma and not your agents. The verse therefore teaches us that “you also” indicates that one can appoint an agent to separate teruma.

The Gemara poses a question with regard to the basic derivation of the halakha of agency: This works out well according to the opinion of Rabbi Yehoshua ben Korḥa, who explains that the verse: “And the whole assembly of the congregation of Israel shall slaughter it in the afternoon” (Exodus 12:6), teaches the halakha of agency with regard to offerings. But according to the opinion of Rabbi Yonatan, who derives a different exposition from this verse, from where do we derive the halakha of agency with regard to offerings? As it is taught in a baraita that Rabbi Yonatan says: From where do we derive that all of the Jews can fulfill their obligations