Terumot, Chapter Three, Mishnah Three
This mishnah deals with two partners who jointly own a pile of produce and each gives terumah. For instance, they together own 50 seahs of wheat and each gives 1 seah of terumah (2 per cent). The question is, are both terumah? Neither? One and not the other?
[Two] partners who took terumah, the one after the other:
1) Rabbi Akiva says: the terumah of them both is terumah.
2) But the sages say: the terumah of the first is terumah.
3) Rabbi Yose says: if the first gave the prescribed amount, the terumah of the second is not terumah, but if the first did not give the prescribed amount, the terumah of the second is terumah.
Section one: According to Rabbi Akiva, half of what each partner gave is terumah. Rabbi Akiva looks at this situation as if each partner gave terumah for the half that belonged to him. So each seah is half terumah and half hullin (non-sacred produce). Since we cant determine which is which, each must treat the mixture as if it was medumma.
Section two: The sages say that only the first terumah is terumah. The second terumah was accidental because had the second person known that the other partner already gave terumah, he would not have given it.
Section three: According to Rabbi Yose, if the first person gave the proper measure (see below 4:3, for more information on the proper measure for terumah) than his terumah alone counts. If the first person did not give the proper measure than the second terumah is also terumah.