Meilah, Chapter 4, Mishnah 3. This chapter is built around the principle of tzeiruf, the joining together of small quantities to reach a halachic minimum. Our mishnah continues that theme with a series of short rulings, and then Rabi Yehoshua steps in with a general rule that explains exactly when two different sources of tum'ah can be added together and when they cannot.
Pigul and notar
"Kol hapigulin mitztarfin zeh im zeh." Any offering rendered pigul can be reckoned together with another offering of the same status. Pigul means a korban invalidated by an improper thought during its avodah, and whoever eats a kezayit of such meat is liable to karet. The mishnah's point is that this kezayit need not be drawn from one single offering. Should a person eat a little from this pigul korban and a little from that one, and the portions together amount to a kezayit, his liability is no different.
"Kol hanotarim mitztarfin zeh im zeh." The identical rule applies to notar, meat of a korban that remained beyond the time in which it was permitted to be eaten. Portions of notar from different korbanot are added together, and once a kezayit has been consumed the person is liable to karet.
Neveilot and sheratzim
"Kol haneveilot mitztarfot zeh im zeh." All neveilot join together. A neveilah is an animal that died without proper shechitah, and it conveys tum'ah to one who touches it, provided there is a kezayit. Here the mishnah teaches that pieces taken from different neveilot combine, whether they come from kosher species or from non-kosher species, and together they reach the kezayit that transmits tum'ah.
"Kol hasheratzim mitztarfin zeh im zeh." So too with the sheratzim, the creeping creatures. One who eats them receives malkut, and small amounts eaten from different species are added to one another until the minimum measure that carries the penalty of malkut has been reached.
"Dam hasheretz uvesaro mitztarfin." The blood of a sheretz and its flesh are also combined with each other, here in order to reach the size of an adashah, a lentil, which is the measure at which a sheretz conveys tum'ah.
The rule of Rabi Yehoshua
Having listed cases where items do join, the mishnah now sets out precisely when two sources of tum'ah may be added together and when each must stand on its own.
"Kelal amar Rabi Yehoshua: kol shetum'ato veshi'uro shavin mitztarfin zeh im zeh." Rabi Yehoshua stated a general rule. Every pair of items that share both the same tum'ah and the same measure combine with one another. Two matters are being compared. The first is the character of the tum'ah, meaning how long the impurity lasts and when the person may become pure again. The second is the shi'ur, the minimum quantity needed to convey tum'ah. When both of these match, as with two pieces taken from two different neveilot, the pieces are added together and transmit tum'ah.
"Tum'ato velo shi'uro." If the nature of the tum'ah is shared but the measure is not, they do not combine. Take a neveilah and a sheretz. In both cases the person who became tamei is purified at nightfall, so the tum'ah itself is alike. But a neveilah conveys tum'ah only at the size of a kezayit, while a sheretz conveys tum'ah already at the size of a lentil. Since the measures differ, the two are not joined.
"Shi'uro velo tum'ato." And if the measure is shared but the nature of the tum'ah is not, again they do not combine. Take a neveilah and a human corpse. For each of them the minimum is a kezayit, so the measures match. But one who became tamei from a corpse cannot become pure until seven days have passed, while one who became tamei from a neveilah is purified at nightfall. The tum'ah is not the same, so they do not join.
"Lo tum'ato velo shi'uro." And where neither the tum'ah nor the measure is shared, certainly they do not combine. A corpse and a sheretz are the example. The tum'ah of a corpse lasts seven days and its measure is a kezayit, whereas a sheretz allows purity already at nightfall and conveys tum'ah at the size of a lentil.
Each of these three cases closes with the same words: "ein mitztarfin zeh im zeh," the one is not reckoned together with the other. Combining is possible only where the pair corresponds on both counts, in how long the impurity holds a person and in the quantity that is required. The moment they part ways on even one of these points, each stands as an independent category, and nothing belonging to one may be counted toward the other.