1)

(a)Our Mishnah states 'Ein ha'Meduma Medame'a Ela l'fi Cheshbon'. This is referring to - a Sa'ah of T'rumah that becomes mixed with a Sa'ah of Chulin, and one Sa'ah of the mixture then falls into less than a hundred Sa'ah of Chulin.

(b)The Tana rules that ...

1. ... a k'Beitzah of Chulin dough which became Chametz when a k'Beitzah of T'rumah dough falls into it, and a k'Beitzah of it then falls into another Chulin dough - will forbid the latter to Zarim, if half a k'Beitzah of dough (according to the Cheshbon) would be able to cause it to rise.

2. ... drawn water that falls into a Mikvah - only forbids it according to the Cheshbon (which will be explained in the Sugya).

3. ... Mei Chatas that one prepared by placing the ashes into the container first - the water is Pasul, because one is required to place the water first, as we shall see.

(c)'Beis ha'Peras' is - a field in which a grave has been dug-up.

(d)When the Tana says 'Ein ...

1. ... Beis ha'Peras Oseh Beis ha'Peras', he mean that - it renders Tamei the area given in the Gemara, but not beyond, even if one continues to plow there.

2.... T'rumah Achar T'rumah', he means that - if one designates two sets of T'rumah, the second set does not take effect.

2)

(a)The Tana Kama rules that neither a Temurah nor a V'lad can make a Temurah. Rebbi Yehudah holds that - a V'lad can (as we have already learned).

(b)The Chachamim counter that - Hekdesh can make a Temurah, but not a V'lad.

3)

(a)Rebbi Chiya bar Aba citing Rebbi Yochanan establishes the opening case of our Mishnah not like Rebbi Eliezer. The Chachamim in a Beraisa rule that if a Sa'ah of T'rumah falls into less than a hundred Sa'ah of Chulin, some of which then falls into another batch of Chulin, it is only Medameh according to the Cheshbon. Rebbi Eliezer rules that - it forbids as if it was Vaday T'rumah ...

(b)... because he considers the second Sa'ah that fell to have been the Sa'ah of T'rumah that fell the first time.

4)

(a)Rebbi Eliezer also disagrees with the second ruling ('Ein ha'Mechametz Mechametz Ela ... '). He rules that in a case where a Chulin yeast and a T'rumah yeast fall into a Chulin dough, assuming that neither yeast could cause the dough to rise on its own - we go after the last one (which combines with the first to render the Chulin dough forbidden) ...

(b)... because he holds (regarding two things that combine to affect a third thing) Zeh ve'Zeh Gorem, Asur (irrespective of which one really fell in last) ...

(c)... and the reason that he said 'Achar Acharon Ani Ba' is - because if the Isur fell in first and he removed it, the dough would be permitted.

(d)The Rabbanan, who hold 'Zeh ve'Zeh Gorem, Mutar' - permit the dough, unless the Isur on its own is able to cause it to rise.

5)

(a)Rebbi Chiya bar Aba Amar Rebbi Yochanan suggests that the ruling of our Mishnah that drawn water only render a Mikvah Pasul according to the Cheshbon, goes like Rebbi Eliezer ben Ya'akov - who permits adding nineteen Sa'ah of drawn water to twenty-one Sa'ah of Kasher water ...

(b)... provided one poured the water into a cavity four Amos away from the Mikvah, from which it flows via a ditch into the Mikvah (known as Hamshachah). Otherwise, three Sa'ah of drawn water would disqualify it.

(c)We refute Rebbi Chiya bar Aba Amar Rebbi Yochanan's suggestion, because we would then extrapolate that the Rabbanan - (who do not agree with Rebbi Eliezer ben Ya'akov's leniency), must argue with the very concept of Hamshachah.

(d)In which case, Ravin who arrived from Eretz Yisrael and quoted Rebbi Yochanan as saying that - 'a Mikveh that consists entirely of drawn water that is poured into it by means of Hamshachah is Kasher' will concur neither with Rebbi Eliezer ben Ya'akov nor with the Rabbanan.

6)

(a)So Rabah (or Rav Papa) equates Mayim She'uvin l'fi Cheshbon with Yosef ben Choni. The Tana Kama in a Beraisa disqualifies a Mikveh into which three Lugin of drawn water are poured, even if they are poured into it using two, three, four or even five utensils. Yosef ben Choni agrees with regard to two or three utenils, but declares the Mikveh Kasher with four or five ...

(b)... and l'fi Cheshbon then means - l'fi Cheshbon Keilim.

7)

(a)Rebbi Chiya bar Aba Amar Rebbi Yochanan establishes our Mishnah ('Ein Mei Chatas Na'sin Mei Chatas Ela im Matan Eifer') not like Rebbi Shimon, who says in a Beraisa - 'Hikdim Afar le'Mayim, Kasher'.

(b)Rebbi Shimon's D'rashah is based on the fact that the Torah spells the word "me'Afar" (in the Pasuk in Chukas "me'Afar S'reifas ha'Chatas") with an 'Ayin' (meaning dust) instead of with an 'Alef' (meaning ashes) - in order to learn a Gezeirah-Shavah "Afar" "Afar" from Sotah.

(c)Rebbi Shimon learns ...

1. ... Parah from Sotah - with regard to the fact that the water takes precedence over the ashes.

2. ... Sotah from Parah - with regard to the fact that if the Kohen places the water first, he is nevertheless Yotzei.

(d)Rebbi Shimon knows that by Sotah, the water can precede the ashes - from the Gezeirah-Shavah "Afar" "Afar" from Parah.

8)

(a)And from the fact that one Pasuk gives the ashes precedence ("ve'Nasan alav Mayim Chayim"), and another Pasuk, the water ("Mayim Chayim el Keli"), he learns that - in effect, the Kohen may do whichever he pleases.

(b)Whereas the basis of the Chachamim's opinion (that it is crucial to place the water in the receptacle first) lies - in the Pasuk "Mayim Chayim el Keli" (which they consider the basic Halachah) ...

(c)... and the Torah writes "ve'Nasan alav Mayim Chayim ... " to teach us that - after adding the ashes, he is obligated to mix them with the water, by stirring them with his finger.

9)

(a)If the Chachamim were to learn the Reisha literally, they would interpret the Seifa "Mayim Chayim el Keli" to mean that - the Kohen is obligated to draw the water from the spring with the receptacle that is being used to sprinkle with (and not with another receptacle and to then transfer it into the aforementioned receptacle afterwards) ...

(b)... and the Chachamim learn the Seifa literally, and not the Reisha - because it is common to place the Machshir (the ashes in this case), on top (as we find by Sotah).

10)

(a)We establish our Mishnah 'Ein Beis ha'P'ras Oseh Beis ha'P'ras' not like Rebbi Eliezer, who says 'Beis ha'P'ras Oseh Beis ha'P'ras', by which he means that - if one finds a dug grave in one field, one has to declare all four surrounding fields Tamei too, in case the plow carried bones into any of them in the process of plowing.

(b)And when Rav Dimi arrived from Eretz Yisrael and quoted ... Resh Lakish as saying that one Beis-ha'Peras makes a Beis ha'Peras up to a Shi'ur of three fields and two furrows - he meant three fields in a row, the entire middle field, and a furrow-length at either end.

(c)A furrow's-length is - one hundred Amos.

(d)They only decreed on two fields and not four - because a plow only carries bones in the direction that it is plowing (either east to west or north to south).