1)

(a)Rebbi Yochanan cited a Machlokes between Rebbi Shimon ben Chalafta and the Rabanan regarding the Shi'ur of the piece of wool of the Parah - one said ten Zuz, the other, a Shekel (two Zuzim).

(b)The Siman to remember that the two opinions are extreme - is 'Echad ha'Marbeh, v'Echad ha'Mam'it (meaning literally that one says a lot, the other, a little).

(c)Others say that their Machlokes did not concern the Parah Adumah, but the Sa'ir ha'Mishtale'ach. They give the Siman to remember the Machlokes as 'Ravya bar Kisi atones like the Sa'ir ha'Mishtale'ach' - because that was the day on which Ravya bar Kisi (a Talmid-Chacham of that time) dies - and the death of Tzadikim atones like the Bigdei Kehunah.

2)

(a)Rav Yitzchak heard about two Shechitos, one, that of the Parah Adumah, the other, that of the Kohen Gadol's bull on Yom Kipur - one of which is Kasher through a Zar, the other, which is Pasul.

(b)Rav learns that the Parah becomes Pasul if it is Shechted by a Zar - because the Torah writes by it "Elazar", and "Chukah" (and Chukah always teaches that it is crucial).

(c)Aharon's bull on Yom Kipur however, does not become Pasul through the Shechitah of a Zar (despite the fact that there too, the Torah writes "Aharon" and "Chukah" - because the Torah writes them by the Shechitah, which is not really an Avodah).

(d)The Parah Adumah could not possibly be Kedushas ha'Guf (i.e. Mizbe'ach) - because its Shechitah took place on the Har ha'Mishchah, and not in the Azarah.

3)

(a)As a precedent to disqualify a Zar, even though it has nothing to do with Kedushas Mizbe'ach - we have the sightings of Nega'im, which only a Kohen is authorized to declare Tamei or Tahor.

(b)Shmuel learns from the combination of Aharon and Chukah that Aharon's bull becomes Pasul if it is Shechted by a Zar. Nevertheless, the Parah remains Kasher - because of the Pasuk "v'Shachat Osah le'Fanav" meaning that a Zar should Shecht it in front of him.

(c)Rav interprets the word "le'Fanav", from which Shmuel derives the previous Derashah - to mean that the Kohen should not remove his mind from the Parah during the Shechitah.

(d)Rav requires two Pesukim ("v'Shachat Osah le'Fanav" and "v'Saraf es ha'Parah l'Einav) for Hesech ha'Da'as, because, from the first Pasuk alone, we would have thought that it is only at the beginning (during the Shechitah) that Hesech ha'Da'as is crucial, but not at the end (by the burning). And had it taught us this at the end, we would have thought that it is specifically there, where the animal becomes valid for what it is being brought for, that Hesech ha'Da'as is crucial, but not by the Shechitah.

4)

(a)Filling the water and mixing it with the ashes also become Pasul through Hesech ha'Da'as - because the Torah writes "l'Mishmeres l'Mei Nidah".

(b)Hesech ha'Da'as by throwing the cedar wood, the hyssop and the piece of red wool into the ashes does not disqualify the Parah - because they are not an intrinsic part of the cow.

5)

(a)From the fact that either "Elazar" or "Kohen" is written by each of the following (with regard to the preparation of the Parah Adumah): the Shechitah; the Kabalas ha'Dam; the Haza'ah; the burning, and the throwing of the cedar wood, the hyssop and the piece of red wool into the ashes - that only a man is permitted to perform them, but not a woman.

(b)And from the word "Zos Chukas ha'Torah" - we learn that they must be performed by day.

(c)We learn from the word "Zos Chukas ha'Torah" - that the one who gathers the ashes, the one who fills the water and the one who mixes the ashes with the water, are precluded from the previous Derashah. Consequently, they may be performed by day.

(d)The reason that we include the first group in the stringency, and exclude the second - is because the first group, like Haza'ah, are Pasul from being performed by women (so we include them in the restriction of the day-time - like Haza'ah); whereas the second group, which (unlike Haza'ah) are Kasher to be performed by women, are rather included in "Zos", to preclude them from the restriction.

6)

(a)We initially reject this proof (from the Beraisa, that if a woman is Pasul, so is a Zar), on the basis of the Haza'ah of its ashes, which is Pasul if performed by a woman, but Kasher if performed by a Zar.

(b)We nevertheless go on to accept the proof from the Din of a woman - on the grounds that, if a woman is Pasul to perform Haza'ah, it is only because the Torah writes the word "Elazar" (from which we Darshen "Elazar" 'v'Lo Ishah'); in that case, a Zar must also be Pasul, because of the Derashah "Elazar" 'v'Lo Zar'.

7)

(a)When the Gemara says that some of the Pesukim in the Parshah of Parah Adumah are 'Motzi Miyad' and some are 'Mimeila' - it means that some of the Pesukim come to preclude from what the previous Pasuk taught, whilst others retain the previous Derashah (each case on its own merit, as we shall now see).

8)

(a)We learn from "u'Nesatem Osah el Elazar ha'Kohen" - that it was only the first Parah Adumah that had to be prepared by Elazar (the deputy Kohen Gadol), but not subsequent ones.

(b)The straightforward way of understanding this is that - in future generations, any Kohen is eligible to prepare the Parah Adumah.

(c)Others however, learn from a 'Gezeirah Shavah' from Yom Kipur from "Chukah" "Chukah" that it requires the Kohen Gadol.

9)

(a)Rebbi learns from "v'Hotzi Osah" - that, even if the Parah refuses to go with the Kohen to be Shechted, it is forbidden to take out a black cow, or another red one, to lure it out.

(b)According to the Tana Kama, if the cow refuses to budge, one may not take out together with it ...

1. ... a black cow - so that people should say that he Shechted a black cow (instead of a red one).

2. ... a red cow - so that people should not say that he Shechted two cows (instead of one).

(c)In spite of the Pasuk "v'Hotzi Osah", the Tana Kama nevertheless requires a reason for it - because the Tana Kama is none other than Rebbi Shimon, who tends to give reasons for the Torah's rulings.

(d)The practical difference between Rebbi and Rebbi Shimon - is whether the Kohen is permitted to lead a donkey (or any other animal other than a cow): according to Rebbi Shimon, it will be permitted to do so, since nobody will accuse the Kohen of Shechting a donkey instead of a cow; whereas according to Rebbi, any second animal is precluded from "Osah".