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1)

(a) As already explained, Rebbi Yehoshua ben Korchah learns from "Kol Kehal Adas Yisrael" that one can appoint a Sheli'ach for Kodshim. Rebbi Yonasan learn from ...

1. ... this Pasuk - that it is possible for the whole of Yisrael to fulfill their obligation with one lamb, despite the fact that inevitably, no-one will receive a k'Zayis (because he holds that the eating of the Pesach is not crucial to the fulfillment of one's obligation).
2. ... the Pasuk there "ve'Yikchu Lahem Ish Seh le'Veis Avos Seh la'Bayis" - that one can appoint a Sheli'ach by Kodshim.

(b) He cannot learn Shelichus from the first Pasuk - since there they are all partners (and we would not know that one could appoint even someone who is not a partner as a Sheli'ach).

(c) It is nevertheless possible to derive it from the second Pasuk (in spite of the fact that they are all partners there too) - because since we already the know the basic Chidush from the first Pasuk, we use the second one for Shelichus even where the Sheli'ach is not a partner ('Im Eino Inyan').

(a) The problem with the previous Limud is - that we need the Pasuk to teach us the Din of Rebbi Yitzchak, who says that a man can acquire on behalf of others, but not a Katan.

(b) We conclude that the source of Rebbi Yitzchak's Din is the Pasuk there "Ish L'fi Ochlo". The problem with this is - that we need that Pasuk too, to teach us that that one may Shecht the Pesach even if it is only on behalf of one person ('Shochtin es ha'Pesach a ha'Yachid').

(c) To which we reply - that Rebbi Yonasan holds 'Ein Shochtin es ha'Pesach al ha'Yachid'.

(a) Rav Gidal Amar Rav learns Shelichus from the Pasuk "va'Nasi Echad Nasi Ehad la'Mateh". He cannot ...

1. ... mean literally Shelichus - because the division of land incorporated land belonging to Ketanim, who cannot appoint a Sheli'ach (as we saw in the Parshah of Get, where the Torah writes "Ish").
2. ... alternatively be teaching the principle 'Zachin le'Adam she'Lo be'Fanav' (since whatever concerns a Katan is considered 'she'Lo be'Fanav), like Rav Gidal Amar Rav says - because the distribution of Eretz Yisrael was not purely a Z'chus; it was also a Chov, seeing as a person might receive a portion of land in mountainous country when he would have preferred it in the valley (or vice-versa), in which case it would be a Chov.

(b) So ultimately, we amend the Limud from there to learn like Rava bar Rav Huna Amar Rav Gidal Amar Rav, who learns - that when Yesomim come to divide their father's property, Beis-Din appoint an agent to distribute it, even though, the gains will inevitably incorporate a slight disadvantage, inasmuch as he receives a portion of land that he would rather have exchanged for another.

(a) When minors come to divide their father's property, to ensure that they get a fair deal, Beis-Din appoint an agent for each heir, who serves the interest of his 'client'. Rav Nachman Amar Shmuel permits the children to revoke the agents' division when they grow up. Rav Nachman himself disagrees - because 'Im-Kein, Mah Ko'ach Beis-Din Yafeh?' (the Beis-Din's authority will be undermined).

(b) The Tana Kama of the Mishnah in Kesuvos rules that if the Beis-Din erred in their assessment of the debtors poeperty by a sixth, the subsequent sale of one of his fields is Batel. Raban Shimon ben Gamliel - validates the subsequent sale, because 'Im-Kein, Mah Ko'ach Beis-Din Yafeh'.

(c) To reconcile Rav Nachman there, who rules like the Chachamim, with his ruling here ('Im-Kein, Mah Ko'ach Beis-Din Yafeh') - we point out that the Mishnah in Kesuvos specifically speaks when the Beis-Din erred, whereas here we are speaking when they did not.

(d) In spite of the fact that we are speaking when the Beis-Din did not err, as we just explained, Shmuel nevertheless grants the children the right to protest - not to redistribute the property from scratch, but to redistribute the portions of land (which remain intact).

5)

(a) If the seller overcharges the purchaser by less than a sixth, the sale is valid, by more than a sixth, it is not. If he overcharges him by exactly a sixth - the sale is valid, but the seller must return the difference.

(b) (Rava Amar) Rav Nachman says - that brothers who divide their deceased father's property have the same Din as buyer and seller in a sale (because he holds 'Ein Bereirah').

(c) Rava qualifies all three Halachos. In his opinion ...

1. ... the sale is invalid even though the Ona'ah is less than a sixth - if the one who was overcharged appointed a Sheli'ach to effect the transaction, because he can then claim that he appointed him a Sheli'ach for his own good, not to his detriment.
2. ... the sale is valid, even though the Ona'ah is more than a sixth - if they initially agreed to have the land assessed by the Beis-Din, like the Rabbanan on the previous Amud who hold 'Im-Kein, Mah Ko'ach Beis-Din Yafeh' (despite his Rebbe, Rav Nachman's having ruled there like Raban Shimon ben Gamliel).
3. ... the sale is fully valid (and he does not need to return the difference) even in a case of exactly one sixth - if the sale was one of land (because 'there is no Ona'ah by Karka'os').

(d) And the sale will be invalid even by a sale of land - in the event that they actually measured the land, because of Rabah's Din, which we will now discuss (and which overrides the principle 'Ein Ona'ah le'Karka'os').

(a) Rabah said - that whenever there is a discrepancy re. something that is measured, weighed or counted, the recipient must return the difference, even if the discrepancy is less than a sixth.

(b) The reason for this is - that, whereas people are willing to forego such a small discrepancy with re. to something that is assessed, they will not permit any discrepancy at all by goods that are measured, weighed or counted (where they expect total accuracy).

(a) The Tana of the Mishnah in Bava Kama rules that if someone places a burning fire in the charge of ...

1. ... a Chashu (Cheresh, Shoteh ve'Katan) - although he is not liable at the hand of Beis-Din to pay for damages, he is morally obligated (be'Dinei Shamayim) to do so.
2. ... a Pike'ach - then the Pike'ach is Chayav.

(b)The Pike'ach is not considered the Sheli'ach of the owner of the fire (in which case, the owner is the one who will be Chayav) - because of the principle 'Ein Sheli'ach li'D'var Aveirah'.

(c) The reason for this is, because the one who sent the Sheli'ach can say to him 'Divrei ha'Rav ve'Divrei ha'Talmid, Divrei Mi Shom'in' ('Whoever would have thought that you would listen to me and not to Hashem?')

(a) When the Tana of the Mishnah in Me'ilah says 'Sheli'ach she'Lo Asah Shelichuso, Sheli'ach Ma'al' - he is referring to someone who has money of Hekdesh by him, and who, not realizing that the money belonged to Hekdesh, asks someone to purchase something with them.

(b) Assuming that the Sheli'ach did fulfill his Shelichus - the sender is Mo'el.

(c) Having just concluded 'Ein Sheli'ach li'D'var Aveirah', the sender is Mo'el and not the Sheli'ach - because we learn via a 'Gezeirah-Shavah' "Chet" "Chet" from Terumah, that there is Shelichus by Me'ilah.

(d) We cannot learn that 'Yesh Sheli'ach li'D'var Aveirah' from Me'ilah - because Me'ilah and Shelichus Yad (a guardian who used the article he is guarding without permission) are 'Sh'nei Kesuvim ha'Ba'im ke'Echad' (according to Beis Hillel, as we shall now see).

(a) Beis Shamai learns from the Pasuk "Al Kol D'var Pesha" that a guardian is Chayav for merely intending to use the article or for saying that he will. Beis Hillel learns from the Pasuk "Im Lo Shalach Yado bi'Meleches Re'eihu" - that he only becomes Chayav if he actually uses the article (and not for just thinking or saying that he will).

(b) Beis Hillel learn from "Al Kol D'var Pesha" - that if he asks his Slave or his Sheli'ach to go and use the article, he is also Chayav (so we see that there is Shelichus by Shelichus Yad, even though it is an Aveirah).