1) THE "KINYAN" OF RIDING AN ANIMAL
QUESTION: The Gemara asks why it is necessary for the Mishnah to teach that when two people are riding an animal and both claim to have found it, the animal is divided between them. Why can this law not be derived from the first case of the Mishnah, in which two people are holding on to a Shtar? The Gemara answers that the Mishnah may intend to teach that a person can acquire an animal by riding it.
RASHI explains that the Gemara means that riding an animal may be a valid Kinyan even when the rider does not use his feet to cause the animal to move ("Manhig b'Raglav") and thus his act does not qualify as "Meshichah."
Rashi's explanation is necessary since there are other sources that teach that Meshichah is Koneh (see Rashi to 8b, DH Manhig), and therefore it would not be necessary for the Mishnah here to teach that it is Koneh.
However, the Gemara later (8b) cites a Machlokes between Rebbi Meir and the Rabanan with regard to whether a person acquires an animal by riding it. Rebbi Meir rules that even one who is sitting on the animal without holding on to the reins as a rider does still acquires it. The Rabanan maintain that a person who is riding an animal does not acquire the animal unless he is Manhig b'Raglav and uses his feet to make it move. The Gemara there says that the Mishnah does not follow the opinion of Rebbi Meir, because if it did it would not have to say that a rider is Koneh, for even one who is sitting on an animal is Koneh. Rather, the Mishnah must follow the view of the Rabanan, and thus it refers to a person who is riding the animal and causing it to move with his feet. Why, then, does the Gemara here say that the Mishnah refers to an act of riding an animal without being Manhig b'Raglav? (ROSH 1:16)
Moreover, why does the Mishnah teach two cases of riding an animal -- one case in which when both claimants are riding (Rochev) the animals, and one case in which one claimant is riding (Rochev) the animal and the other is guiding (Manhig) the animal?
ANSWERS:
(a) The ROSH disagrees with Rashi and explains the Chidush of the Mishnah differently. The Mishnah is discussing a rider who causes the animal to move. The Chidush of the Mishnah is that even when two people are riding an animal and are causing it to move, the one sitting farther back is also Koneh. Without the Mishnah, one might have thought that the rider sitting in front is considered the primary rider who causes the animal to move, while the one sitting behind him does not cause the animal to move in a normal manner and thus he should not be Koneh the animal.
The case in which one is riding (Rochev) and the other is guiding (Manhig) the animal teaches that even when the rider is Manhig b'Raglav and therefore is doing more than the one who is Manhig alone, both the rider and the Manhig are Koneh the animal.
(b) Rashi understands that according to the Gemara's conclusion (8b), the main point of the Mishnah is to teach that when one claimant is Rochev and one is Manhig, neither one's act overrides the other's, and they are both Koneh. This teaching applies both according to the Rabanan (who say that the person who is riding is also Manhig b'Raglav), and according to Rebbi Meir (who says that the person is riding it without using his feet to make it move).
The Mishnah mentions the first case, in which both are riding it, only in order to lead into the second case, in which one is riding and one is pulling the animal, and it is not intended to teach something new.
How, though, can the Mishnah be discussing a rider who is not Manhig b'Raglav and be following the opinion of Rebbi Meir? The Gemara asks (8b) that if the Gemara is following the opinion of Rebbi Meir, the Mishnah should not discuss only Rochev, since even one who is Yoshev is Koneh. The Mishnah should mention Yoshev as well!
Rashi answers this question (8b, DH Rachuv Mibayei) by explaining that the Gemara is not asking that the Mishnah should have discussed Yoshev rather than Rochev (see MAHARI ABUHAV and RASHBA, cited by the Shitah Mekubetzes). As the Gemara points out, holding on to the reins does not make any difference with regard to Kinyan, and therefore Yoshev and Rochev are identical. The Gemara's question is only that it would not be necessary for Rebbi Meir to teach a second time that Rochev is Koneh, since he already taught that Halachah in Maseches Kil'ayim.
The Gemara answers that even according to the Rabanan, the Mishnah is not teaching a new Halachah when it discusses two people riding an animal, since it refers to two people who are both Manhig b'Raglav, which is a normal form of a Kinyan Meshichah. Rather, according to both Rebbi Meir and the Rabanan, the case of two people riding the animal was mentioned in order to lead into the Halachah that when one of them is riding and one is guiding (Manhig), they are both Koneh, as the MAHARSHA writes. (According to Rebbi Meir, they are Koneh even when the rider is not Manhig b'Raglav, and according to the Rabanan, only when the rider is Manhig b'Raglav is he Koneh it.)

8b----------------------------------------8b

2) ACQUIRING AN ANIMAL THROUGH "YOSHEV," "ROCHEV," OR "MANHIG"
QUESTION: The Gemara attempts to prove from the Mishnah that one who is riding (Rochev) an animal acquires the animal even though he is not using his feet to cause the animal to move (Manhig b'Raglav), according to the Rabanan who disagree with Rebbi Meir. Although one does not acquire the animal by sitting on it (Yoshev), he does acquire it by riding it because he holds on to the reins.
The Gemara proves this from the Mishnah's ruling in the case of two people who are riding an animal, or where one is riding it and one is guiding it (Manhig), and each one claims that the animal is his. The Mishnah rules that they split the animal ("Yachloku").
The Gemara says that the Mishnah does not follow the opinion of Rebbi Meir, because if it did it would not have to say that a rider (Rochev) is Koneh, for Rebbi Meir maintains (Kil'ayim 8:3) that even Yoshev is Koneh (see previous Insight). Rather, the Mishnah must follow the view of the Rabanan, and it teaches that Rochev is Koneh even though Yoshev is not Koneh.
The Gemara concludes that the Mishnah indeed follows the view of the Rabanan, but it refers to a person who is both Rochev and Manhig b'Raglav (he uses his feet to cause the animal to move). The primary Chidush of the Mishnah is not that one who is Rochev and Manhig b'Raglav is Koneh the animal (see MAHARSHA), but rather that when one person is Rochev and one is Manhig, they split the animal even though the one who is Rochev is doing more than the Manhig is doing (since the Rochev is riding and guiding the animal with his feet, and he is also holding on to the animal by the reins).
Why does the Gemara not answer that the Mishnah follows the opinion of Rebbi Meir, and that the reason why the Mishnah writes specifically that Rochev is Koneh as opposed to Yoshev is that when one person is Manhig and one person is Yoshev, the Yoshev is not Koneh since his act of Kinyan is overpowered by that of the one who is Manhig? (RAMBAN)
ANSWERS:
(a) The TOSFOS HA'ROSH answers that the Gemara takes it for granted that holding on to the reins does not improve the act of Kinyan of one who is Rochev. Therefore, if the claimant who is Rochev receives half of the animal when the other claimant is Manhig, then one who is Yoshev also should receive half in such a situation. Only according to the Rabanan is it possible that holding on to the reins might improve his act of Kinyan -- that is, when the rider is doing everything that the Manhig is doing, and in addition he is holding on to the reins. In such a case, one might have thought that the act of the Manhig is insignificant, and thus the Mishnah teaches that the Manhig is Koneh nevertheless. (See TOSFOS DH Mahu d'Teima, and MAHARSHA in MAHADURA BASRA.)
(b) The RAMBAN writes that if an act of Yoshev alone is Koneh, then a person who is Rochev certainly will be Koneh even when another person is Manhig the animal, since the rider's act of Kinyan cannot be worse than that of a person who is sitting with no one else leading the animal.
(c) The RIVAN cited by the Tosfos ha'Rosh answers that the Mishnah in Kil'ayim in which Rebbi Meir says that one who is Yoshev is considered to be moving the animal refers to a situation in which someone else is leading the animal at the same time. The Mishnah there is not giving two different cases -- one case in which a person is leading the animal and another in which a person is sitting in the wagon. Accordingly, the Mishnah in Kil'ayim teaches that Yoshev is considered an act of Kinyan even when someone else is Manhig, and thus certainly Rochev is considered an act of Kinyan.
(d) According to the way we explained the Gemara according to Rashi (see previous Insight), the Gemara is not asking that the Mishnah should have said "Yoshev" instead of "Rochev" according to Rebbi Meir. Rather, the Gemara is asking what the Mishnah teaches when it says that two people riding an animal split it. According to Rebbi Meir, this Halachah (that Rochev is Koneh) is already taught in the Mishnah in Kil'ayim. It must be that the Mishnah here intends to teach that even according to the Rabanan, Rochev is Koneh, and Yoshev is not Koneh.
The Gemara answers that the Mishnah's case of two people riding an animal indeed teaches no new Halachah. Rather, the Halachah that the Mishnah teaches is that when one person is Rochev and one is Manhig, they split the animal. This Halachah is a Chidush both according to the Rabanan (because it teaches that Rochev who is Manhig b'Raglav does not overpower one who is Manhig) and according to Rebbi Meir (because it teaches that Manhig does not overpower the act of a person who is merely Rochev or Yoshev on the animal without being Manhig b'Raglav).