1) HALACHAH: THE UPPERMOST POINT AT WHICH THE CUT OF "SHECHITAH" MAY BE PERFORMED
OPINIONS: The Gemara concludes that "Hagramah" (slanting the cut above the point that delimits the part of the neck upon which Shechitah may be performed) occurs only when the cut is made from the "Shipuy Kova" -- the slope of the "cap" (the thyroid cartilage) at the top of the rings of cartilage -- and upwards. The Gemara says that this area of the neck is the area referred to by the opinion that maintains that the Shechitah is valid when part of the "Chiti" -- the two glands inside the "Taba'as ha'Gedolah" (the cricoid cartilage, or the uppermost ring around the trachea) -- are cut, as long as some of the glands are left uncut. (This is the explanation of RASHI and most Rishonim here, who explain that even if the "Chiti" are cut, the Shechitah is valid as long as some of the "Chiti" remain above the point at which the cut reached (that is, the "Shipuy Kova" is the upper limit).)
What, in practice, is the upper limit of where the cut may be performed?
(a) The SHULCHAN ARUCH (YD 20:1) records the Halachah as described above. The REMA adds that, l'Chatchilah, the Shechitah should be performed below the "Taba'as ha'Gedolah," the uppermost ring.
(b) The SHACH (YD 20:1) cites a number of Acharonim who are stringent and invalidate the Shechitah if the cut extends even partially beyond the uppermost ring (except in a case of great monetary loss, in which case they agree that one may rely on the lenient opinion). The Shach explains that the reason for this stringency is the concern that an unknowledgeable Shochet will not realize that at least a small part of the "Chiti" must remain uncut in order for the Shechitah to be valid, and he will cut above the "Chiti." Due to this concern, the Halachah requires that the Shechitah be done below the "Taba'as ha'Gedolah" altogether, so that the cut does not come near the "Chiti."
2) CUTTING A MAJORITY OF THE "VESHET"
QUESTION: The Rabanan (Tana Kama) in the Mishnah (18a) maintain that even the smallest amount of "Hagramah" (slanting the cut above the point that delimits the part of the neck upon which Shechitah may be performed) above the permitted area for Shechitah invalidates the Shechitah. Rebbi Yosi b'Rebbi Yehudah argues and maintains that as long as the majority of the cut was done in the permitted area, and only a minority of the cut was done above the permitted area, the Shechitah is valid.
Rav Huna in the name of Rav Asi explains that the Machlokes involves a case in which the first third of the Shechitah was done with "Hagramah," and the final two-thirds of the cut was done in the proper place. In a case in which the first two-thirds of the cut was done properly, and the last third was done with "Hagramah," both agree that the Shechitah is valid.
The Gemara attempts to bring support for Rav Asi's understanding of the Machlokes from the Mishnah later (27a) that states, with regard to the Shechitah of a bird, that even when only the majority of one Siman is cut, the Shechitah is valid. This shows that it suffices to cut a majority in order for the Shechitah to be valid ("Rubo k'Chulo"), and, consequently, if the rest of the cut was done with "Hagramah," it is inconsequential. The Gemara rejects this proof, saying that perhaps the Mishnah there is expressing only the view of Rebbi Yosi b'Rebbi Yehudah and not the view of the Rabanan.
TOSFOS (DH Dilma) asks that the Gemara could have given a more basic answer to the proof from the Mishnah later. The Gemara could have said that the Mishnah there is referring to the Veshet (esophagus), while the subject of the Mishnah here (18a) is the cutting of the Kaneh (trachea). The Rabanan do not discuss the cutting of the Veshet at all; perhaps they agree that cutting a majority of the Veshet suffices (while cutting a majority of the Kaneh does not suffice). Why, then, does the Gemara say that the Mishnah (27a) is expressing the view of Rebbi Yosi b'Rebbi Yehudah and not the Rabanan?
REBBI AKIVA EIGER challenges the question of Tosfos. How can Tosfos suggest that the Mishnah (27a) is discussing only the Veshet? The end of the Mishnah there explicitly states, "[Cutting] the majority of one Siman (when slaughtering a bird) or the majority of two Simanim (when slaughtering an animal) is a valid Shechitah." The Mishnah clearly mentions both of the Simanim, and not just the Veshet!
ANSWER: There are two ways to understand why cutting the majority of a Siman (in the case of a bird) or a majority of the Simanim (in the case of animal) constitutes a valid Shechitah. The first way to understand why a majority suffices is that the Torah requires that only a majority (Rov) of the Siman be cut in order for the Shechitah to be valid, and it does not require that the entire Siman be cut.
The second way to understand why cutting a majority suffices is that it works because of the principle of "Rubo k'Chulo." The Torah indeed requires that the entire Siman be cut, but cutting a majority of the Siman is considered like cutting the entire Siman because of the principle of "Rubo k'Chulo."
From the Gemara here it is apparent that the reason why cutting a majority of the Siman suffices is the rule, "Rubo k'Chulo." This is why Rebbi Yosi b'Rebbi Yehudah cites this principle as proof for his ruling that only the majority of the Shechitah must be below the "Taba'as ha'Gedolah."
However, the principle of "Rubo k'Chulo" may apply only in the case of a bird, where only one Siman is slaughtered altogether. The Torah requires that the entire Siman of the bird ("Kulo") be cut, but cutting a majority of the Siman is considered as though the entire Siman was cut ("Rubo k'Chulo"). In the case of an animal, however, perhaps it suffices to cut the majority of the Siman not because of "Rubo k'Chulo" but because a majority of the Siman is all that the Torah requires to be cut! In this case, even the Rabanan who argue with Rebbi Yosi agree that cutting a majority suffices (since it has nothing to do with the principle of "Rubo k'Chulo"). Only where the Torah requires "Kulo" do the Rabanan maintain that Rov does not suffice.
The proof of the Gemara here is from the Mishnah (27a) that says, with regard to the Shechitah of a bird, that "Rov of a Siman is like the entire Siman," clearly expressing that the principle of "Rubo k'Chulo" applies to the Shechitah of a bird. Consequently, the Mishnah's ruling that "Rubo k'Chulo" indeed may refer only to the cutting of the Veshet of a bird, and not to the cutting of the Kaneh of a bird, and Tosfos' question is justified. Although the Mishnah there also states that it suffices to slaughter most of the two Simanim of an animal, that may not be because of the principle of "Rubo k'Chulo" but rather because a majority of the Simanim is all that the Torah requires to be cut when slaughtering an animal. Hence, the Gemara cannot cite that part of the Mishnah as proof that Hagramah will not invalidate the Shechitah of a bird if the Hagramah is performed during the final part of the cutting of the Kaneh, since the Shechitah of a bird requires that the entire Siman be cut and it is only due to the principle of "Rubo k'Chulo" that it suffices to cut most of the Siman. (NEZER HA'KODESH of Rav Moshe Rosen) (Z. Wainstein)

19b----------------------------------------19b

3) THE AMOUNT OF THE CUT OF "HAGRAMAH" THAT INVALIDATES THE "SHECHITAH"
OPINIONS: The Rabanan (Tana Kama) in the Mishnah (18a) maintain that even the smallest amount of "Hagramah" (slanting the cut above the point that delimits the part of the neck upon which Shechitah may be performed) above the permitted area for Shechitah invalidates the Shechitah. Rebbi Yosi b'Rebbi Yehudah argues and maintains that as long as the majority of the cut was done in the permitted area, and only a minority of the cut was done above the permitted area, the Shechitah is valid.
Which opinion does the Halachah follow?
(a) RASHI (30b, DH Teiku) maintains that the Halachah follows the view of the Rabanan. The Gemara there (30b) asks whether the Shechitah is valid in a case in which the Shochet does "Chaladah" (he inserts the knife into the middle of the thickness of the neck and cuts from there outwards) on a minority of the Simanim. The Gemara does not resolve the question ("Teiku").
RASHI explains that the Gemara there is discussing a situation in which a majority of the Simanim were slaughtered properly, and after the majority of the Simanim were slaughtered the Shochet did "Chaladah." RASHI infers from the Gemara there that a mistake in the cutting that occurs even after most of the Simanim have been properly cut invalidates the Shechitah, whether the mistake is "Chaladah" or "Hagramah." This is in accordance with the view of the Rabanan of the Mishnah here (18a) who maintain that even if a small part of the cut of Shechitah was done with "Hagramah," the Shechitah is invalid.
(b) The other Rishonim disagree with Rashi. They explain that the last bit (a minority) of the cut of Shechitah can invalidate the Shechitah only through "Chaladah" or "Shehiyah" (pausing in the middle of the cut). In contrast, cutting a minority with "Hagramah" or "Ikur" (tearing out the Simanim) cannot invalidate the Shechitah. Since the "Hagramah" cut was above the area reserved for Shechitah, it cannot be considered part of the Shechitah, and, therefore, it is considered as though one is cutting ordinary meat and not performing Shechitah. ("Hagramah" invalidates the Shechitah only when it is done before most of the Simanim are cut.)
Since the Gemara (18a) clearly concurs with the opinion of Rebbi Yosi b'Rebbi Yehudah, it is clear that if the Shochet does "Hagramah" in the final bit of the Shechitah, the Shechitah is still valid.
The RASHBA agrees with Rashi that "Hagramah" at the beginning of the Shechitah invalidates the rest of the Shechitah (even if a majority of the Shechitah was done without "Hagramah"; see 19a, "Lishna Acharina").
(c) The RAMBAN (in Milchamos) maintains that as long as an uninterrupted majority of the Simanim were cut correctly, the Shechitah is valid, even if that majority was the last two-thirds of the Shechitah.
(d) The RAMBAM, ROSH, and TUR rule that as long as the majority of the entire Shechitah was done correctly, the Shechitah is valid. Even if the first third was done correctly, the second third was done with "Hagramah," and the last third was done correctly, the Shechitah is still valid (since a total of two-thirds of the Shechitah was done in the correct part of the neck).
HALACHAH: The SHULCHAN ARUCH (YD 24:12-13) rules like the Rambam. The REMA asserts that the custom is to be Machmir like Rashi. (Z. Wainstein)

OTHER D.A.F. RESOURCES
ON THIS DAF