Mishnayos Chullin Perek 1 Mishnah 3

השוחט מתוך הטבעת – In the large ring [of the trachea] which is above all of them, is [what the Mishnah] is speaking of.

ושייר בה מלא החוט של פני כולה – on the side of the head, for he did not incline the knife to exit from the ring to the side of the head until he completed [cutting] the entire ring, it is considered valid.

מלוא החוט – that is to say, a bit, but if it was before he completed the entire [ring], he slanted the knife to the side of the head and completed the ritual slaughter above from the ring which was not the place of the ritual slaughter, which is הגרמה (cutting the animal’s throat in a slanting direction – letting the knife slide beyond the space ritually designed for cutting), even though most of the windpipe was cut at the place of the ritual slaughter, the Rabbis invalidated it, since it concluded with a disqualification.

רבי יוסי בר' יהודה אומר מלוא החוט על פני רובה – If he left in it as much as the breadth of a thread of the hair from the ring [of the trachea] at the side of the head over the majority of the ring, that is to say, he cut most of the windpipe within the ring, but the minority of it was cut in a slanted direction and it left its [body] at the side of its head, and he completed the slaughter above it, it is considered valid, as he slaughtered most it in a valid manner, but the other part, he slaughters by cutting mere skin. And the legal decision is that a person who slaughters above the large ring, where the thyroid cartilage (Adam’s apple) begins to protrude and above it is considered invalid, whereas from the thyroid cartilage and below is considered valid. And that means that he left glands, that he slaughtered these two glands of the flesh that are above the large ring but below the thyroid cartilage, and he left a bit of them at the side of the head.