Quand l'un des tuyaux a été percé pour tuer la volaille, et tous les deux pour tuer le bétail, ils sont Cashér; également lorsque la plus grande partie de ceux-ci avait été coupée. R. Jehudah dit: "Il est nécessaire qu'en tuant des volailles, les veines du côté de la gorge soient également coupées." Si seulement la moitié [de la trachée] est coupée chez la volaille, et une moitié [c'est-à-dire la trachée et la moitié de l'œsophage] chez le bétail, elle est inapte; mais si la plus grande partie d'un tube est coupée chez la volaille, et la plus grande partie des deux chez le bétail, c'est Cashér.
Tosefta Chullin
Everyone is permitted to slaughter [an animal for non-consecrated purposes, see Hul. 1:1], even a Samaritan, even an uncircumcised Israelite, and even an Israelite who changes his belief to idolatry (lit., "worship of the stars"). The slaughter by an idolater, behold, that is invalid, and the slaughter by a monkey, behold, that is invalid, as it is said, "And you shall slaughter…and you shall eat” (Deut. 27:7). Not that "the idolater shall slaughter," and not that "the monkey shall slaughter," and not that the slaughter shall be accidental. An Israelite that [commenced the] slaughter, and an idolater finished the slaughter with his own hands, the slaughter is invalid. If he slaughtered two [simanim, the gullet and the windpipe, see Hul. 2:1], or the majority of two, his slaughter is valid. An idolater that [commenced the] slaughter, and an Israelite finished the slaughter with his own hands, the slaughter is valid. If [the idolater commenced the] slaughter with something that does not render [the slaughter] a tereifa (i.e., prohibited from consumption, see Hul. 3:1), and the Israelite came and finished, it is permitted to eat. An Israelite and an idolater that were holding the knife, and they slaughter -- even [if] one was on top and one was on the bottom (Hul. 2:2) -- their slaughter is valid.
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Tosefta Chullin
One who slaughters [by cutting] two halves [of the simanim] of a bird, his slaughter is invalid (Hul. 2:1), and needless to say, [cutting] two halves of [the simanim] of an animal [is invalid]. Rabbi Yehuda invalidates any [slaughter] unless [the animal] is slaughtered [by cutting] the gullet and the two veins (i.e., the two major blood vessels in the neck). If he slaughtered half of the windpipe of a fowl and waited according to [the amount of time to perform a complete] slaughter, and afterwards completed the slaughter, his slaughter is valid. [If a slaughter involved the cutting of] one siman or the majority of one in a fowl, even though the it an extended period of time, the slaughter is valid. [If] there as a butcher who cut off the head in one swing, if he intended that [outcome], his slaughter is invalid, but if he did not intend it, his slaughter is valid. If the windpipe was severed and afterwards he slaughtered the gullet, his slaughter is invalid. If he slaughtered the gullet, and found the windpipe [already] severed, there is a doubt [whether the windpipe became severed] before he began the act of slaughter, and a doubt [whether it occurred] once the slaughter had begun. There was once such a situation, and they came and asked the Sages, and they said, "Every doubt involving a severed [organ renders the slaughter] invalid."
