Midrash for Chullin 55:41
מאי לאו בעוף ומאי גמרו גמרו לקנה
Come and hear: If a man cut half of the windpipe and paused for the length of time required for another slaughtering, and then finished it, the slaughtering is valid,<span class="x" onmousemove="('comment',' For the cutting of the first half of the windpipe is not reckoned as part of the slaughtering, since even if half of the windpipe was mutilated by an accident the subsequent cutting of the remainder of the windpipe would be valid; therefore whatever fault occurs at this stage of the cutting is of no consequence.');"><sup>15</sup></span>
Sifrei Devarim
R. Elazar Hakappar says: Now what did we learn from deer and hart? It came (ostensibly) to teach, but it (in the end) it was found to be taught, viz.: Just as a beast (must be slaughtered) through shechitah, so, an animal (e.g., deer and hart), through shechitah, (but a bird [must be slaughtered through shechitah] only by ordinance of the scribes). Rebbi says: "as He commanded you" (Ibid. 21) apprises us that Moses was commanded as to gullet and windpipe (as being the loci of shechitah) and as to the (cutting of) the major portion of one (of these being the criterion for shechitah) in a bird and of both, in a beast.
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