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מסכת חולין פרק ב משנה א
השוחט אחד בעוף  One who slices one [of the two simanim which must be severed during shechita, which are the trachea and esophagus] by a bird
ושנים בבהמה

or two [of the simanim] by an animal,

שחיטתו כשרה his slaughtering is valid,
ורבו של אחד כמוהו and [slicing through] most of one [of the simanim] is like its entirety.
רבי יהודה אומר Rabbi Yehuda says:
עד שישחט את הורידין

until he slices the veridin (these are blood vessels that run next to the simanim, the jugular veins and/or carotid arteries).

חצי אחד בעוף

[If one slices only] half of one [siman] by a bird

ואחד וחצי בבהמה

or one and a half by an animal

שחיטתו פסולה

the slaughtering is invalid;

רוב אחד בעוף

most of one by a bird

ורוב שנים בבהמה

or most of [each of the] two by an animal,

שחיטתו כשרה

his slaughtering is valid.


משנה ב

השוחט שני ראשין כאחד

One who slices two heads as one,

שחיטתו כשרה

his slaughtering is valid.

שנים אוחזים בסכין ושוחטין

if two hold a knife and slaughter

אפילו אחד למעלה ואחד למטה

even if one is above and one is below,

שחיטתן כשרה

their slaughtering is valid.


עד שישחט את הורידין - Rabbi Yehuda is not stating that the שחיטה is פסול, but rather that these blood vessels must be slit during שחיטה to drain their blood properly.  While this can be accomplished with other organs via salting, in this case he holds that salt will not remove the blood from these organs. 

אפילו אחד למעלה ואחד למטה - There are different opinions of that this refers to.  Some say that the two people are hold the knife at either end, one at the handle and one at the blade.  Others say if refers to a case where they do actually each hold the knife at different heights, as a result of which the blade is diagonal.  Another interpretation in the גמרא is that the two people each hold a separate knife at different points on the throat of the animal.