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מסכת חולין פרק ד משנה ד
בהמה המקשה לילד An animal having difficulty in labor
והוציא העבר את ידו and the fetus extends its leg
וחתכה and one cuts it off (the leg)
ואחר כך שחט את אימו and then slaughters the mother,
הבשר טהור the meat [of the fetus] is tahor (even though it was in contact with the severed, and therefore tamei, limb, the fetus cannot contract tunah while still alive).
שחט את אימו If one slaughters the mother
ואחר כך חתכה

and then cuts off [the fetus's leg which, at the time of the slaughtering, had extended outside her body],

הבשר מגע נבלה the meat [of the fetus] is regarded as having contacted a neveilah,
דברי רבי מאיר

these are the words of Rabbi Meir (who holds that the part of the fetus extending outside of her the mother when she was slaughtered is considered as if it had been severed.  The the rest of the fetus is considered to have been slaughtered with the mother, and so is not considered to have been alive when it touched the 'severed' limb).

וחכמים אומרים And the Sages say
מגע טריפה שחוטה it has contacted a slaughtered treifah. (They do not consider a fetus's limb that extended outside of the mother to have become detached at the time of the mother's slaughter; also they hold the mother's slaughter prevents the limb from being considered a neveilah, rather they give it the status of a treifah that had been properly slaughtered.)
מה מצינו בטרפה [The Sages reasoned:] "That which we find by a treifah
ששחיטתה מטהרתה that its slaughter renders it tahor (as a properly slaughtered treifah, while not kosher for consumption, does not impart the tumah of a neveilah),
אף שחיטת הבהמה so too the slaughter of an animal (in this case the mother)
תטהר את האבר renders its limb (in this case the leg that protrudes outside the mother) tahor."
אמר להם רבי מאיר לא Rabbi Meir said to them: "No,
אם טהרה שחיטת טרפה אותה if the slaughter of a treifah renders it tahor
דבר שבגופה - a thing that is part of its body -
תטהר את האבר should it render the limb tahor
דבר שאינו גופה - a thing that is not part of its body?"
מנין [Rabbi Meir continued:] "From where do we know
לטריפה ששחיטתה מטהרתה that for a treifah slaughtering it renders it tahor?
בהמה טמאה אסורה באכילה

A non-kosher animal is prohibited from consumption,

אף טריפה אסורה באכילה so too a treifah is prohibited from consumption.
מה בהמה טמאה Just as a non-kosher animal
אין שחיטתה מטהרתה slaughter does not render it tahor
אף טריפה so too a treifah
לא תטהרנה שחיטתה is not rendered tahor by its slaughter."
לא [The Sages replied:] "No,
אם אמרת בבהמה טמאה if you say this by a non-kosher animal
שלא היתה לה שעת הכשר that never had a moment of being kosher,
תאמר בטרפה can you say it by a treifah
שהיתה לה שעת הכשר that had a time when it was kosher?"
טל לך מה שהבאת [Rabbi Meir responded:] "Take back what you have brought.
הרי שנולדה טריפה מן הבטן If it was a treifah from birth
מנין how would we know [that it is any different than a non-kosher animal]?
לא [Replied the Sages:] "No,
אם אמרת בבהמה טמאה if you say this by a non-kosher animal
שכן אין במינה שחיטה whose species does not have shechitah,
תאמר בטרפה

can you say it by a treifah

שיש במינה שחיטה whose species does have shechitah?"
בן שמונה חי [The mishnah concludes:] An living eight-month-old fetus (which is not regarded as viable, but yet survives birth, is deemed a separate species),
אין שחיטתה מטהרתו slaughtering does not render it tahor
לפי שאין במינו שחיטה as there is no shechitah for its species.

משנה ה

השוחט את הבהמה

If one slaughtered an animal

ומצא בה בן שמונה and finds inside it an eight-month-old [fetus],
חי alive (in which case the mother's slaughter renders it kosher)
או מת or dead (in which case it is considered a part of the mother, and also therefore kosher)
או בן תשעה מת or a dead nine-month-old,

he tears it open (meaning he does not have to use shechitah as the method)

ומוציא את דמו

and takes out its blood (as the blood may not be consumed).

מצא בה בן תשעה חי

If he finds inside it a live nine-month-old,

טעון שחיטה

it requires shechitah

וחיב באותו ואת בנו

and is subject to [the prohibition of slaughtering on the same day] "it and its mother,"

דברי רבי מאיר

these are the words of Rabbi Meir.

וחכמים אומרים And the Sages say
שחיטת אמו מטהרתו the slaughtering of its mother renders it kosher (and it does not require its own shechitah.  However the Sages did decree that shechitah be done once the animal steps on the ground.)
רבי שמעון שזורי אומר Rabbi Shimon Shezuri (who disagrees with this decree) says
אפילו בן שמנה שנים even if it is eight-year-old (after being born under such circumstances)
וחורש בשדה and is plowing the field,
שחיטת אמו מטהרתו the slaughter of its mother renders it kosher.
קרעה [If the mother dies without having been properly slaughtered, and] he rips her open
ומצא בה בן תשעה חי and finds in her a live nine-month-old [fetus]
טעון שחיטה

it requires slaughtering

לפי שלא נשחטה אמו

as its mother was not slaughtered.