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מסכת חולין פרק ט משנה ג
המפשיט בבהמה ובחיה One who skins a domestic animal or wild animal,
בטהורה ובטמאה whether kosher or non-kosher,
בדקה ובגסה whether small or large,
לשטיח [if the hide is] to be a spread [a rug, mat or table cover] (in this case the animal is first sliced along its belly from neck to tail, and then the hide is peeled to the sides away from this incision),
כדי אחיזה

[it can convey or contract tumah until enough of the hide has been peeled] to hold onto [i.e. two tefachim]. (A hide, which is not food and so is not ordinarily susceptible to the tumah of food or neveilah, has the status of a yad, or a handle, for the meat on the carcass to which it is still attached.  As such it can contract or convey tumah.  However, once this amount has been flayed using this method, the hide is no longer normally used as a handle to move the carcass, and so it is not considered a yad and will not contract tumah.)

ולחמת [If the hide is] to be a flask (in which case the skin is not sliced, but is peeled or folded down off the flesh, starting from the neck and on down the carcass, so that the the skin is turned inside out, but remains uncut)
עד שיפשיט את החזה

[can convey or contract tumah] until he has skinned the breast (which is the hardest part to skin, once that point has been passed the remainder of the hide is easily flayed, and so one would not usually need to move the carcass by grasping the hide).

המרגיל If one skins from the hind feet (i.e. using the same method of folding and not cutting used to form a flask, but starting from the rear of the animal instead of its neck)
כלו חבור לטמאה it is all [considered] attached for tumah
לטמא ולטמא to contract tumah and to convey tumah (i.e. the hide is considered a yad);
עור שעל הצוואר the hide that is on the neck (this refers to last case where the carcass has been skinned from the rump forward; the hide about the neck is very loose, and comes off by itself once the breast has been flayed.  Thus the question is whether, once the breast has been flayed, which is the last part before the neck, is it considered as f the entire hide has been flayed and is no longer a yad?)
רבי יוחנן בן נורי אומר Rabbi Yochanan ben Nuri says
אינו חבור

it is not attached (meaning if the hide is only connected to the carcass at the neck, it is as if it has been completely detached and is no longer a yad)

וחכמים אומרים and the Sages say
חבור it is attached
עד שיפשיט את כלו until he has skinned its entirety.

פרק ט משנה ד

עור שיש עליו כזית בשר

A hide which has an olive's worth of meat on it (and the meat has the status of a neveilah),

הנוגע בציב היוצא ממנו one who touches a tuft of [the meat] (even though the tuft is less than an olive's worth, it is attached to and considered part of the neveilah)
ובשערה שכנגדו or the hair that is opposite it (and is considered a shomer of the meat of a neveilah)
טמא is tamei.
היו עליו כשני חצאי זיתים If there were on it [the hide] two [separate] half's of an olive's worth [of meat of a neveilah],
מטמא במשא one contract [from this hide] tumah by carrying it (as he would have carried an olive's worth of a neveilah),
ולא במגע but not through contact (even if he touches both pieces at the same time, as two acts of touching do not combine),
דברי רבי ישמעאל these are the words of Rabbi Yishmael.
רבי עקיבה אומר Rabbi Akiva says
לא במגע ולא במשא

[one will not contract tumah] neither through touching nor through carrying;

ומודה רבי עקיבה and Rabbi Akiva concedes
בשני חצאי זיתים by two half olive's worth [of meat of a neveilah]
שתחבן בקיסם והסיטן that he pierced with a splinter and moved
שהוא טמא that he is tamei (so long that they were not both attached to a hide).
ומפני מה And because of what
רבי עקיבה מטהר בעור does Rabbi Akiva say that one is tahor [when moving two such pieces together] with a hide?
מפני שהעור מבטלן Because the hide nullifies them (i.e. they have no status of their own, and are merely considered a part of the hide, which is tahor).