The following Insight does not acknowledge that Tosfos DH Im asks the question and goes with a different approach to answer. Perhaps we wish to add a paragraph incorporating this.

QUESTION: The Mishnah teaches that when a Gid ha'Nasheh is cooked with the thigh, if the Gid is large enough to impart its taste to the thigh, then the entire dish is prohibited.

The words of the Mishnah imply that when the Gid is large enough to impart its taste to the thigh, the entire dish is prohibited even when there are other items in the pot together with the Gid and thigh. We do not take into account these other items and say that since the Gid is not large enough to impart its taste to the total amount of permitted food, the mixture is permitted. Rather, we ignore all of the other items in the pot as if they were not there. (See HAGAHOS ASHIRI.)

However, this seems to contradict the statement of Rebbi Chanina (97b). Rebbi Chanina says that in a case of prohibited food in a pot, when we assess whether there is sixty times more permitted food than prohibited food in the mixture we take into account all of the gravy, congealed fat, pieces of meat, and the pot itself to reach the figure of sixty in order to annul the Isur. Why does the Mishnah here not include the other permitted items, besides the thigh, that are in the pot, when it assesses the total amount of permitted food in the pot?

ANSWER: The SHACH (YD 100:8) cites a number of Rishonim who infer from the Mishnah the principle that an "Isur Davuk" -- a prohibited food that is attached to a permitted food -- is annulled only when the permitted food to which it is attached is at least sixty times greater. This principle teaches that when the Isur is situated in its natural place -- next to the Heter -- in which it was situated while the animal was alive, we do not include the rest of the food in the mixture when determining whether there is sixty times more permitted food than Isur.

The DARCHEI MOSHE (YD 92:1) cites the ISUR V'HETER who quotes the Mishnah later (108a) that states that when a drop of milk falls onto a piece of meat, and the drop is large enough to impart taste into the meat, the meat is forbidden. TOSFOS there (DH Tipas) writes that the Mishnah's law applies only when the piece of meat is outside of the gravy. When the piece of meat is inside of the gravy, then all of the contents of the pot may be included to reach the measure of sixty times more meat than milk to annul the drop of milk. However, this applies only to a drop of milk or some other Isur that fell onto the piece of meat. When, however, an unsalted heart or liver (which are forbidden because of their blood content), or a piece of Chelev, is connected naturally to the meat, the rest of the contents of the pot are not included in the measure of sixty in order to annul the Isur. We are concerned that since the Isur is "Davuk" to the Heter, at one time the two items may have been outside of the gravy, or the Isur remained alone with the Heter in the pot, in which case the Isur makes the Heter forbidden, because, at that time, there was not sixty times more permitted food than Isur. (See TIFERES YAKOV to Tosfos 96b, DH Im. The Tiferes Yakov points out that according to this explanation, even when the pot is stirred and covered, as mentioned in the Mishnah (108a), when the liver is "Davuk" the stirring of the mixture is not effective to be Mevatel the Isur.)

Therefore, in the case of the Mishnah here, since the Gid is naturally attached to the thigh, it is considered an Isur Davuk and the thigh is permitted only when it is sixty times larger than the Gid. It does not suffice for there to be sixty times more permitted foods in the rest of the mixture. (See also BI'UR HA'GRA YD 73.26.) (D. Bloom)<<