1) A BREACH IN THE WALL OF A MAVOY FOUR TEFACHIM FROM THE ENTRANCEWAY
QUESTION: The Gemara teaches that one is permitted to carry in a Mavoy (with a Lechi or Korah) that has a solid wall that extends four Tefachim from the entranceway before there is a breach (up to ten Amos wide) in the wall. If, however, the Mavoy's wall extends less than four Tefachim before the breach, then one is not permitted to carry there. The reason for this is that four Tefachim is the minimum length of a Mavoy.
RASHI (DH Matir) explains that if people start using the breach as the entrance to the Mavoy, they will stop using the regular entrance (and any usage that they make of the regular entrance will be to enter only an area that is less than four Tefachim long, i.e. the part of the Mavoy before the breach). Therefore, that entrance is not considered a valid entranceway. Since that opening is no longer considered an entranceway, the Korah over it no longer serves to permit one to carry in the Mavoy.
Rashi's explanation is difficult to understand. Why does Rashi not explain simply that the Mavoy to which the main entrance leads is invalid because its wall does not extend four Tefachim, and therefore the Korah is not placed on a valid Mavoy! It is not necessary to say that the Korah is not a valid Korah (because the opening that it covers is no longer considered a proper entranceway)!
(a) The RITVA answers that Rashi's explanation is based on the Gemara's conclusion. This Mavoy once was a valid Mavoy, but it was breached. The Gemara concludes that it is more difficult to invalidate a Mavoy that was built properly than to invalidate a Mavoy that has not yet been built properly. Consequently, since this Mavoy was once a valid Mavoy, it takes more to invalidate it than the mere fact that the Mavoy is no longer four Tefachim long. What invalidates this Mavoy is a combination of two problems. First, the original opening is no longer considered an entranceway because people are not using it. Second, the Korah is not a valid Korah on top of the entrance to a Mavoy because the entrance does not open into an area more than four Tefachim long.
(b) Alternatively, Rashi may mean to say that we do not view the area in the Mavoy before the breach as an entirely separate Mavoy. If we would view it in that way, the Korah would not permit one to carry in the Mavoy even if the break was more than four Tefachim away from the entrance, since the Korah is on a different Mavoy. Rather, if the entrance above which the Korah is placed is not used to gain access to an area of at least four by four Tefachim, it is not considered an entranceway. The Mavoy is still considered a valid Mavoy; it is the doorway which has lost its status. (M. KORNFELD)
2) FITTING A FOUR-TEFACH WIDE DOORWAY INTO A FOUR-TEFACH WIDE WALL
QUESTION: The Gemara says that it is possible to have two four-Tefach-wide doors open into the sides of a four-Tefach-long Mavoy, by having the doors open at the corners of the Mavoy. RASHI explains that each door opens at an angle, covering three Tefachim of the length of the Mavoy's wall, and one Tefach of the end of the Mavoy (see Rashi's diagram).
TOSFOS asks an obvious question. The hypotenuse of a right triangle whose legs are three Tefachim and one Tefach long is less than four Tefachim (or approximately 3.16). How, then, can doors that are four Tefachim long open into a Mavoy which is four Tefachim long?
ANSWER: Perhaps Rashi maintains that at least one Tefach must be left from the walls of the Mavoy in order for it to be considered a valid Mavoy (perhaps this is because the minimum width of a Korah is one Tefach, and thus the walls must have an area upon which to place the Korah). Therefore, the length of the doors cannot be a full four Tefachim.
Rashi seems to be following his own opinion as expressed elsewhere. In Shabbos (85a, see Insights there), Rashi writes that seeds draw nourishment from the ground up to a distance of one and a half Tefachim away. Since one plant's area of nourishment must be kept away from the area of nourishment of another type of plant, the two plants must be three Tefachim away from each other. Rashi there (85a, end of DH v'Ha Ika; see Tosfos there, end of 85b) explains that a length of the hypotenuse of a right triangle with legs of two Tefachim and one Tefach is a sufficient distance to separate two types of plants. Even though this distance is less than three Tefachim, Rashi maintains that the Rabanan allowed the three Tefachim to be measured by adding the two legs of the triangle (2 + 1). Similarly, Rashi here maintains that the four Tefachim necessary for the doorway of our Sugya may be measured by adding the legs of the triangle (3 + 1).