1) PLANTING MULTIPLE TYPES OF SEEDS IN A GARDEN PATCH
OPINIONS: The Mishnah says that one may plant up to five types of seeds in an Arugah (garden patch) which is six Tefachim long and six Tefachim wide, and one does not transgress the prohibition of Kil'ayim. In what formation are the seeds planted in this small area?
(a) Both RASHI and TOSFOS write that each plant draws nourishment from the ground from an area of 1 1/2 Tefachim around it. It is prohibited by the Rabanan for two plants of different species to draw nourishment from the same area, because it appears as though the two plants were planted together. Therefore, the plants must be separated from each other by a distance of at least three Tefachim.
RASHI explains that this is accomplished by planting one seed in the center of the six by six Tefachim of the Arugah, and four lines of seeds on the four sides, leaving the corners unsown. A space of three Tefachim separate each outer row of seeds from the inner seed, while the outer sides -- which run perpendicular to each other (such as the north and east sides) -- are separated from each other by the empty space. Even though there are not three Tefachim that separate the two types of seeds near the corners, the fact that each row is sown in a different direction and a small gap separates them is sufficient indication to any onlooker that these two rows of seeds are separate from each other. (This type of indication is referred to as "Rosh Tor" -- literally, "the top of a triangle" which, due to the contrast that it creates, serves to indicate that the rows of seeds are indeed separate from each other.)
(b) TOSFOS maintains that the Mishnah does not use the Heter of "Rosh Tor." If "Rosh Tor" is not utilized in the Mishnah's case, the only way to permit the five types of seeds to be planted in the Arugah is to have a space of three Tefachim that separates between the five types of seeds. Tosfos says that this is accomplished by sowing one seed in the middle of the Arugah (as Rashi says), and sowing a line of 1 5/7 (approximately 1.714) Tefachim of seeds in the middle of each outer side. This leaves 2 1/7 Tefachim on each side of the row of seeds (for a total length of six Tefachim). The end of the row of seeds of one side is now three Tefachim away from the closest end of the row of seeds of any adjacent side. (This is based on the calculation of the hypotenuse of the triangle formed by the two spaces of 2 1/7 Tefachim left fallow, using the approximated 1.4:1 ratio of the hypotenuse to the side of a right triangle that the Rishonim use, as opposed to the actual 1.414:1 ratio. See the inside of the picture in TOSFOS 85a; note that the diagonal sections at each corner of the Arugah are not part of this Tosfos' explanation, but are relevant to Tosfos' explanation of the Gemara later on 85b. Also note that the seeds are actually sown in one line, taking up almost no width, and not half a Tefach, as it appears in the picture on the Daf. See Graphic #2, and Girsa section of the Background to Daf 85a.)
According to the explanations of both Rashi and Tosfos, there seems to be a difficulty. Since a separation of three Tefachim between each type of seed is required, why is it permissible to plant on the sides of the Arugah? Since the Arugah is exactly six Tefachim wide, the space that each row of seeds occupies diminishes the distance between the middle seed and those rows, so that it is less than three Tefachim!
1. RABEINU TAM answers that the measurement of the Arugah as expressed by the Mishnah (six by six Tefachim) refers to "Tefachim Sochakos," or broad Tefachim (the length of one's fist held loosely closed), which are a little larger than normal Tefachim. Hence, the Arugah is actually larger in width and length than six normal Tefachim, allowing for a distance of three normal Tefachim between each type of seed.
2. The RI in Tosfos answers that the Mishnah does not require exactly three Tefachim between each type of seed. It means three Tefachim including the space that the seed itself takes up.
3. The RAMBAN answers, based on the Yerushalmi, that the row of seeds sown on the outer sides is sown outside the borders of the Arugah, and not inside.