QUESTION: 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
without transgressing any prohibition of Kilayim. How exactly are these
seeds planted in this small area?
(a) Both RASHI and TOSFOS write that each plant draws nourishment from the
ground 1.5 Tefachim around it. It is prohibited by the Rabanan for two
plants of different species to draw nourishment from the same ground,
because it appears as if the two plants were planted together. Therefore,
the plants must be separated from each other a distance of *3* Tefachim.
RASHI explains that this is accomplished by planting one seed in the center
of the 6-by-6 Arugah, and four lines of seeds on the four sides, leaving
the corners unsown. 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 separating the two
types of seeds near the corners, nevertheless 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" -- lit.
"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
(b) TOSFOS maintains that the Mishnah is *not* using the Heter of "Rosh
Tor." If "Rosh Tor" is not utilized in the Mishnah's case, the only way to
permit planting the five types of seeds is if there are three Tefachim
separating between all of them. Tosfos says that this is accomplished by
sowing one seed in the middle of the Arugah (like Rashi), and sowing a line
of 1 5/7 (appx. 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 6 Tefachim). The end of the row of seeds of one side is now 3
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 2 1/7 Tefachim spaces 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 our Background to Daf 85a)
According to the explanations of both Rashi and Tosfos, there seems to be a
question. 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 (6-by-6 Tefachim) is referring to "Tefachim Sochakos," or broad
Tefachim (the length of one's fist held slightly loose), 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