Kilayim, Chapter 3, Mishnah 1. In learning this mishnah we will make use of three diagrams printed in the Kehati edition of the Mishnayos, as well as in the standard editions, which will help us understand what it says. The mishnah deals with a unique law stated regarding an arugah - a small vegetable bed, to which the Sages gave special rules in the laws of kilayim. Although in the previous chapter we learned that a separation of six handbreadths is required between one vegetable and another, in an arugah the Sages were lenient for some reason. It is interesting to note that the mishnah in Tractate Shabbos even brings a verse that hints at how many different species may be planted in such beds.
Two preliminary principles before we begin:
Rosh tor: a law mentioned in the previous chapter - when a plot is sown in the shape of a triangle, and only the tip of the triangle meets another species, it is permitted, since it looks like two distinct units, separate from one another.
The measure of the shironka: a vegetable draws its nourishment from an area of a handbreadth and a half around it. Therefore, although everywhere else a separation of six handbreadths is required between one vegetable and another, in an arugah a separation of a handbreadth and a half between two species is enough.
The mishnah opens:
"Arugah shehi shishah tefachim al shishah tefachim - zor'im besochah chamishah zer'onim" - in a vegetable bed measuring six handbreadths by six handbreadths one may sow five different species of seed. Where are they placed? As shown in Diagram A, the first diagram: "arba'ah be'arba ruchos ha'arugah ve'echad ba'emtza" - four species along the four sides of the bed, and a fifth species in its center.
The reason for the permission, as can be seen in Diagram A, is that the species meet each other only at their corners: the four handbreadths at the corners of the bed are left empty, and consequently the four patches along the sides meet only at the corners. Even the large species in the center meets the four sides only at the corners, and therefore it is permitted.
A bed that has a border:
The mishnah continues: if, in addition to the plot that is six by six, the bed has a border - a raised rim a handbreadth high and a handbreadth wide - a full handbreadth is added on each side, and the bed effectively becomes eight by eight. Its capacity thereby increases: "vezor'in besochah sheloshah asar, sheloshah al kol gevul ugevul ve'echad ba'emtza" - three species on each of the rims along the sides, and one species in the center, as shown in Diagram C.
Let us explain the arithmetic: each side of the rim is eight handbreadths long, since it surrounds a plot of six handbreadths. Within those eight handbreadths three species are sown, and between one and the next there is a handbreadth and a half and a handbreadth and a half - three handbreadths; together with the three sown handbreadths that makes six, and with the addition of the two corners, a handbreadth and another handbreadth, we reach eight. Once this is done on each of the four sides, we have twelve species, and in the center a larger plot is sown, permitted by the law of rosh tor - for it meets the others only at the corners of the triangle.
The Yerushalmi notes a further point: although in the center, within that border, there is an area of six handbreadths by six handbreadths, and at the beginning of the mishnah we learned that in such an area one may sow five different species, here only one species is permitted in the center. The reason is that if the four species were sown along the sides as in the first diagram, there would be a distance of only one handbreadth between them and the species on the rim, whereas at least a handbreadth and a half is required. Therefore this is not possible, and in the center there is nothing but that one large rhombus.
The mishnah then brings an exception: "lo yita rosh haleft besoch hagevul mipnei shehu memal'ehu" - one may not plant the root of a turnip on that rim, because by the nature of this vegetable it fills the entire rim, and it looks like kilayim.
Finally the opinion of Rabbi Yehudah is brought: "Rabbi Yehudah omer: shishah ba'emtza" - in his view, in a case where the bed has a rim, there is no need to make do with a single large unit in the center; rather, one may sow six rhombuses in the center containing six different species. Some understand that Rabbi Yehudah disagrees in the opening clause as well, in the very first case: even in a bed that has no border, which is six by six, according to one opinion the sowing is not limited to five species, but one may arrange those same six rhombuses in it.
In summary: in this mishnah we learned the laws of the arugah - six by six, in which five species are sown (four along the sides and one in the center) because they meet only at the corners; a bed that has a border a handbreadth high, in which thirteen species are sown (three on each border and one in the center by the law of rosh tor); the words of the Yerushalmi explaining why there is only one species in the center; the prohibition against planting the root of a turnip on the border because it fills it; and the opinion of Rabbi Yehudah, that six species may be sown in the center as well.