Kilayim, Chapter 5, Mishnah 5. In the previous chapter (Chapter 4, Mishnah 5) we learned the dispute between Beis Shammai and Beis Hillel regarding one who sows kilayim alongside a vineyard: how much of the vineyard becomes forbidden. Beis Shammai said that only a single row is forbidden, and Beis Hillel said two rows, and this depends on the question of what quantity is considered a 'vineyard.' All of that, however, was said about one who sows outside the vineyard; regarding one who sows inside the vineyard itself, there is a different calculation as to the scope of the prohibition.
The basis of the calculation:
The starting assumption is that everything located within sixteen amos of the kilayim - of the foreign plant growing inside the vineyard - becomes forbidden. Our Mishnah teaches that the standard way of planting vines in a vineyard is one vine every four amos. Accordingly, when the vines are planted in a square formation four amos apart from one another, we must calculate how many vines are included within a circle whose radius is sixteen amos (not its diameter, but its radius - that is, thirty two amos across).
The words of the Mishnah: "HaNotea yarak b'kerem o mekayem" - one who plants a vegetable in a vineyard, which is forbidden because of kilei hakerem, and even one who merely maintains it (such as where it grew on its own and he did not uproot it) - in both cases there is a transgression of kilayim here, and the vineyard becomes forbidden. And how much of it is forbidden? "Harei zeh mekadesh arba'im v'chameish gefanim" - 'mekadesh' here means: renders it forbidden. Forty five vines become forbidden, and beyond them it is permitted - for this is the number of vines included within a radius of sixteen amos in every direction.
"Eimasai" - at what planting distance:
"Bizman shehayu netuos al arba arba o al chameish chameish" - at a distance of four amos from one another, and likewise at a distance of five amos. Even though with a planting of five amos there are not really forty five complete vines, since some of them fall at the edge - and in fact there are only thirty seven there - since in overall appearance it closely resembles a planting of four amos, they gave it the same law.
"Hayu netuos al sheish sheish o al sheva sheva - harei zeh mekadesh sheish esrei amah l'chol ruach" - a planting of six or seven amos no longer has the appearance of a planting of four amos, and therefore every vine located within a radius of sixteen amos in every direction is forbidden, according to the actual number that is there in practice.
The principle of the matter: a distance of five amos resembles in appearance a distance of four, and therefore we round the calculation to forty five vines even though in practice there are fewer. But a distance of six does not resemble four, and all the more so a distance of seven; therefore only the actual number that is there becomes forbidden, whatever it may be, according to the distance from the kilayim.
"Agulos v'lo meruba'os":
This calculation is made according to a circle - according to the span of a circle - and not according to a square. Only what falls within the circle itself is forbidden.
Why did the Mishnah stop at seven amos?
The Mishnah went only as far as seven amos, because once the vines are planted every eight amos, it is not considered a vineyard at all: it does not have the status of a vineyard, and only the vine that is actually within six tefachim of the vegetable becomes forbidden.
And even though in the previous chapter (Chapter 4, Mishnah 9) the Tanna Kamma held that a vineyard loses the status of a vineyard only when the vines are sixteen amos apart from one another, and not at eight amos - the opinion of Rabbi Meir and Rabbi Shimon there is that anything more than eight amos is not considered a vineyard. And the distinction is this: the words of the Tanna Kamma were said only l'chatchilah, that is, with respect to defining a vineyard in which it is forbidden to sow. But b'dieved, with respect to what actually renders the vines forbidden, all agree that the vines must be within eight amos of one another in order to be considered a vineyard for this purpose - that the vines within sixteen amos of the vegetable sown there, of the kilayim, are considered forbidden.
In summary: This Mishnah taught how much of the vineyard becomes forbidden when kilayim were sown within it: when the vines are planted every four or five amos - it renders forty five vines forbidden; when they are planted every six or seven amos - everything within sixteen amos in every direction becomes forbidden, according to the calculation of "agulos v'lo meruba'os." And with respect to the prohibition in practice all agree that if the vines are planted eight amos apart or more, there is no status of a vineyard here, and the entire vineyard does not become forbidden within the measure of sixteen amos.