Before us is mishnah 9 in chapter 6 of Maseches Kilayim, and it contains two topics: the extent of the area that becomes forbidden for sowing because of a branch that extends out from the aris (a vine trained along a trellis), and the law of one who stretches a vine shoot from one vine to another by means of a rope.
A branch that extends out from the aris:
Regarding a branch that is a continuation of the vine and extends out from the aris and spreads beyond it, even if it extends beyond the area of "avodas hagefen" (the working area of the vine), that is, beyond the zone in which sowing is forbidden, we learned: "Ro'in oso ke'ilu metuteles teluyah bo" - we view it as though a plumb line were hanging from it, and everything directly beneath that plumb line is forbidden for sowing.
It emerges that the prohibition extends to every place that this branch reaches, even though this is an area outside the working area of the vine, which is the only place where sowing is forbidden by the basic law.
"Vechen badalah" - and so too with a dallah:
This law is not limited to an aris, which has the status of a vineyard. Even with a single vine that is trained and spreads out, we measure in the same manner: even if it extends beyond six tefachim, it is forbidden to sow beneath the area over which it spreads.
One who stretches a vine shoot from one vine to another:
One who stretches a shoot from one vine to another: beneath that shoot it is forbidden to sow. And what is the law when the shoot is not long enough to reach the second vine, and he lengthens it with a rope or with gemi (a reed-like material resembling a rope) and ties it so that it stretches across by means of it? Here we must distinguish:
A rope placed only for the purpose of the stretching: beneath the addition, that is, the rope or the gemi, it is permitted to sow, since this is not the vine itself.
A rope placed so that the shoot should travel along it: if he placed the rope so that the vine should actually continue to grow along it, it is forbidden to sow even beneath the rope itself, since this area will ultimately have the vine growing over it.
In summary: in this mishnah we learned that a branch extending out from the aris is viewed as though a plumb line were hanging from it, and the area beneath it is forbidden for sowing even outside the working area of the vine; that the same applies to a dallah, a single vine that spreads even beyond six tefachim; and that with regard to one who stretches a shoot from vine to vine, beneath the rope or the gemi it is permitted to sow when it was placed only for the purpose of the stretching, and it is forbidden when it was placed so that the shoot should travel along it and grow over it.