Eruvin, Chapter 5, Mishnah 3. This Mishnah continues the idea expressed in the previous Mishnah: when the distance between two towns is one hundred forty-one and a third amos or less, the two towns are considered joined into a single town, and the Shabbos boundary is measured from the outer side of both of them as though they were one town.
The novel point of our Mishnah:
Our Mishnah presents an expanded version of this principle: two towns whose distance from one another is greater than one hundred forty-one and a third amos, and a third town comes along and joins them. This third town is not situated directly on the line between the two, but off to the side, within two thousand amos of both towns, so that the three towns form a triangle.
The Mishnah states: "Shloshah kefarim hameshulashin - im yesh bein shnayim hachitzonim me'ah ve'arba'im ve'achas ushlish" - three villages arranged in a triangle, if between the two outer ones there is one hundred forty-one and a third. The condition is that if we were able to take the middle town and set it down between the two outer ones, the result would be:
A distance of one hundred forty-one and a third amos between the middle town and the town on the right.
A distance of one hundred forty-one and a third amos between the middle town and the town on the left.
The Mishnah does not mean, then, that there are actually one hundred forty-one and a third amos between the two outer towns; there may well be more than that between them. The measurement is theoretical: what the distance would be if the middle town were placed between them.
In such a case we take the middle town and regard it as though it were standing in the middle, and the three towns become literally one town. From here on, the two thousand amos of the Shabbos boundary are measured from the outer edge of the three towns outward.
In summary: Three towns standing in the form of a triangle join together into a single town, even though the distance between the two outer ones exceeds one hundred forty-one and a third amos, provided that the middle town, had it been placed between them, would have been only one hundred forty-one and a third amos from each of the outer ones. All three are then considered one town, and the two thousand amah boundary is measured from their outer edge.