When One Cord Bears the Whole Weight; the Intercentric Line
Two figures on how the intercentric line divides the load, and its governing nature
Leonardo compares two figures of a weight r hung from two cords. In the first, the intercentric line m o cuts the angle p into two triangles n p m and m p o, and the loads on the cords stand in the same proportion as those triangles. In the second, the line passes along one cord so that a single triangle remains and no proportion can be formed, which forces the conclusion that the whole weight rests on that one cord. He closes by stating the 'nature of the intercentric line': all suspended gravity lies on it, and the support nearest the line carries the most.
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First figure: load split as the triangles n p m and m p o
When the intercentric line m o cuts the angle p made by the two cords n p and o p that support weight r, the angle n p o is divided into triangles n p m and m p o, and the loads on the cords stand in the same proportion as those two triangles.
Second figure: the line along one cord makes it bear all
In the second figure the intercentric line passes along one of the cords rather than cutting the angle, so a single triangle remains and no proportion can be formed; therefore the whole weight rests on the one cord through which the line passes. Labels: a, d, b, c.
Nature of the intercentric line
All suspended gravity always lies on its intercentric line, and the support that comes nearest that line is the one most loaded with the weight.
