Weights on Right-Angled Arms: Equilibrium by Position
Weights n and m held equal by position on perpendicular lines resting at right angles
The page studies weights suspended from bent, right-angled balance arms. The notes observe that the figures a n m f g h are all right-angled, with the right angle g placed in the middle, and that one such figure shares the nature of its opposite. In the main argument, weight n is by its position as powerful as m because both hang from perpendicular lines resting on the two right angles f and b: neither can descend unless the other rises, the relation being one of double proportion mirrored in the opposite supporting arms. Rows of triangular diagrams with suspended weights illustrate the cases.
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Right-angled figures with the right angle in the middle
The note states that the figures a n m f g h are all right-angled, but with the right angle g set in the middle, and adds that one figure is of the nature of its opposite.
Weights n and m equal by position
The weight n is by its position as powerful as m, since both are attached to perpendicular lines resting on the two right angles f and b. m cannot descend unless n rises, and n cannot descend unless m is lifted; being in double proportion, so too are the opposite arms that support them, whose pendants set out between perpendicular lines.