Real and Potential Arms of the Balance
Why the balance's real arms grow longer nearer the center of the world
Under 'Of heaviness', Leonardo distinguishes the 'real' arms of a balance from its 'potential' arms and states that their junction with the pendants of the weights is only a potential right angle, never a real one unless the arms are oblique. He holds that the real arms are always longer than the potential arms, and the more so the nearer the balance lies to the center of the world. The main column develops this geometrically: the central line of the arms and the central line of the pendants share a common origin only at the pole, and the two sets of arms are not in the same proportion, growing more divergent toward the center of the earth. Marginal figures show a balance beam and its suspended weights.
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Real arms longer than potential arms near the earth's center
The junction of the pendants with the arms of a balance is always a potential right angle and cannot be a real one unless the arms are oblique. The real arms of the balance are always longer than the potential arms, and the more so the nearer they lie to the center of the world.
The four central lines of the balance and their common origin
The central line running along the arms never meets the central line of the pendants at a right angle. The line of power of the arms is concentric with their natural central line only at the pole, whence the four lines take common origin. The junction of the arm-ends with the pendants of the hung weights is never a right angle.
Real and potential arms are not in the same proportion
The real arms of the balance are not in the same proportion among themselves as the potential arms are among themselves; rather they grow more divergent, the nearer they approach the center of the world.