Weight of a Beam and the Eight-to-One Balance Arm
How the center of a beam bears its weight, and one pound lifts eight
Continuing 'Of weight', Leonardo treats an oblique beam hung from a pulley and shows that the center of the beam is the center of all its heaviness whatever its slope, so that a pendant descending straight over that center carries the beam's whole weight. He then draws a right-angled balance arm a b d and reasons that if one arm goes eight times into the other, a single pound at e lifts eight pounds at c. Repeated figures make the point that both real and potential arms originate from the center of rotation, in the balance as in the lever and counter-lever. The margin shows beams, pulleys and a laddered balance beam.
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The center of a beam is the center of all its heaviness
For an oblique beam hung by a pulley, the center of the beam is always the center of all its heaviness, however it is tilted. And when the supporting pendant descends in a straight line over that center, the whole weight of the beam rests on that pendant, whatever the beam's obliquity.
A balance arm eight times its opposite: one pound lifts eight
When arm a b of the right-angled balance a b d goes eight times into its opposite arm, and that arm a d weighs eight pounds at c, then a single pound placed at e will lift the eight pounds at c. The pendant that ends at the center of the heavy body always bears the whole of its weight.
Real and potential arms spring from the center of rotation
The real and potential arms always take their origin from the center of rotation, both in the balance and in the lever and counter-lever. When the potential pendant is contained within the real pendant, the real one supports the simple weight of the whole beam.