Descending balls and the dragging of beams
Degrees and time of motion; composition of forces on a pulled beam
The opening note reasons about the time and degrees of motion of balls sliding along the lines p R and p K, contrasting ball K in its first degree of motion with ball a in its first degree of slowness, while ball b nears the last degree of motion. A second study asks whether the beam n m or the beam o p is harder to move and describes two joined beams dragged by a cord a b, likened to a four-wheeled cart turning a corner. A large fan of lines radiating from point K, studded with small circles, maps these degrees of motion.
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Time and degrees of motion of the balls
The proportion of the length p K to the line p R governs the time of motion along p R compared with p K, lengthened by the weight b as it becomes lighter. Ball K stands in the first degree of motion and ball a in the first degree of slowness, while ball b lies almost at the last degree of motion, acting as a small descending weight.
Finite and infinite stability of motion
Because the line h a is infinite in that it never touches the plane, the stability of the motion a is likewise infinite in itself. The line K b, by contrast, is finite with the plane, so the stability b will be finite.
Which beam is harder to drag
Leonardo asks which motion is more difficult, the beam n m or the beam o p, comparing the two beams to a four-wheeled cart turning a corner. One beam obeys the pull along the line of force given it, and a second beam, pinned at its head but set on an oblique line, is joined to it and dragged by the cord a b.
Fanned construction of the motion lines
A sheaf of straight lines radiates from the point K, each crossing a row of small circles that step down in a curve. The construction lays out geometrically the successive positions and proportional intervals used to reason about the balls' motion.