Heavy bodies falling to the centre of the world
With paired buckets on a pulley and studies of many-sided pyramids
On the left leaf (f. 68v) Leonardo sketches a system of pulleys carrying two buckets, noting that as one bucket rises full the other descends empty, alongside a triangle, columnar shapes and a stepped structure. The right leaf (f. 65r) is dense with drawings of many-sided pyramids and a physics argument on how a weight falling toward the centre of the world does not stop at once but oscillates up and down about that centre over time. He distinguishes the natural centre of a heavy body from its accidental centre and states rules for the curved final motions of the pyramid around the world's centre. A short note also observes that water runs from a to b.
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Paired buckets on a pulley
A pulley arrangement carries two buckets, a and b. Leonardo observes that when one bucket comes back up full the other goes down empty, so the two are coupled in opposite motion.
Oscillation of a falling weight about the centre of the world
A weight falling toward the centre of the world does not halt there immediately but runs up and down about that centre over a length of time. Only when the natural centre of the weight coincides with the centre of the world does the body come to rest, and its motions around the centre are made in equal times though unequal in length.
Natural centre falls only after the accidental centre
The natural centre of heavy bodies does not direct itself nor fall to the centre of the world except after the fall of the centre of accidental gravity. The rule ties the sequence of motions to the two distinct centres of a heavy body.
Where the axes of many-sided pyramids intersect
The lower axes of the many-sided pyramids, arising at the third of the axis of their base, intersect at the quarter of their length toward the base. The many tetrahedral figures drawn on f. 65r illustrate this proportional construction.