Joined circle sectors and a sphere resting on a sphere
Comparing the areas of curved figures, with a note on spherical equilibrium
The sheet is filled with geometrical studies of circular sectors, cones, pyramids and spheres, part of Leonardo's long inquiry into the equipartition and squaring of curved figures. One note reasons about two joined circle-sectors (labelled with e, b, o, a, f, r, d, c, m, g), arguing that when equal parts are removed the upper region loses twice as much as the lower. A separate note, written after turning the sheet, observes that a spherical body set upon another sphere can rest only at the single point where it first came to rest. Much additional faint writing surrounds the diagrams that is not part of the transcription.
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Two joined circle-sectors and the doubling of their parts
Reasoning over two joined circular sectors, the note states that a e b g is double c n d g, so that the part a e b cnd equals the remainder. If one removes only c n d from each side, the upper part is said to lose twice as much as the lower part.
A sphere set upon a sphere rests only at its first point
A physical note claims it lies within nature's power that a spherical body placed upon another spherical body cannot come to rest anywhere except at the very point where it first settled. It expresses the instability of one sphere balanced on another.