Centres of gravity of a body and its parts
Propositions on natural versus accidental centres of gravity, with two small cube diagrams
Both pages are filled with closely reasoned propositions distinguishing the 'natural' from the 'accidental' centre of gravity of a body, and asking when the centre of the whole can be recovered from the centres of its parts, or the reverse. Leonardo repeatedly states which combinations of natural and accidental centres make the remaining centre findable and which make it impossible. At the lower right of f.123r are two small sketches of a cube crossed by internal diagonals, drawn but not transcribed in the source.
On this page
Finding the centre of the remainder
With the natural centre of gravity of a whole body and that of one of its parts, the natural centre of gravity of the remainder can be found; and from the natural centres of all the parts, the natural centre of the whole is investigated. But mixing an accidental centre with a natural one defeats the search.
Natural versus accidental centres
Given the natural centre of gravity of a whole body, it is still not possible to find the natural centre of its parts; but given the accidental centres of the parts, the accidental centre of the whole can be found. The natural centre of one part combined with the accidental centre of another yields neither centre of the whole.
A cube crossed by its diagonals
Two small cubes drawn in perspective, each crossed by internal diagonals, appear at the foot of f.123r. No text accompanies them in the source; they sit beside the discussion of the centre of gravity of a solid body.