The centre of gravity of a body and its parts
Propositions on the natural and accidental centres of gravity
Both pages of this opening are filled with a systematic series of propositions on the centre of gravity, distinguishing the 'natural' centre of a body from its 'accidental' centre. Leonardo works methodically through which centres can and cannot be deduced from the centres of a body's parts or of its whole. Geometric solids — prisms, a parallelepiped, and a tetrahedron-like figure — are drawn in the margins to accompany the reasoning.
On this page
Finding the centre of gravity 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 is found. Leonardo insists that this holds only for natural centres: mixing an accidental centre with a natural one makes the remainder's centre impossible to determine.
What can and cannot be deduced
Given the natural centre of a body one still cannot find the natural centre of its parts, but given the accidental centres of the parts one can find the accidental centre of the whole, and given the natural centres of each part one can find the natural centre of the whole. From a single centre alone, or from a natural and an accidental centre together, nothing can be deduced.
Solids drawn for the reasoning
The propositions are accompanied by drawn solids — long prisms, a parallelepiped, and a tetrahedron-like figure with internal lines — illustrating the bodies whose centres of gravity are under discussion.