The Three Centres of a Pyramid
Centre of magnitude, centre of accidental gravity, and centre of natural gravity
Leonardo defines the three centres of a 'pyramid' — here a tapering triangular body: the centre of magnitude that halves its length, the centre of accidental gravity at which it hangs level when suspended, and the centre of natural gravity through which any straight cut leaves two parts of equal weight. He states that a straight line through the centre of accidental gravity always leaves 5/9 of the whole body toward the base, and that this centre lies at a third of the length from the base for a body with two equidistant sides. An elongated triangle drawn suspended near the points q and S illustrates the discussion.
On this page
The three centres defined
The centre of magnitude divides the pyramid's length into 2 equal parts; the centre of accidental gravity is the point from which, when suspended, the body rests level with the extremities of its central line; the centre of natural gravity is that above which any straight cut leaves 2 parts of equal weight.
Where the centre of accidental gravity lies (the 5/9 rule)
A straight line dividing the pyramid through the centre of accidental gravity, in any direction, always leaves 5/9 of the whole toward the base; for a body of two equidistant sides this centre lies at a third of the length from the base.
Elongated triangle suspended for the demonstration
A long, tapering triangle is drawn hanging from a suspension mark near q and S, with points lettered along it, giving the tapering 'pyramid' whose centres the text discusses.