The three species of centres within a heavy body
Diametral centres, the common centre of gravity, and a definition of diameter
This densely written page sets out Leonardo's classification of the centres contained within any heavy body into three kinds. The first are the 'diametral centres', standing at the midpoint of every possible diameter, and thus as numerous and varied as the diameters themselves; the second (also called the 'common' or particular centre) is the single centre of gravity that divides the body into equal weights in any direction. He argues that a stone dropped through a hole bored across the earth would finally settle its centre at the centre of the universe, and adds a geometric definition of a diameter as a line passing through a body from surface to surface through its centre. A few small circle diagrams are drawn in the right margin.
On this page
Diametral centres at the midpoint of every diameter
Every heavy body encloses innumerable centres of three kinds; the first species are the diametral centres, standing at the middle of each diameter. They are of as great a number as the diameters a body can contain, and occupy as many varied sites as there are varied the lengths or shortnesses of those diameters.
The common centre of gravity and a hole through the earth
The common centre is the single one residing at the middle of a body's gravity, so that any straight cut over it leaves the divided parts of equal weight; the part where it dwells guides the body's motion. If the world were bored across its centre and a stone thrown through, the stone would at last set its centre at the very site of the universal centre.
Definition of a diameter
A diameter is that which passes through bodies from one surface to the other, all such lines passing through the centre of the body.