The three centres of gravity of a heavy body
Centre of gravity of the triangle and descent to the centre of the world
The left leaf (f. 72v) sets out that every heavy figure has three centres, of natural gravity, of accidental gravity, and of magnitude, and locates the centre of gravity of a triangle where the line dividing the third of its area meets the axis. Geometric figures, a square inscribing a circle and further triangles support the argument, while a numerical note plays 3 and 4 (the quarter and third of 12) against a hypothetical fall of 4000 miles toward the earth's centre. Leonardo labels three lettered centres a n, b m and c o, and observes that the descent of a body is not rectilinear all the way to the centre of the world. The right leaf (f. 69r) adds that a descending body makes two motions before it stops, as the natural centre drives the accidental centre from the world's centre and takes its place.
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Centre of gravity of a triangle and the three centres
The centre of gravity of every triangle lies where the line dividing the third of its area meets its axis. In every heavy figure there are three centres: the centre of natural gravity, the centre of accidental gravity, and the centre of magnitude of the body.
The twelfth reckoned as 4000 miles
The quarter of 12 is 3 and the third of 12 is 4, so the difference is 1/12. Imagining that twelfth as 4000 miles, were the earth not in its place and a pyramid to fall toward that centre, the centre of gravity would be 4000 miles distant.
Three lettered centres of the figure
Leonardo labels the centres: a n is the centre of the length, b m is the centre of accidental gravity, and c o is the centre of natural gravity. The point t stands above the central line directed to the centre of the world.
Descent to the world's centre is not rectilinear
The point t always stands above the central line directed to the centre of the world, while x stands only with that centre, so that the natural descent of the body is not a straight line as far as the centre of the world.
A descending body makes two motions before stopping
When the accidental centre unites with the centre of the world, the natural centre reacts, drives the accidental centre away and enters in its place. Because of this the descending body makes two motions before it comes to rest.