The figure of the elements: refuting Plato's solids
Why the nested elements leave no vacuum, and why water's sphere is spherical
Leonardo argues against those who, following Plato, hold that if the elements clothed one another as Platonic polyhedra a vacuum would form between them. He replies that a clothing element need not be of uniform thickness: the sphere of water plainly varies in depth and molds itself over the earth's countless rocky angles, roundnesses and hollows, and the air likewise wraps water, mountains and valleys, so no vacuum arises. He restates that every flexible or liquid element must have a spherical surface, proved by four conceptions about height, the centre of the world, and water moving only when it descends, while margin notes extend the reasoning to the weight and percussion of air within fire and to how winds may arise from air moving within air. Diagrams show sections of three nested geometric solids and a double figure of the elemental spheres.
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Against Plato: the elements clothe one another without vacuum
Against those who deny it, Leonardo holds that the elements clothing one another as Plato's figures would not cause a vacuum between them; a clothing element need not be of equal thickness throughout, so no void forms between the elemental spheres.
The sphere of water molds to the earth's rocks and hollows
The sphere of water is plainly of various thicknesses from surface to bottom; it clothes an earth with innumerable rocky angles covered by water and various roundnesses and concavities, generating no vacuum between water and earth, just as the air wraps water, mountains and valleys without leaving a void.
Sections of three nested geometric solids
Drawings show the sections of three geometric solids contained one within another, illustrating the discussion of the figures Plato assigns to the elements.
Every flexible element has a spherical surface
Every flexible or liquid element necessarily has a spherical surface, proved by the sphere of water. Four conceptions serve the proof: what is higher is more remote from the centre of the world, and water does not move of itself unless it descends, so its surface is equidistant from that centre (in great quantities, not droplets that draw one another as steel draws its filings).
The weight and percussion of air within fire
The weight of air when it is in the region of fire has the same proportion as water has when it is in the air, and air falling from the fire into the other air would give the same percussion as water gives falling from the air into the other water.
How winds arise from air moving within air
Winds might arise from the motion of air within air, as the motion of water within water, each being a motion of the element within itself that springs from the falling of the lighter element, as air fallen from the fire, whence it might rain.