Why the horizon never sits at the eye's height
Convex sky, concave earth, and where flat horizons would cross
Continuing the eighth part on the horizon, Leonardo argues that the perspectivists' rule placing the horizon at eye height would hold only if sky and earth were infinitely distant parallel planes. Because the sky is convex and the earth concave, every part of the earth's surface can serve as a horizon, and the horizon never lies exactly at the beholder's eye. A long wedge-shaped diagram (sky a b, earth f e, eye g, wall c d) shows where the flat horizons a f would cut at points n m. He closes that the nearer a figure stands to the horizon the closer the horizon drops to its feet, and that a thing is higher the farther it is from the centre of the world.
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The perspectivists' horizon would require infinite parallel planes
The perspectivists place the horizon at the height of the eye that sees it, but Leonardo objects that parallel spaces would have to be infinitely distant to appear to converge to a line at the eye. Because the earth affords less plane than the sky, when the sky's plane descends level with the eye the earth's horizon would rise to the beholder's navel, so the two never converge at one point.
Convex sky and concave earth: where flat horizons cross
Sky and earth are not divided by a parallel, equidistant plane but by a space convex on the side of the sky and concave on the side clothing the earth, so any part of the earth's surface can be a horizon. The diagram shows sky a b and earth f e, the eye at g and the wall c d, where the flat horizons a f cut at points n m.
The horizon is never level with the eye
Leonardo states the horizon will never equal the height of the eye that sees it. A figure standing nearer the horizon has that horizon nearer to its feet while the observer stands still, and (marked H) a thing is higher the more distant it is from the centre of the world.