The horizon of sky and earth in perspective
The visual pyramid, the true horizon, and the sphere of water
This page of the Treatise's eighth part treats the horizon as a problem of perspective and vision. Leonardo distinguishes the finite visual pyramid a t b - here only seven miles deep - from the infinite pyramid that true perspective would demand, and argues that the horizon of sky and earth ends in a single line where air a seems joined to earth f. He then defines the 'true horizon' as the boundary of the immobile sphere of water, whose surface stays equidistant from the centre of the world. Three small geometric diagrams accompany the argument, lettered with the spheres of earth (d n m) and air (a r p).
On this page
The finite visual pyramid versus the pyramid perspective demands
The figure a t sees the smaller figure r u near it at the far end of the pyramid a t b, so that r u is smaller than a t. Leonardo notes this is not the pyramid perspective requires, since that one has infinite space from base to point, whereas this one measures only seven miles from base to apex.
The horizon of sky and earth ends in one line
The horizon of sky and earth is said to end in one and the same line. With the sphere of the earth as d n m and the sphere of the air as a r p, the beholder's eye at b sees the earth's horizon f where the sight of the air ends, so that the air a appears joined to the earth f.
The true horizon as boundary of the sphere of water
The true horizon is defined as the boundary of the sphere of water, taken to be immobile; that immobility gives it a surface equidistant from the centre of the world. Leonardo begins to consider what would follow if sky and earth were instead flat surfaces separated by equidistant space.