Perspective of vision, projectile motion, and the tides
Visual rays and diminution with distance; the arrow's bent flight; and the tides of the Mediterranean
On the upper fragment Leonardo pursues the geometry of sight: paired eyes compare a flat and a hemispherical object, and he asks why a painted thing looks larger than the same thing in relief. Ray-diagrams and columns of notes demonstrate how apparent size diminishes with distance, one showing the near line a b taking 12 parts against 3 for the more distant c d. A small auger is drawn at the right. The lower strip couples the bending of an arrow's flight and the gravity felt by a moving body with an account of the Mediterranean's flux and reflux, attributed to the exchange of water with the Ocean through the strait of Gades.
On this page
Flat versus relief object seen by two eyes
Two eyes observe a flat and a hemispherical object, marked a; c a b; c b, where line c d appears the size of a b. Leonardo asks why a painted thing seems larger than the same thing in relief: on a round body the concourse of lines cuts and circumscribes the opposite object, while in flat painting the cut lines are all flat.
Diminution of size with distance
Among things of equal size, that appears smaller which is more remote from the eye. Leonardo argues that visual lines and solar rays are generated from the base and terminate at the apex of the pyramid just as they are generated at the apex and terminate at their base, and titles a column simply 'demonstration of the diminution in receding.'
Ray-scheme: near line a b against distant c d
In a scheme of visual rays (c a - d b), the line a b, made near the meeting of the pyramids, appears three-quarters larger than the more distant c d. By the proof of the dilated lines a b takes 12 and c d occupies 3 — a quarter of 12 — though the two are of equal size.
The arrow's bent flight and a moving body's weight
The bending of the arrow's straight motion is cited from Leonardo's 'book of my motions.' He adds that the cord of a moving body does not feel all the gravity of its mover's excess, but feels less as the body rises with the same velocity that an excess descends.
The tides of the Mediterranean at the strait of Gades
The waters brought to the Mediterranean by rains and rivers return to the Ocean through the strait of Gades (Gibraltar) with as much less water as the veins drink and the sun evaporates. This excess causes the flux and reflux: in flux the Mediterranean is engorged by the returning Ocean, in reflux it pours out again.
An auger
A figure of an auger (trivella), a boring tool, is drawn at the right of the upper fragment.