Pyramids of incident and reflected light rays
Ray geometry with proportional compasses and marginal calculations
A blue-paper sheet of light-ray geometry: large fan-shaped figures of incident and reflected rays are analysed as pyramids (cones) whose value depends on whether they spring from a narrow base or from the whole diameter of the luminous body. Leonardo argues that a reflected image gains splendour, and heat, in proportion as the reflecting element is smaller, and draws proportional compasses (sesto di proporzionalita) shown in profile and face-on with a movable pivot for handling irrational proportions. A block of squared numbers occupies the lower margin.
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Pyramids of incident and refracted rays
The parallel incident lines K g p f are refracted from the angle of their incidence, forming the pyramid p f a. This pyramid is worth far less than the pyramid p f L, because it springs only from the first base K g, whereas the second springs from the whole diameter a b, the diameter of the entire power of the luminous body.
Pyramids from parallel and convergent lines
The pyramid a n h is born from the parallels K g n h, the pyramid a o b from the convergent lines a a o b, and the pyramid n L h from the same convergent lines. The construction distinguishes cones of light generated by parallel versus converging rays.
Splendour and heat of a reflected image
A ray reflected from c to b will have as much greater splendour than the image c as b is smaller than c. It will also be of greater heat in the same proportion as the splendour.
Proportional compass with movable pivot
A compass of proportionality is drawn in profile and face-on; its pivot is movable. Leonardo notes that this instrument serves for irrational proportions.
Squared numbers in the lower margin
The lower margin carries a column of calculations involving squares such as 256, 1024 and 4096. The figures relate the proportional reasoning of the ray pyramids to numerical values.