Notebook on Mechanics and Natural Philosophy

To know the proportion of the difference between light and shadow, it is necessary to measure the diameters of the bodies that create said shadow and the diameters of the light.

On the difference between doubling the length of a light or doubling its proximity to the object f f.

Every light or every heat source that is doubled by doubling its length Leonardo refers to "length" here as the physical dimension or size of the light source, such as making a candle flame twice as long. does not double its power; rather, in doubling that length, it doubles that power within the same distance. But if that light remains at its first length and its proximity to the object h h is doubled, then its power is doubled at h h; and this is proved because the light f f f doubled in length occupies the space h h as if it were doubled in proximity.

But such light doubled in length occupies those pyramidal rays pyramidal rays original: "ragi piramidali"; Leonardo conceived of light traveling in "pyramids" or cones from the source to the eye or object.—one shall be doubled in length and the other in proximity. And to double such proximity, it will cover the space a d and h b b, and to double such length f f f d into f f f f f f. But having doubled that length of that light f f f into f f f f f f, that light shall be tripled Leonardo's math here reflects an early attempt to calculate surface area and intensity; while doubling a linear dimension usually quadruples area, his geometric diagram leads him to a "tripled" conclusion here. in the surface of that pyramid of rays, and by doubling the proximity h h, it shall be quadrupled.

So there is a great difference between one doubling of power and the other, because if you double the proximity h h, it shall be of quadruple power This is a remarkable early observation of the inverse-square law, suggesting that halving the distance (doubling proximity) increases intensity fourfold., and if you double the length, it shall be of double power.

The power power original: "potentia"; referring to the intensity or concentrated force of light or heat. of the solar rays is multiplied when the proximity of these rays is doubled through the reflection reflection original: "rinflexione"; Leonardo uses this term to describe both the bouncing of light and the concentration of rays within a specific area. of one ray upon another, in order to place them within the same surface, whether it be heat or light.