ON THE LOW AND HIGH SUN. LETTER I.

The following scientific diagram illustrates the geometry of shadows. A larger circular light source labeled D projects rays past a smaller opaque body: an object that blocks light labeled A onto a flat surface FG. These rays converge to form a narrow shadow at point F. Below this, a smaller light source E projects rays past another opaque body B. Because source E is smaller, the rays are less convergent. This results in a broader shadow at point G. This demonstrates that a larger light source produces a narrower shadow at a set distance.

...let A be an opaque body; and let another body, B, be either the same or equal to it. Let the larger light source be D. Let the smaller light source be E. I do not ask now which shadow would turn out to be longer, if they were imagined to continue beyond point F or G. I want both shadows to be limited to the plane: a flat surface used as a screen FG, from which the distance of opaque body A and opaque body B is the same. This being established, it is not necessary for me to demonstrate to you that the shadow of opaque body A, created by that larger light source and received at F, is more constricted: made narrower or more tapered than the shadow of opaque body B, created by the smaller light source E and received at G. The matter is obvious enough in itself.

I say only this: if we suppose the Sun, while near the horizon, is the light source D, and when it is high, it is the light source E, it should follow that if the Sun is larger at the horizon, it should cast a smaller shadow, specifically like the one at F. Likewise, if it is smaller when high in the sky, it should cast a larger shadow, specifically like the one at G. However, the matter does not behave this way, as far as is clear to me from observation. Indeed, near the horizon, the Sun casts a larger shadow original: "maiorem... vmbram", such as the one at G. In that position, it behaves as if it were the smaller light source E. When it is high, it casts a smaller shadow, such as the one at F, so that it then behaves as if it were the larger light source.