The Moon's Spots and the Angle of Incidence
Proportionalities, a water sphere, and a circular sector (f. 19r)
The leaf opens with Leonardo on the spots of the moon, which he says he drew himself and which vary because clouds rising from the moon's waters keep them from mirroring the sun. Marginal notes then set out two proportionalities, direct and intersected, for finding the angle of incidence, illustrated by lettered triangles, and add that the sphere of water keeps its center on the world even were the earth displaced by a bird or a droplet. A closing figure gives a rule on the curvature of a circular sector.
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The spots of the moon and the clouds over its waters
Keeping the small parts of the moon's spots under watch, Leonardo finds great variety in them, as he proved by drawing them himself. He attributes the variation to clouds rising from the moon's waters that cast shadow between sun and water, so the water stays dark and cannot mirror the solar body.
Two proportionalities for finding the angle of incidence
A marginal note states that two proportionalities serve to find the angle of incidence. One is labelled direct (straight) proportionality and the other intersected proportionality.
Intersected proportionality of triangles a b f and f c d
In the intersected figure a b is to c d as e f is to f g, and the whole triangle a b f is to triangle f c d likewise; but triangle a e f is not to c g f in the same ratio, so the relation is called conversed or intersected rather than direct, being like that of e b f to f c g.
The water sphere keeps its center though the earth shift
Leonardo notes the surface of the sphere of water does not leave the world's center it clothes, even were the earth, its vessel, to leave that center. The earth is moved from its place by the weight of a small bird that alights on it, and the water's surface by a single droplet that descends into it.
Curvature of a circular sector
The sector of a circle that contains the lesser quantity of the circumference's line will have the smaller curvature.
