The Light of the Moon: Is the Moon Water?
The sun mirrored in water (f, c, b, a, n, m, d) reasoned by the rule of three toward a watery moon
Headed by a note that Pico gave his opinions on the matter, this page attacks the light of the moon through the reflection of the sun in water. A red-chalk diagram labelled f, c, b, a, n, m, d shows the sun f mirrored in the water surface n-m, appearing at d as far below the surface as the sun is above it. Leonardo argues that as the eye draws back from b to c the reflected image a doubles, and by the rule of three the full ('fifteenth-day') moon could never give the light it does if it were a smooth sphere, so the moon must be covered with water.
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The moon must be covered with water
Reasoning from how much the sun's reflection would grow as the eye recedes all the way to the moon, Leonardo concludes that the light the moon shows at the full ('fifteenth day') could never come from a smooth sphere. Therefore, he argues, the moon must be water.
The sun mirrored in water grows with the eye's distance
The sun f, mirrored in the water surface n-m, appears at d, as far under water as the sun is above; to the eye b it appears of size a, and moving the eye from b to c the image a doubles. The lettered figure sets up the scaling of a specular reflection with viewing distance.
Scaling the reflection by the rule of three
Leonardo instructs the reader to work the growth of the reflected image with the rule of three, extrapolating from the doubling between eye positions b and c out to the distance of the moon. The proportion drives the conclusion about the moon's surface.