Measuring the sun and moon's size from their distance
Using the visual pyramid and rule of three to find the moon's true diameter; the sun's image shared by many eyes.
Leonardo describes how, knowing a body's distance, one can find its magnitude with the visual pyramid: cut the pyramid on a screen near the eye, move it back until the section doubles, note the space, and by proportion deduce the moon's true diameter from how much it grows across that space. A lettered figure shows several eyes a, b, c and the more remote d, h and f all seeing the solar image that occupies the stretch of sea m n. A third, unlettered figure is captioned as the measurement of the sun's greatness once the distance is known.
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The moon's true diameter from its distance
With the distance of a body known, its magnitude follows from the visual pyramid: cut it on a wall near the eye, move it away until the section doubles, and note the space between the two cuts to derive the true diameter of the moon.
The sun's image shared by many eyes over the sea
A lettered figure shows the eyes a, b, c seeing the solar image (simulacrum) that occupies the sea m n; the two more remote eyes d, h see the same, and the still more remote f sees the like.
A rule-of-three for measuring the sun
The proportional method is stated as a rule of three: if in the measured space the moon's diameter grows a given amount above the first cut, one asks what it will make across the whole space from eye to moon, giving the true diameter. An unlettered figure is captioned as the measurement of the sun's greatness knowing the distance.