Measuring the earth's center and the size of the sun
Tower-and-plumb triangulation to the earth's core, and a camera-obscura method for the sun's dimensions
Leonardo lays out a method to measure the distance from the earth's surface to its center: because plumb lines all point toward that center, a hundred-braccia bell tower rigged with staves and two lead-weighted wires lets him compare how much narrower the spread r-S is than c-b, and the proportion yields the distance to the core. A companion note observes that a four-hundred-braccia tower built on plumb lines would be narrower at its base than its top, forming the beginning of a pyramid. The lower half turns to the sun: paired towers set far apart sight it so that the lines to the earth's center form an angle, and a camera-obscura detail shows the sun's disk cast through a hole b onto wall a. A closing method 'for knowing how large the sun is' fixes the distance a b at one hundred braccia with a hole of one-sixteenth of a braccio, measuring how much the ray widens where it strikes.
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Measuring the distance to the earth's center with tower and plumb lines
Climb a bell tower one hundred braccia high (d-e), extend two staves c-d and d-b, and hang from each two fine wires with lead weights to the ground (c-r and b-S). Measure how much narrower r-S is than c-b: if it is narrower by a b, then as many times as a b enters into a S, so many times c b enters into the distance to the center of the world.
Plumb lines converge, so a tall tower forms a pyramid
If you make a four-hundred-braccia tower using plumb lines, it will be narrower at the base than at the top, and this will be the beginning of a pyramid.
A proportional rule from the terrestrial triangle
As much as a b enters into a n, so much c b enters into c f. If at a height of 100 braccia and a width of 25, m n is narrower than c b by one thread, then as many threads as fit into c b, so many hundreds of braccia there are from c b to the center.
Measuring how large the sun is with a fixed pinhole
Let the distance a b be one hundred braccia and the hole through which the solar rays pass be one-sixteenth of a braccio; then note how much the ray has increased at its point of percussion.
The sun's disk cast through a pinhole
A camera-obscura sketch, drawn over the sight-lines running to the earth's center, shows the sun's rays passing through a hole b in one wall and striking the opposite wall a, where the round image of the sun's disk appears.