Measuring the sun's height and distance from two hilltops
Paired sighting huts, pinhole boards and gunpowder flashes to triangulate the sun across fifty miles
Two coordinated observers-one on hill n with a sighting instrument, the other on hill m-use a gunpowder flash to mark the instant the sun or a star lines up, then triangulate its height. A companion diagram sets two great towers on the earth's disk, sighting the sun so the lines to the earth's center form a measurable angle, with instrument n large and bent to a 45-degree angle and instrument m small and vertical. In a third scheme, two houses fifty miles apart admit the sun through a small hole onto a board a b or a marked floor at c, and by comparing how many times c e fits into e d Leonardo derives the distance to the sun. He adds the maxim that the larger the instrument used to measure large things, the closer it comes to the truth.
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Flash signals to sight a planet from two hills
To measure a planet, when the star matches up with m, make a flash using powder, and the observer at n will immediately do the same, so that both fix the same instant.
Sighting instruments set for measuring the sun
These show how the instruments below ought to be positioned for measuring the sun: instrument n should be large, while for instrument m a small one suffices. One is bent to 45 degrees on its base hinge to aim diagonally, the other points vertically.
Larger instruments measure large things more truly
The larger an instrument is that measures large things, the closer it comes to the truth.
Two huts fifty miles apart to find the sun's height
Find two distant mountains of near-equal height; build a board hut on each with a small hole so the sun's rays graze a perpendicular board a b. When the sun grazes a b, make a large cloud of smoke with gunpowder and vinegar-wetted straw; your companion marks where his aperture strikes the floor, at c. Measure how many times c e goes into e d: so many times does the hut distance c b enter into the distance from b to the sun.