The Nine Chapters on the Mathematical Art, Vols. 1-3

Measure their shadows at the exact moment of noon on the same day. Use the difference in the shadows as the divisor, and multiply the height of the gnomons by the distance between them as the dividend. Divide the dividend by the divisor; the result added to the height of the gnomons is the distance from the sun to the earth. Multiply the shadow of the southern gnomon by the distance between the gnomons as the dividend, and divide by the divisor; the result is the distance from the southern gnomon to the point directly below the sun. Use the distance to the point below the sun and the distance of the sun from the earth as the two legs of a right triangle, and solve for the hypotenuse; this is the distance from the sun to the observer. Using a tube with a one-inch diameter to observe the sun from the south, if the sun perfectly fills the opening of the tube, fix the length of the tube to serve as the "leg ratio" the altitude, and use the diameter of the tube as the "base ratio" the horizontal leg. The distance from the sun to the person serves as the large leg; the base corresponding to this large leg is the diameter of the sun. Even the appearance of the celestial sphere can be measured in this way, let alone the height of Mount Tai or the breadth of the rivers and seas. I believe that today’s historical records only briefly list the objects of heaven and earth to discuss...