Abu Rayhan al-Biruni was an 11th-century scholar. From a summit of known height in present-day Pakistan, he sighted the horizon and measured the dip angle θ between the horizontal and his line of sight.
That line is tangent to the Earth: it touches it at exactly one point. From one triangle he recovered the radius of the entire planet, a thousand years before satellites.
R = h · cos θ / (1 − cos θ)
The thing being measured.
A line that touches the Earth at exactly one point.
The point of measurement, where the sightline meets the Earth.
A summit then. A satellite now.
Deep navy is the sky al-Biruni worked under. Brass is the instrument: astrolabes, quadrants, the tools of Golden-Age measurement. In the mark it marks only the observer, the tangency and the IQ.
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