In addition to its numerous astronomical uses, the plane astrolabe found several applications in terrestrial surveying. It combined the specific functions of other instruments such as the surveyor's cross, portable quadrant, and radio latino.
Besides the customary graduated scale, the backs of certain astrolabes also carry the shadow square, so called because it shows the ratio between the length of a gnomon and the length of its shadow for different altitudes of the Sun.
With the alidade, also inserted into the back of the astrolabe, the observer can aim, for example, at the top of a tower. To calculate its height, when the distance between the observer and the base of the tower is known, the observer simply multiplies the distance by the ratio between the gnomon and the measured length of its shadow.
If the distance is not known, the observer can still measure the angle between the horizon and the summit of the tower and, moving away a few steps, repeat the measurement. Thanks to the properties of similar triangles, the observer can determine either the distance or the height of the tower by applying the rules of geometrical proportion.
Variants of the two systems were used to measure the depth of a well from its known width, or the distance of a remote point.
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