Shadow Square

A shadow square is a scale engraved on the back of many astrolabes that allows the instrument to measure the height of a distant object from the length of its shadow, working together with the astrolabes alidade, or sighting arm, for the angular observation involved. It simulates the ratio between an upright object, typically a gnomon, and the shadow that object casts, and its design switches which of two axes is read depending on the suns angle, using the vertical axis for angles between zero and forty five degrees and the horizontal axis for angles between forty five and ninety degrees, with the two axes agreeing exactly at forty five degrees. An early written description of the device appears in an Arabic treatise thought to date from ninth or tenth century Baghdad, and medieval astronomers used shadow squares to track the sun and other celestial bodies before more advanced instruments became available, a method of measuring the altitude of a visible celestial object that remains mathematically valid today.