Museo Galileo
italiano
Virtual Museum
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Shadow square
Shadow square

The shadow square, also called altitude scale, generally placed on the back of astrolabes and quadrants, is the basic element of the so-called geometrical square. The instrument serves to measure heights and distances by simulating the ratio between a gnomon and its shadow. The umbra recta simulates the shadow cast on the horizontal plane by a vertical gnomon when the Sun's ray is inclined between 0 and 45. The umbra versa simulates the shadow cast on the vertical plane by a horizontal gnomon when the Sun's ray is inclined between 45 and 90. To each value of the umbra recta corresponds a value of the umbra versa. When the ray is inclined by 45, the two shadows are equal (umbra media).