Museo Galileo
italiano
Virtual Museum
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Geometrical square
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The geometrical square is an enlarged reproduction of the shadow square of the astrolabe. The vertical side, called the vertical shadow, is intended to measure the shadow cast by a horizontal gnomon when the Sun's inclination ranges between 0 and 45 degrees. The horizontal side, called the right shadow, measures the shadow of a vertical gnomon when the Sun's inclination ranges between 45 and 90 degrees. Both sides are divided into 12 equal parts and each value of the vertical shadow is matched by a value of the right shadow. As the graduated rule simulates the inclination of the Sun, if we use the instrument to measure the distance of a point, we will obtain the length of the shadow cast by a gnomon. If we know the value of the vertical shadow, indicated by the graduated rule in point 3, for example, we will also find the value of the right shadow—in other words, the distance of the point—by comparing the two similar triangles ABC and CDE.

Objects
Geometrical square

Geometrical square

Inv. 121
Maker unknown, Italian?, 16th cent.