Shadow square

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The shadow square, also known as an altitude scale,[1] was an instrument used to determine the linear height of an object, in conjunction with the alidade, for angular observations. It is an early example of an analog computer.[2][not in citation given] It was invented by Muhammad ibn Mūsā al-Khwārizmī in 9th-century Baghdad.[3][not in citation given] Shadow squares are often found on the backs of astrolabes.


The main use of a shadow square is to measure the linear height of an object using its shadow. It does so by simulating the ratio between an object, generally a gnomon, and its shadow.If the sun's ray is between 0 degrees and 45 degrees the umbra recta (Horizontal axis) is used, between 45 degrees and 90 degrees the umbra versa (Vertical axis) is used and when the sun's ray is a t 45 degrees its shadow falls exactly on the umbra media (y=x) [4]


A gnomon is used along with a shadow box commonly. A gnomon is a stick placed vertically in a sunny place so that it casts a shadow that can be measured. By studying the shadow of the gnomon you can learn glean a lot of information about the motion of the sun. Gnomons were most likely independently discovered by many ancient civilizations, but it is known that they were used in the 5th century BC in Greece. Most likely for the measurement of the winter and summer solstices. "Herodotus says in his Histories written around 450 B.C., that the Greeks learned the use of the gnomon from the Babylonians. [5]


If your shadow is 4 feet long in your own feet, then what is the altitude of the sun. This problem can be solved through the use of the shadow box. The shadow box is divided in half, one half is calibrated by sixes the other by tens. Because it is a shadow cast by the human body the sixes are more convenient. By moving the alidade to the four (the same as your shadows length) and then reading the altitude scale you will see the sun is at an altitude of 56.3 degrees.[6]


  1. ^ "Shadow Square". Retrieved 2009-07-18. 
  2. ^ "Astrolabe detail within shadow square". National Maritime Museum. Retrieved 2009-07-18. 
  3. ^ King, David A. (2002). "A Vetustissimus Arabic Text on the Quadrans Vetus". Journal for the History of Astronomy 33: 237–255. Bibcode:2002JHA....33..237K. 
  4. ^ "Shadow Square". Museo Galilieo. Retrieved March 12th 2014. 
  5. ^ Evans, James (1998). The history and Practice of Ancient Astronomy. Oxford: Oxford University Press. p. 27. ISBN 0-19-509539-1. 
  6. ^ Evans, James (1998). The history and Practice of Ancient Astronomy. Oxford: Oxford University Press. p. 149. ISBN 0-19-509539-1.