By the sixteenth century, European makers of astronomical and navigational instruments sometimes included trigonometric scales on the instruments they made. The scales made it possible to look up values of functions such as the sine and the cosine, for use in computing heights. In Georg Hartman’s astrolabe of 1557, these functions are found on the rectangular shadow square on the back of the instrument. The back of an Iranian instrument from about 1715 has a grid of perpendicular lines that represent sines and cosines. Similar scales appeared on a form of sundial known as a horary quadrant.
