Astronomy · a Light

Two rolling circles turn a circle into a straight line

Ptolemy's planetary models needed a device called the equant, a point about which a planet swept equal angles although it was not the centre of the circle it moved on. It predicted well and it broke the rule that motion in the heavens is uniform and circular, and astronomers had complained about it for centuries. In 1247 Nasir al-Din al-Tusi published a way round it. Roll a small circle inside a circle of twice its diameter, and any point on the small circle traces a straight line, back and forth. Circular motions alone can therefore produce oscillation. The construction is called the Tusi couple. It appears, drawn the same way and with no attribution, in Copernicus's book of 1543, and how it got there is a standing question.

Nasir al-Din al-Tusi · Maragha, 1247