On picturing the past: arithmetic and geometry as wings of the mind (Q842505)

Illustrated by many figures the article delineates episodes from the history of the metaphor `arithmetic and geometry as wings of the mind' including its iconography. The author starts with a description of the famous astronomical clock in Strasbourg (finished in 1574) where Urania, the muse of astronomy, is painted with two wings labeled with `geometria' and `arithmetica'. He then presents the metaphor's probable inventor Philip Melanchthon (1497-1560) who wrote prefaces to various mathematical textbooks. In one of these Melanchthon refers to Plato's dialogue Phaidros and states that ``the wings of the human mind are arithmetic and geometry''. Finally, he mentions various 16th and 17th century authors using the metaphor, amongst others, Raimarus Ursus (1583), Johannes Kepler (1619), Martinus Hortensius (1634), Robert Boyle (1671), and Andrea Argoli (1644). The article closes with the winged mathematics in the fine arts typified by Cesare Ripa's iconologia (1603).