9 - Measuring past geometers: a history of non-metric projective anachronism

Summary

A recurring historical narrative depicts Jean-Victor Poncelet, Michel Chasles, Jakob Steiner, and other early-nineteenth-century geometers as striving and failing to create a non-metric projective geometry. According to this historiographical view, only in the middle of the century with Karl Christian Georg von Staudt would projective geometry be liberated from its ties to measurement. This claim for geometers before von Staudt is what I will call the non-metric projective anachronism. This chapter will consider how and why pure geometers of the early nineteenth century came to be seen as opposed to measurement. A focus on Klein will capture features of late-nineteenth-century mathematics that made the non-metric projective anachronism so appealing.