The geometry of the unknown: Bombelli's algebra linearia

Abstract

This paper studies the ways algebra and geometry are related in Bombelli's L'algebra. I show that despite Bombelli's careful adherence to a from of homogeneity, he constructs several different ways of relating between algebra and geometry, building on Greek, Arabic, abbacist and original approaches. I further show how Bombelli's technique of reading diagrams, especially when representing algebraic unknowns, requires a multiple view that makes lines stand for much more than the diagrams present to an untrained eye. This multiplicity reflects an exploratory approach that seeks to integrate the algebraic and geometric strata without reducing one to the other and without suppressing the idiosyncrasies of either stratum.