(Article I.7.) Broad Lines – A Forgotten Geometrical Ambiguity

Abstract

The following pages explore the traces of a way of thinking of areas and lengths that seems strange to us but which in a number of mathematical cultures was so familiar that there was no need to explain it: so strange and so familiar, indeed, that modern historians have declared passages in the sources that reflect this conceptual structure to be erroneous, confused or meaningless. I refer to the habit to imagine lines as carriers of a virtual breadth equal to one length unit, and areas as composed of such unit strips. This habit was widely spread in many environments of practical mensuration. In these it was easy to agree on using the basic unit of length as standardized breadth: land was, so to speak, measured as cloth is still sold nowadays, with its physically determined breadth. But it is also reflected in texts which are more theoretical in origin though still inspired or coloured by practical mensuration and its language.

Originally published as “Linee larghe: Un’ambiguità geometrica dimenticata” Bollettino di Storia delle Scienze Matematiche 15 (1995)

A few additions to the translation in 〚…〛