Benedetti's constructions of ovals

Abstract

Giovanni Battista Benedetti (1530--1590) derived two constructions of ovals given their minor and major axes. These were published in 1585 and seem to be the first solution to this problem. Therefore, the generally accepted view that ``the geometrical construction for drawing an oval for any given proportion was not known in the sixteenth century'' (Ana L\'opez-Mozo, 2011; Nexus Network Journal, p. 571) has to be revised. We provide a transcription of Benedetti's Latin text as well as a translation into English and analyze his mathematical reasoning in detail. This is the first main focus of the present note. The second focus is the impact of Benedetti's contributions to ovals. In particular, it is observed that they were rarely mentioned in the mathematical and architectural literature.