Benedetti’s constructions of ovals

• In 1585 Giovanni Battista Benedetti (1530–1590) published the first general constructions of ovals given the axes. • They were included in a letter to Pietro Pizzamano (1512–1571). • It is plausible that Benedetti discovered them when solving a purely geometrical problem posed by Pizzamano, described in a separate letter. • Only one of the two constructions was included in recent surveys on oval constructions but wrongly attributed to much later authors. 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 López Mozo, 2011; Nexus Network Journal, p. 571) has to be revised. We provide a transcription of Benedetti’s Latin text and a translation, analyze his mathematical reasoning in detail, and review Benedetti’s impact on the construction of ovals.