Abstract
In his Commentary on the Phaenomena of Aratus and Eudoxus (II.2.24-II.2.27), Hipparchus gives the results, but not the details, of several computations involving a star now known as υ Boötis. 1 Historians of astronomy have long wondered how he performed these calculations, as some of them seem at first sight to require techniques developed only later, such as Menelaus’s theorem, the foundation of later Greek spherical trigonometry. (Given the equatorial coordinates of the star and the fact that it is setting, to find the degree of the ecliptic at the meridian, and the degree of the ecliptic that is rising.)
At JHA, we received, at around the same time, two independent papers that address this question. One is “Dia tōn grammōn: Hipparchus on Simultaneous Risings and Settings” by Enrico Landi and Francesca Schironi and the other the other is “Hipparchos and the Ancient Analemma” by Nathan Sidoli. The two papers independently showed that Hipparchus could have carried out the calculations without recourse to Menelaus’s theorem or any other version of spherical trigonometry, using only methods known to have been available at the time. Subsequently, the two teams learned of one another’s work and had a chance to exchange ideas that led to minor revisions of both papers. We are pleased to present both papers here.