Eudoxus' simultaneous risings and settings (Q6100772)

The works of fourth-century BCE astronomer Eudoxus of Cnidus included two treatises -- the \textit{Phaenomena} and the \textit{Enoptron} -- that identified constellations that rise above, or set below, the horizon when certain other constellations rise. Reconstructing the precise meanings of Eudoxus's reports is difficult, partly because the fragments of Eudoxus's writings that we have come from works by Aratus and by Hipparchus of Rhodes a couple of centuries later. The author clears up some confusion about these fragments by postulating that Eudoxus used two different reporting systems: (i) the constellations that rose/set when a zodiacal constellation was beginning to rise; and (ii) the constellations that rose/set during the entire time it takes a zodiacal constellation to rise.