APOLLINARIUS (Aizanoi, Phrygia, fl. first or early second century CE)

Apollinarius was among the most prominent Greek astronomers of the time immediately preceding Ptolemy, a period in the history of Greek astronomy about which scholars are very poorly informed. His chief contributions were apparently in lunar theory.

In his second century CE commentary on Hippocrates’s Airs, Waters, Places(c. 400 BCE), a work extant only in Arabic translation, Galen found occasion to attack intellectuals of his time living at Rome for their ignorance of the writings of the most important astronomers. Among them he lists Apollinarius of Aizanoi (a city in Phrygia) along with Hipparchus (second century BCE), two other men otherwise unknown, and—if the name is not an interpolation in the Arabic text—Ptolemy (second century CE). Like Galen’s catalogue of astronomers as a whole, Apollinarius is emblematic of the tenuous knowledge of Greco-Roman science, for though he is frequently mentioned in sources, none of his works has survived or is even known by title.

One specimen of Apollinarius’s writings survives, a passage of about five hundred words quoted in a fragment of an anonymous commentary on Ptolemy’s Handy Tables, composed in the early third century CE and fortuitously preserved in a medieval astrological manuscript. Apollinarius begins by defining terms for the various periodicities associated with the Moon—the synodic month and the sidereal, anomalistic, and dracontic months—and he explains how the Moon’s anomalistic motion, characterized by its varying distance from the Earth, affects the length of the synodic month. The bulk of the passage, however, sets out Apollinarius’s correct contention that the Moon’s motion in latitude, reckoned as its progress in the plane of its orbit relative to the nodal line, is also affected by the anomaly, contrary, he says, to what the “Chaldeans” (Babylonian astronomers) believed. Hence, if one seeks a precise value for the dracontic month by comparing pairs of observed lunar eclipses widely spaced in time, ideally one ought to look for eclipses such that the Sun and Moon are in the same situations with respect to their anomalies as well as at precisely the same locations in the zodiac; these conditions, however, cannot be fulfilled within a span shorter than “many myriads of years.” The fragment breaks off at this point, but it is enough to show that Apollinarius was criticizing the kind of approach to measuring lunar periodicities that Ptolemy attributes to Hipparchus in Book IV of the Almagest.

The late-second-century astrologer Vettius Valens claims to have used Apollinarius’s tables for computing positions of the Sun and Moon, and that these tables employed the Babylonian convention according to which the vernal equinoctial point is at the eighth degree in Aries, not the beginning of the sign as Hipparchus and Ptolemy assumed. From numerical details given elsewhere in Valens’s work, it appears that Apollinarius’s lunar tables were of a type well-known from Greco-Egyptian papyri, using Babylonian-style zigzag functions to represent the Moon’s daily motion in longitude and argument of latitude. By contrast, Paul of Alexandria (fourth century CE) and Porphyry (third century CE) both group Apollinarius with Ptolemy as astronomers who computed ascensional arcs by means of spherical trigonometry rather than the Babylonian arithmetical methods in common use.


Jones, Alexander. Ptolemy’s First Commentator. Philadelphia: American Philosophical Society, 1990. The testimonia concerning Apollinarius are listed and discussed here.

Neugebauer, Otto. A History of Ancient Mathematical Astronomy. Vol. 2. Berlin; New York: Springer-Verlag, 1975. The testimonia regarding Apollinarius are presented and considered.

Toomer, Gerald J. “Galen on the Astronomers and Astrologers.” Archive for History of Exact Sciences 32 (1985): 193–206. Contains Galen’s Hippocratic commentary.



[1] "" by Alexander Jones

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