Hipparchus

Hipparchus, a Greek astronomer, geographer, and mathematician, is credited with founding trigonometry, though he is best known for accidentally discovering the precession of the equinoxes. Born in Nicaea, Bithynia, he likely died on the island of Rhodes, Greece. His active career as an astronomer spanned from 162 to 127 BC.

Regarded as the finest astronomical observer of the ancient world—and by some as antiquity's greatest astronomer overall—Hipparchus produced the first surviving quantitative and accurate models for the Sun and Moon's motions. To do so, he drew on centuries of observations and mathematical methods from the Babylonians, as well as from earlier Greek figures like Meton of Athens, Timocharis, Aristyllus, Aristarchus of Samos, and Eratosthenes.

Beyond trigonometry and its tables, he solved problems in spherical trigonometry. His other accomplishments include measuring Earth's precession, compiling the Western world's first known comprehensive star catalog, and possibly inventing the astrolabe and the armillary sphere (which he may have used for that catalog). He also contributed to optics with an atomist theory of light. In 1817, Jean Baptiste Joseph Delambre dubbed him the "father of astronomy."

**Life and work** Hipparchus was born in Nicaea, Bithynia. His exact dates are unknown, but Ptolemy records his astronomical observations from 147 to 127 BC, some made in Rhodes; earlier observations from 162 BC may also be his. Delambre calculated his birth year from clues in his work. He must have lived past 127 BC, as he analyzed and published observations from that year. He gathered information from Alexandria and Babylon, though it is unclear if he ever visited either. He is thought to have died on Rhodes, where he spent most of his later life. In the second and third centuries, Bithynian coins bearing his name and a globe were minted in his honor.

Little of Hipparchus's direct work survives. He wrote at least fourteen books, but only his commentary on Aratus's popular astronomical poem was preserved by later copyists. Most knowledge of him comes from Strabo's *Geography* and Pliny's *Natural History* (first century), Ptolemy's *Almagest* (second century), and fourth-century commentaries by Pappus and Theon of Alexandria.

His sole surviving work is *Commentary on the Phaenomena of Eudoxus and Aratus*, a critical two-book analysis of Aratus's poem, itself based on Eudoxus. He also listed his major works (about fourteen books), known only through later references. His famous star catalog was incorporated into Ptolemy's, and can be nearly perfectly reconstructed by subtracting two and two-thirds degrees from Ptolemy's star longitudes. The first trigonometric table is attributed to Hipparchus, earning him the title "father of trigonometry."

**Babylonian sources** Earlier Greek astronomers were influenced by Babylonian astronomy—for instance, the Metonic and Saros cycles likely came from Babylonian sources. Hipparchus seems to have been the first to systematically exploit Babylonian astronomical knowledge and techniques. Eudoxus (4th century BC) and Timocharis and Aristillus (3rd century BC) divided the ecliptic into 360 degrees of 60 arcminutes, a tradition Hipparchus continued. This division was applied to all circles in mathematics only in Hipparchus's time (2nd century BC), likely by his contemporary Hypsicles. Eratosthenes (3rd century BC) used a simpler sexagesimal system dividing a circle into 60 parts. Hipparchus also adopted the Babylonian astronomical cubit (equivalent to 2° or 2.5° for the "large cubit").

Hipparchus probably compiled a list of Babylonian astronomical observations; historian Gerald J. Toomer suggests that Ptolemy's knowledge of eclipse records and other Babylonian data in the *Almagest* came from such a list. While Hipparchus's use of Babylonian sources has long been known from Ptolemy, the only surviving text by Hipparchus does not clarify whether his knowledge (e.g., units like cubit and finger, degrees and minutes, or the concept of hour stars) was directly based on Babylonian practice. However, Franz Xaver Kugler showed that the synodic and anomalistic periods Ptolemy attributes to Hipparchus already appeared in Babylonian ephemerides, particularly the "System B" texts sometimes linked to Kidinnu.

Hipparchus's long draconitic lunar period (5,458 months = 5,923 lunar nodal periods) also appears in Babylonian records, but the only explicitly dated tablet is post-Hipparchus, leaving the direction of transmission uncertain.

**Geometry, trigonometry, and other mathematical techniques** Hipparchus is recognized as the first mathematician known to have possessed a trigonometric table, which he needed to compute the eccentricity of the Moon's and Sun's orbits. He tabulated values for the chord function, which for a cent...