[11][12] Hipparchus's only preserved work is Commentary on the Phaenomena of Eudoxus and Aratus (Ancient Greek: Τῶν Ἀράτου καὶ Εὐδόξου φαινομένων ἐξήγησις).

In modern terms, the chord subtended by a central angle in a circle of given radius R equals R times twice the sine of half of the angle, i.e.: The now-lost work in which Hipparchus is said to have developed his chord table, is called Tōn en kuklōi eutheiōn (Of Lines Inside a Circle) in Theon of Alexandria's fourth-century commentary on section I.10 of the Almagest.

He also might have used the relationship between sides and diagonals of a cyclic quadrilateral, today called Ptolemy's theorem because its earliest extant source is a proof in the Almagest (I.10).

There are several indications that Hipparchus knew spherical trigonometry, but the first surviving text discussing it is by Menelaus of Alexandria in the first century, who now, on that basis, commonly is credited with its discovery.

Ptolemy later used spherical trigonometry to compute things such as the rising and setting points of the ecliptic, or to take account of the lunar parallax.

[b] What was so exceptional and useful about the cycle was that all 345-year-interval eclipse pairs occur slightly more than 126,007 days apart within a tight range of only approximately ±1⁄2 hour, guaranteeing (after division by 4,267) an estimate of the synodic month correct to one part in order of magnitude 10 million.

[29] (The maximum angular deviation producible by this geometry is the arcsin of 5+1⁄4 divided by 60, or approximately 5° 1', a figure that is sometimes therefore quoted as the equivalent of the Moon's equation of the center in the Hipparchan model.)

It is known today that the planets, including the Earth, move in approximate ellipses around the Sun, but this was not discovered until Johannes Kepler published his first two laws of planetary motion in 1609.

The value for the eccentricity attributed to Hipparchus by Ptolemy is that the offset is 1⁄24 of the radius of the orbit (which is a little too large), and the direction of the apogee would be at longitude 65.5° from the vernal equinox.

[34] It was total in the region of the Hellespont (and in his birthplace, Nicaea); at the time Toomer proposes the Romans were preparing for war with Antiochus III in the area, and the eclipse is mentioned by Livy in his Ab Urbe Condita Libri VIII.2.

The result that two solar eclipses can occur one month apart is important, because this can not be based on observations: one is visible on the northern and the other on the southern hemisphere—as Pliny indicates—and the latter was inaccessible to the Greek.

According to Synesius of Ptolemais (4th century) he made the first astrolabion: this may have been an armillary sphere (which Ptolemy however says he constructed, in Almagest V.1); or the predecessor of the planar instrument called astrolabe (also mentioned by Theon of Alexandria).

Previously this was done at daytime by measuring the shadow cast by a gnomon, by recording the length of the longest day of the year or with the portable instrument known as a scaphe.

Ptolemy mentions (Almagest V.14) that he used a similar instrument as Hipparchus, called dioptra, to measure the apparent diameter of the Sun and Moon.

Before him a grid system had been used by Dicaearchus of Messana, but Hipparchus was the first to apply mathematical rigor to the determination of the latitude and longitude of places on the Earth.

It seems he did not introduce many improvements in methods, but he did propose a means to determine the geographical longitudes of different cities at lunar eclipses (Strabo Geographia 1 January 2012).

His approach would give accurate results if it were correctly carried out but the limitations of timekeeping accuracy in his era made this method impractical.

[36] In 2022, it was announced that a part of it was discovered in a medieval parchment manuscript, Codex Climaci Rescriptus, from Saint Catherine's Monastery in the Sinai Peninsula, Egypt as hidden text (palimpsest).

[36] Previously, Eudoxus of Cnidus in the fourth century BC had described the stars and constellations in two books called Phaenomena and Entropon.

Hipparchus wrote a commentary on the Arateia—his only preserved work—which contains many stellar positions and times for rising, culmination, and setting of the constellations, and these are likely to have been based on his own measurements.

In this way it might be easily discovered, not only whether they were destroyed or produced, but whether they changed their relative positions, and likewise, whether they were increased or diminished; the heavens being thus left as an inheritance to any one, who might be found competent to complete his plan.This passage reports that It is unknown what instrument he used.

[16] Delambre in his Histoire de l'Astronomie Ancienne (1817) concluded that Hipparchus knew and used the equatorial coordinate system, a conclusion challenged by Otto Neugebauer in his History of Ancient Mathematical Astronomy (1975).

This opinion was confirmed by the careful investigation of Hoffmann[41] who independently studied the material, potential sources, techniques and results of Hipparchus and reconstructed his celestial globe and its making.

As with most of his work, Hipparchus's star catalog was adopted and perhaps expanded by Ptolemy, who has (since Brahe in 1598) been accused by some[47] of fraud for stating (Syntaxis, book 7, chapter 4) that he observed all 1025 stars—critics claim that, for almost every star, he used Hipparchus's data and precessed it to his own epoch 2+2⁄3 centuries later by adding 2°40' to the longitude, using an erroneously small precession constant of 1° per century.

True is only that "the ancient star catalogue" that was initiated by Hipparchus in the second century BC, was reworked and improved multiple times in the 265 years to the Almagest (which is good scientific practise even today).

The ecliptic was marked and divided in 12 sections of equal length (the "signs", which he called zodion or dodekatemoria in order to distinguish them from constellations (astron).

[50] Most of our knowledge of it comes from Strabo, according to whom Hipparchus thoroughly and often unfairly criticized Eratosthenes, mainly for internal contradictions and inaccuracy in determining positions of geographical localities.

Hipparchus insists that a geographic map must be based only on astronomical measurements of latitudes and longitudes and triangulation for finding unknown distances.

[59][60] Hipparchos was suggested in a 2013 paper to have accidentally observed the planet Uranus in 128 BC and catalogued it as a star, over a millennium and a half before its formal discovery in 1781.

[64] Johannes Kepler had great respect for Tycho Brahe's methods and the accuracy of his observations, and considered him to be the new Hipparchus, who would provide the foundation for a restoration of the science of astronomy.