Hipparchus

HipparchosHipparchus of NicaeaHipparchus of NiceaHipparchianHipparchus of RhodesObservatory at Rhodes
Hipparchus of Nicaea (Ἵππαρχος, Hipparkhos; ) was a Greek astronomer, geographer, and mathematician.wikipedia
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Axial precession

precession of the equinoxesprecessionprecession of equinoxes
He is considered the founder of trigonometry but is most famous for his incidental discovery of precession of the equinoxes.
the discovery of the precession of the equinoxes is usually attributed in the West to the 2nd-century-BC astronomer Hipparchus.

Trigonometry

trigonometrictrigonometricaltrigonometrically
He is considered the founder of trigonometry but is most famous for his incidental discovery of precession of the equinoxes.
In 140 BC, Hipparchus (from Nicaea, Asia Minor) gave the first tables of chords, analogous to modern tables of sine values, and used them to solve problems in trigonometry and spherical trigonometry.

Rhodes

RhodianRhodiansRodi
Hipparchus was born in Nicaea, Bithynia (now İznik, Turkey), and probably died on the island of Rhodes, Greece. The exact dates of his life are not known, but Ptolemy attributes astronomical observations to him in the period from 147–127, and some of these are stated as made in Rhodes; earlier observations since 162 might also have been made by him.
Its famous schools of philosophy, science, literature and rhetoric shared masters with Alexandria: the Athenian rhetorician Aeschines, who formed a school at Rhodes; Apollonius of Rhodes; the observations and works of the astronomers Hipparchus and Geminus, the rhetorician Dionysius Thrax.

Astrolabe

astrolabesAstrolabAstrolabium
His other reputed achievements include the discovery and measurement of Earth's precession, the compilation of the first comprehensive star catalog of the western world, and possibly the invention of the astrolabe, also of the armillary sphere, which he used during the creation of much of the star catalogue.
An early astrolabe was invented in the Hellenistic civilization by Apollonius of Perga between 220 and 150 BC, often attributed to Hipparchus.

Lunar theory

Earth–Moon systemBabylonian lunar astronomyanomaly
With his solar and lunar theories and his trigonometry, he may have been the first to develop a reliable method to predict solar eclipses.
Thereafter, from Hipparchus and Ptolemy in the Bithynian and Ptolemaic epochs down to the time of Newton's work in the seventeenth century, lunar theories were composed mainly with the help of geometrical ideas, inspired more or less directly by long series of positional observations of the moon.

Star catalogue

star catalogNLTTLHS
His other reputed achievements include the discovery and measurement of Earth's precession, the compilation of the first comprehensive star catalog of the western world, and possibly the invention of the astrolabe, also of the armillary sphere, which he used during the creation of much of the star catalogue.
Hipparchus (c.

Geographica

GeographyGeographikaStrabo
Most of what is known about Hipparchus comes from Strabo's Geography and Pliny's Natural History in the 1st century; Ptolemy's 2nd-century Almagest; and additional references to him in the 4th century by Pappus and Theon of Alexandria in their commentaries on the Almagest.

Eudoxus of Cnidus

EudoxusEudoxus of CnidosEudoxan planetary model
This is a highly critical commentary in the form of two books on a popular poem by Aratus based on the work by Eudoxus.
All of his works are lost, though some fragments are preserved in Hipparchus' commentary on Aratus's poem on astronomy.

Ptolemy

Claudius PtolemyClaudius PtolemaeusPtolemaic
The exact dates of his life are not known, but Ptolemy attributes astronomical observations to him in the period from 147–127, and some of these are stated as made in Rhodes; earlier observations since 162 might also have been made by him.
Babylonian astronomers had developed arithmetical techniques for calculating astronomical phenomena; Greek astronomers such as Hipparchus had produced geometric models for calculating celestial motions.

Ancient Greek astronomy

Greek astronomyGreek astronomerastronomy
Hipparchus of Nicaea (Ἵππαρχος, Hipparkhos; ) was a Greek astronomer, geographer, and mathematician.
In the 2nd century BC, Hipparchus, aware of the extraordinary accuracy with which Babylonian astronomers could predict the planets' motions, insisted that Greek astronomers achieve similar levels of accuracy.

Heliocentrism

heliocentricheliocentric modelheliocentric theory
Hipparchus was amongst the first to calculate a heliocentric system, but he abandoned his work because the calculations showed the orbits were not perfectly circular as believed to be mandatory by the science of the time.
He may have used early trigonometric methods that were available in his time, as he was a contemporary of Hipparchus.

Almagest

cataloghis book on astronomyMagna Syntaxis
Most of what is known about Hipparchus comes from Strabo's Geography and Pliny's Natural History in the 1st century; Ptolemy's 2nd-century Almagest; and additional references to him in the 4th century by Pappus and Theon of Alexandria in their commentaries on the Almagest.
He states that he found that the longitudes had increased by 2° 40′ since the time of Hipparchos.

Armillary sphere

armillaryarmillary spheresArmil
His other reputed achievements include the discovery and measurement of Earth's precession, the compilation of the first comprehensive star catalog of the western world, and possibly the invention of the astrolabe, also of the armillary sphere, which he used during the creation of much of the star catalogue.
The Greek astronomer Hipparchus (c.

Lucio Russo

Russo, Lucio
Lucio Russo has said that Plutarch, in his work On the Face in the Moon, was reporting some physical theories that we consider to be Newtonian and that these may have come originally from Hipparchus; he goes on to say that Newton may have been influenced by them.
In the history of science, he has reconstructed some contributions of the Hellenistic astronomer Hipparchus, through the analysis of his surviving works, and the proof of heliocentrism attributed by Plutarch to Seleucus of Seleucia and studied the history of theories of tides, from the Hellenistic to modern age.

Saros (astronomy)

Saros cycleSarosSeries
Earlier Greek astronomers and mathematicians were influenced by Babylonian astronomy to some extent, for instance the period relations of the Metonic cycle and Saros cycle may have come from Babylonian sources (see "Babylonian astronomical diaries").
It was later known to Hipparchus, Pliny and Ptolemy.

Aratus

Aratus of SoliAratus SolensisAratos
This is a highly critical commentary in the form of two books on a popular poem by Aratus based on the work by Eudoxus. Although he wrote at least fourteen books, only his commentary on the popular astronomical poem by Aratus was preserved by later copyists.
We are told by the biographers of Aratus that it was the desire of Antigonus to have them turned into verse, which gave rise to the Phenomena of Aratus; and it appears from the fragments of them preserved by Hipparchus, that Aratus has in fact versified, or closely imitated parts of them both, but especially of the first.

Schröder–Hipparchus number

Schröder-Hipparchus numbersuper Catalan number
103,049 is the tenth Schröder–Hipparchus number, which counts the number of ways of adding one or more pairs of parentheses around consecutive subsequences of two or more items in any sequence of ten symbols.
:1, 1, 3, 11, 45, 197, 903, 4279, 20793, 103049, ... .They are also called the super-Catalan numbers, the little Schröder numbers, or the Hipparchus numbers, after Eugène Charles Catalan and his Catalan numbers, Ernst Schröder and the closely related Schröder numbers, and the ancient Greek mathematician Hipparchus who appears from evidence in Plutarch to have known of these numbers.

Natural History (Pliny)

Natural HistoryNaturalis HistoriaHistoria Naturalis
Most of what is known about Hipparchus comes from Strabo's Geography and Pliny's Natural History in the 1st century; Ptolemy's 2nd-century Almagest; and additional references to him in the 4th century by Pappus and Theon of Alexandria in their commentaries on the Almagest.
He mentions eclipses, but considers Hipparchus's almanac grandiose for seeming to know how Nature works.

Seleucus of Seleucia

Seleucus
Although a contemporary of Hipparchus', Seleucus of Seleucia, remained a proponent of the heliocentric model, Hipparchus' rejection of heliocentrism, supported by ideas from Aristotle, remained dominant for nearly 2000 years until Copernican heliocentrism turned the tide of the debate.
He may have used trigonometric methods that were available in his time, as he was a contemporary of Hipparchus.

Degree (angle)

°degreesdegree
Except for Timocharis and Aristillus, he was the first Greek known to divide the circle in 360 degrees of 60 arc minutes (Eratosthenes before him used a simpler sexagesimal system dividing a circle into 60 parts); he also adopted the Babylonian astronomical cubit unit (Akkadian ammatu, Greek πῆχυς pēchys) which was equivalent to 2° or 2.5° ('large cubit').
Aristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically.

Stereographic projection

stereographicLittle planet effectstereographically projected
Hipparchus was the first to show that the stereographic projection is conformal, and that it transforms circles on the sphere that do not pass through the center of projection to circles on the plane.
The stereographic projection was known to Hipparchus, Ptolemy and probably earlier to the Egyptians.

Deferent and epicycle

epicyclesdeferentdeferents and epicycles
In the Hipparchian, Ptolemaic, and Copernican systems of astronomy, the epicycle (from, literally upon the circle, meaning circle moving on another circle ) was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets.

Bithynia

ancient BithyniaKingdom of BithyniaBithynian
Hipparchus was born in Nicaea, Bithynia (now İznik, Turkey), and probably died on the island of Rhodes, Greece.

Kidinnu

KidenasKiddinu
However, Franz Xaver Kugler demonstrated that the synodic and anomalistic periods that Ptolemy attributes to Hipparchus had already been used in Babylonian ephemerides, specifically the collection of texts nowadays called "System B" (sometimes attributed to Kidinnu).
Hipparchus confirmed this value for the lunation length.

Chord (geometry)

chordchords chord
He tabulated values for the chord function, which gives the length of the chord for each angle.
The first known trigonometric table, compiled by Hipparchus, tabulated the value of the chord function for every 7.5 degrees.