Hipparchus
Hipparchus | |
|---|---|
.jpg) | |
| Born | c. 190 BC |
| Died | c. 120 BC (around age 70) |
| Occupations | |
Hipparchus (/hɪˈpɑːrkəs/; Greek: Ἵππαρχος, Hípparkhos; c. 190 – c. 120 BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry,[1] but is most famous for his incidental discovery of the precession of the equinoxes.[2] Hipparchus was born in Nicaea, Bithynia, and probably died on the island of Rhodes, Greece. He is known to have been a working astronomer between 162 and 127 BC.[3]
Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity.[4][5] He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. For this he certainly made use of the observations and perhaps the mathematical techniques accumulated over centuries by the Babylonians and by Meton of Athens (fifth century BC), Timocharis, Aristyllus, Aristarchus of Samos, and Eratosthenes, among others.[6]
He developed trigonometry and constructed trigonometric tables, and he solved several problems of spherical trigonometry. His other reputed achievements include the discovery and measurement of Earth's precession, the compilation of the first known comprehensive star catalog from the western world, and possibly the invention of the astrolabe, as well as of the armillary sphere that he may have used in creating the star catalogue. He contributed to optics, developing an atomist theory of light. He is often called the "father of astronomy",[7][8] a title conferred on him by Jean Baptiste Joseph Delambre in 1817.[9]
Life and work
[edit]
Hipparchus was born in Nicaea (Ancient Greek: Νίκαια), in Bithynia. The exact dates of his life are not known, but Ptolemy attributes astronomical observations to him in the period from 147 to 127 BC, and some of these are stated as made in Rhodes; earlier observations since 162 BC might also have been made by him. His birth date (c. 190 BC) was calculated by Delambre based on clues in his work. Hipparchus must have lived some time after 127 BC because he analyzed and published his observations from that year. Hipparchus obtained information from Alexandria as well as Babylon, but it is not known when or if he visited these places. He is believed to have died on the island of Rhodes, where he seems to have spent most of his later life.
In the second and third centuries, coins were made in his honour in Bithynia that bear his name and show him with a globe.[10]
Relatively little of Hipparchus's direct work survives into modern times. Although he wrote at least fourteen books, only his commentary on the popular astronomical poem by Aratus was preserved by later copyists. Most of what is known about Hipparchus comes from Strabo's Geography and Pliny's Natural History in the first century; Ptolemy's second-century Almagest; and additional references to him in the fourth century by Pappus and Theon of Alexandria in their commentaries on the Almagest.[11][12]
Hipparchus's only preserved work is Commentary on the Phaenomena of Eudoxus and Aratus (Ancient Greek: Τῶν Ἀράτου καὶ Εὐδόξου φαινομένων ἐξήγησις). This is a highly critical commentary in the form of two books on a popular poem by Aratus based on the work by Eudoxus.[13] Hipparchus also made a list of his major works that apparently mentioned about fourteen books, but which is only known from references by later authors. His famous star catalog was incorporated into the one by Ptolemy and may be almost perfectly reconstructed by subtraction of two and two-thirds degrees from the longitudes of Ptolemy's stars [citation needed][dubious – discuss]. The first trigonometric table was apparently compiled by Hipparchus, who is consequently now known as "the father of trigonometry".
Babylonian sources
[edit]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"). Hipparchus seems to have been the first to exploit Babylonian astronomical knowledge and techniques systematically.[14] Eudoxus in the 4th century BC and Timocharis and Aristillus in the 3rd century BC already divided the ecliptic in 360 parts (our degrees, Greek: moira) of 60 arcminutes and Hipparchus continued this tradition. It was only in Hipparchus's time (2nd century BC) when this division was introduced (probably by Hipparchus's contemporary Hypsicles) for all circles in mathematics. Eratosthenes (3rd century BC), in contrast, used a simpler sexagesimal system dividing a circle into 60 parts. Hipparchus also adopted the Babylonian astronomical cubit unit (Akkadian ammatu, Greek πῆχυς pēchys) that was equivalent to 2° or 2.5° ('large cubit').[15]
Hipparchus probably compiled a list of Babylonian astronomical observations; Gerald J. Toomer, a historian of astronomy, has suggested that Ptolemy's knowledge of eclipse records and other Babylonian observations in the Almagest came from a list made by Hipparchus. Hipparchus's use of Babylonian sources has always been known in a general way, because of Ptolemy's statements, but the only text by Hipparchus that survives does not provide sufficient information to decide whether Hipparchus's knowledge (such as his usage of the units cubit and finger, degrees and minutes, or the concept of hour stars) was based on Babylonian practice.[16] 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).[17][pages needed]
Hipparchus's long draconitic lunar period (5,458 months = 5,923 lunar nodal periods) also appears a few times in Babylonian records.[18] But the only such tablet explicitly dated is post-Hipparchus, so the direction of transmission is not settled by the tablets.
Geometry, trigonometry and other mathematical techniques
[edit]Hipparchus was recognized as the first mathematician known to have possessed a trigonometric table, which he needed when computing the eccentricity of the orbits of the Moon and Sun. He tabulated values for the chord function, which for a central angle in a circle gives the length of the straight line segment between the points where the angle intersects the circle. He may have computed this for a circle with a circumference of 21,600 units and a radius (rounded) of 3,438 units; this circle has a unit length for each arcminute along its perimeter. (This was “proven” by Toomer,[19] but he later “cast doubt“ upon his earlier affirmation.[20] Other authors have argued that a circle of radius 3,600 units may instead have been used by Hipparchus.[21]) He tabulated the chords for angles with increments of 7.5°. 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. Some claim the table of Hipparchus may have survived in astronomical treatises in India, such as the Surya Siddhanta. Trigonometry was a significant innovation, because it allowed Greek astronomers to solve any triangle, and made it possible to make quantitative astronomical models and predictions using their preferred geometric techniques.[19]
Hipparchus must have used a better approximation for π than the one given by Archimedes of between 3+10⁄71 (≈ 3.1408) and 3+1⁄7 (≈ 3.1429). Perhaps he had the approximation later used by Ptolemy, sexagesimal 3;08,30 (≈ 3.1417) (Almagest VI.7).
Hipparchus could have constructed his chord table using the Pythagorean theorem and a theorem known to Archimedes. 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).
The stereographic projection was ambiguously attributed to Hipparchus by Synesius (c. 400 AD), and on that basis Hipparchus is often credited with inventing it or at least knowing of it. However, some scholars believe this conclusion to be unjustified by available evidence.[22] The oldest extant description of the stereographic projection is found in Ptolemy's Planisphere (2nd century AD).[23]
Besides geometry, Hipparchus also used arithmetic techniques developed by the Chaldeans. He was one of the first Greek mathematicians to do this and, in this way, expanded the techniques available to astronomers and geographers.
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. (Previous to the finding of the proofs of Menelaus a century ago, Ptolemy was credited with the invention of spherical trigonometry.) 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. If he did not use spherical trigonometry, Hipparchus may have used a globe for these tasks, reading values off coordinate grids drawn on it, or he may have made approximations from planar geometry, or perhaps used arithmetical approximations developed by the Chaldeans.
