An imprecise but systematic determination of the magnitude of objects was introduced by which Greek astronomer, geographer, and mathematician?
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Magnitude (astronomy) In astronomy, magnitude is a logarithmic measure of the brightness of an object, measured in a specific wavelength or passband, usually in the visible or near-infrared spectrum. An imprecise but systematic determination of the magnitude of objects was introduced in ancient times by Hipparchus.
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Hipparchus Hipparchus of Nicaea ( ; Greek: Ἵππαρχος, "Hipparkhos" ;  ) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry but is most famous for his incidental discovery of precession of the equinoxes.
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Hephaestion of Thebes Hephaestion, Hephaistion, or Hephaistio of Thebes (Ancient Greek: Ἡφαιστίων , "Hēphaistíōn") was a Hellenized Egyptian astrologer of late Antiquity who wrote a Greek treatise known as the "Apotelesmatics" or "Apotelesmatika" around  415. Much of the work appears to be an attempt to synthesize the earlier works of the 1st century astrologer Dorotheus of Sidon and the 2nd century astrologer Claudius Ptolemy. Hephaestion is seen mainly as one of the later compilers of the Hellenistic tradition of astrology since he mainly draws from earlier astrologers, including Antiochus of Athens, and he summarizes large portions of Ptolemy and Dorotheus, which is helpful to modern scholars since we have no other record of many of the authorities that he quotes.
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Hippasus Hippasus of Metapontum ( ; Greek: Ἵππασος ὁ Μεταποντῖνος , "Híppasos"; fl. 5th century BC), was a Pythagorean philosopher. Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers. The discovery of irrational numbers is said to have been shocking to the Pythagoreans, and Hippasus is supposed to have drowned at sea, apparently as a punishment from the gods for divulging this. However, the few ancient sources which describe this story either do not mention Hippasus by name (e.g. Pappus) or alternatively tell that Hippasus drowned because he revealed how to construct a dodecahedron inside a sphere. The discovery of irrationality is not specifically ascribed to Hippasus by any ancient writer. Some modern scholars though have suggested that he discovered the irrationality of √2, which is believed to have been discovered around the time that he lived.
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Al-Battani Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī aṣ-Ṣābiʾ al-Battānī (Arabic: محمد بن جابر بن سنان البتاني) (Latinized as Albategnius, Albategni or Albatenius) (c. 858 – 929) was an Arab astronomer, astrologer, and mathematician. He introduced a number of trigonometric relations, and his "Kitāb az-Zīj" was frequently quoted by many medieval astronomers, including Copernicus.
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Barycentric coordinate system In geometry, the barycentric coordinate system is a coordinate system in which the location of a point of a simplex (a triangle, tetrahedron, etc.) is specified as the center of mass, or barycenter, of usually unequal masses placed at its vertices. Coordinates also extend outside the simplex, where one or more coordinates become negative. The system was introduced (1827) by August Ferdinand Möbius.
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Liu Hui's π algorithm Liu Hui's π algorithm was invented by Liu Hui (fl. 3rd century), a mathematician of the Wei Kingdom. Before his time, the ratio of the circumference of a circle to its diameter was often taken experimentally as three in China, while Zhang Heng (78–139) rendered it as 3.1724 (from the proportion of the celestial circle to the diameter of the earth, 92/29 ) or as formula_1. Liu Hui was not satisfied with this value. He commented that it was too large and overshot the mark. Another mathematician Wan Fan (219–257) provided π ≈ 142/45 ≈ 3.156 . All these empirical π values were accurate to two digits (i.e. one decimal place). Liu Hui was the first Chinese mathematician to provide a rigorous algorithm for calculation of π to any accuracy. Liu Hui's own calculation with a 96-gon provided an accuracy of five digits: π ≈ 3.1416 .
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Ammon (geometer) Ammon (Greek Ἄμμων ) was a geometrician who made a measurement of the walls of Rome, around the time of the first invasion of the Goths, that is, the 3rd century, and found them to be 21 miles in circumference.
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Archytas Archytas ( ; Greek: Ἀρχύτας ; 428–347 BC) was an Ancient Greek philosopher, mathematician, astronomer, statesman, and strategist. He was a scientist of the Pythagorean school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato.
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Ali Qushji Ala al-Dīn Ali ibn Muhammed (1403 – 16 December 1474), known as Ali Qushji (Ottoman Turkish/Persian language: علی قوشچی, "kuşçu" – falconer in Turkish; Latin: "Ali Kushgii") was an astronomer, mathematician and physicist originally from Samarkand, who settled in the Ottoman Empire some time before 1472. As a disciple of Ulugh Beg, he is best known for the development of astronomical physics independent from natural philosophy, and for providing empirical evidence for the Earth's rotation in his treatise, "Concerning the Supposed Dependence of Astronomy upon Philosophy". In addition to his contributions to Ulugh Beg's famous work Zij-i-Sultani and to the founding of Sahn-ı Seman Medrese, one of the first centers for the study of various traditional Islamic sciences in the Ottoman caliphate, Ali Kuşçu was also the author of several scientific works and textbooks on astronomy.
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Hippocrates of Chios Hippocrates of Chios (Greek: Ἱπποκράτης ὁ Χῖος ) was an ancient Greek mathematician, geometer, and astronomer who lived c. 470 – c. 410 BC.
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Epsilon numbers (mathematics) In mathematics, the epsilon numbers are a collection of transfinite numbers whose defining property is that they are fixed points of an exponential map. Consequently, they are not reachable from 0 via a finite series of applications of the chosen exponential map and of "weaker" operations like addition and multiplication. The original epsilon numbers were introduced by Georg Cantor in the context of ordinal arithmetic; they are the ordinal numbers ε that satisfy the equation
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Mathematics in medieval Islam Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta). Important progress was made, such as the full development of the decimal place-value system to include decimal fractions, the first systematised study of algebra (named for "The Compendious Book on Calculation by Completion and Balancing" by scholar Al-Khwarizmi), and advances in geometry and trigonometry.
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Nicolas Fatio de Duillier Nicolas Fatio de Duillier {'1': ", '2': ", '3': ", '4': "} (also spelled Faccio or Facio; 16 February 1664 – 12 May 1753) was a Swiss-born mathematician, natural philosopher, and inventor. He spent much of his adult life in England and Holland. Fatio is known for his work on the zodiacal light problem in astronomy, for originating the "push" or "shadow" theory of gravitation, for his close association with both Christiaan Huygens and Isaac Newton, and for his role in the Newton v. Leibniz calculus controversy. He also invented and developed the first method for fabricating jewel bearings for mechanical watches and clocks.
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A Celestial Atlas A Celestial Atlas, full title: A Celestial Atlas: Comprising A Systematic Display of the Heavens in a Series of Thirty Maps Illustrated by Scientific Description of their Contents, And accompanied by Catalogues of the Stars and Astronomical Exercises is a star atlas by British author Alexander Jamieson, published in 1822. The atlas includes 30 plates, 26 of which are constellation maps with a sinusoidal projection. Some of the plates are hand-colored. The atlas includes a then-new, now-obsolete constellation "Noctua", "Norma Nilotica", and "Solarium". Two celestial hemispheres of the atlas are centered on the equatorial poles via polar projection and geocentric alignment. The atlas comprises stars visible only to the naked eye, making it less cluttered.
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Nonius (device) Nonius is a measuring tool used in navigation and astronomy named in honour of its inventor, Pedro Nunes (Latin: Petrus Nonius), a Portuguese author, mathematician and navigator. The nonius was created in 1542 as a system for taking finer measurements on circular instruments such as the astrolabe. The system was eventually adapted into the vernier scale in 1631 by the French mathematician Pierre Vernier.
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Equant Equant (or punctum aequans) is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of the planets. The equant is used to explain the observed speed change in planetary orbit during different stages of the orbit. This planetary concept allowed Ptolemy to keep the theory of uniform circular motion alive by stating that the path of heavenly bodies was uniform around one point and circular around another point.
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Arabic mile The Arab, Arabic, or Arabian mile (Arabic: الميل‎ ‎ , "al-mīl") was a historical Arabic unit of length. Its precise length is disputed, lying between 1.8 and 2.0 km. It was used by medieval Arab geographers and astronomers. The predecessor of the modern nautical mile, it extended the Roman mile to fit an astronomical approximation of 1 minute of an arc of latitude measured along a north-south meridian. The distance between two pillars whose latitudes differed by 1 degree in a north-south direction was measured using sighting pegs along a flat desert plane.
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Pierre Bouguer Pierre Bouguer (] ) (16 February 1698, Croisic – 15 August 1758, Paris) was a French mathematician, geophysicist, geodesist, and astronomer. He is also known as "the father of naval architecture".
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Histoire Céleste Française Histoire Céleste Française ("French Celestial History") is an astrometric star catalogue published in 1801 by the French astronomer Jérôme Lalande and his staff at the Paris Observatory. This star catalog consists of the locations and apparent magnitudes of 47,390 stars, up to magnitude 9. Stars are identified by common name, Bayer designation or Flamsteed designation, when available. It also contains observations of other astronomical phenomena. It was the largest and most complete star catalog of its day. This publication is a collection of several books of astronomical recordings taken over the previous decade at the observatory.
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Infinity (philosophy) In philosophy and theology, infinity is explored in articles under headings such as the Ultimate, the Absolute, God, and Zeno's paradoxes. In Greek philosophy, for example in Anaximander, 'the Boundless' is the origin of all that is. He took the beginning or first principle to be an endless, unlimited primordial mass (ἄπειρον, "apeiron"). The Jain metaphysics and mathematics was the first to define and delineate different "types" of infinities. The work of the mathematician Georg Cantor first placed infinity into a coherent mathematical framework. Keenly aware of his departure from traditional wisdom, Cantor also presented a comprehensive historical and philosophical discussion of infinity. In Judeo-Christian theology, for example in the work of Duns Scotus, the infinite nature of God invokes a sense of being without constraint, rather than a sense of being unlimited in quantity. In ethics infinity plays an important role designating that which cannot be defined or reduced to knowledge or power.
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Heraclides Ponticus Heraclides Ponticus (Ancient Greek: Ἡρακλείδης ὁ Ποντικός "Herakleides"; c. 390 BC – c. 310 BC ) was a Greek philosopher and astronomer who was born in Heraclea Pontica, now Karadeniz Ereğli, Turkey, and migrated to Athens. He is best remembered for proposing that the Earth rotates on its axis, from west to east, once every 24 hours. He is also frequently hailed as the originator of the heliocentric theory, although this is doubted.