The Planisphaerium is a work by Ptolemy. The title can be translated as "celestial plane" or "star chart". In this work Ptolemy explored the mathematics of mapping figures inscribed in the celestial sphere onto a plane by what is now known as stereographic projection. This method of projection preserves the properties of circles.
Originally written in Ancient Greek, Planisphaerium was one of many scientific works which survived from antiquity in Arabic translation. One reason why Planisphaerium attracted interest was that stereographic projection was the mathematical basis of the plane astrolabe, an instrument which was widely used in the medieval Islamic world. In the 12th century the work was translated from Arabic into Latin by Herman of Carinthia, who also translated commentaries by Maslamah Ibn Ahmad al-Majriti. The oldest known translation is in Arabic done by an unknown scholar as part of the Translation Movement in Baghdad.
The word planisphere (Latin planisphaerium) was originally used in the second century by Ptolemy to describe the representation of a spherical Earth by a map drawn in the plane.
Claudius Ptolemy was a mathematician, astronomer, geographer and astrologer who wrote several scientific treatises, three of which were of importance to later Byzantine, Islamic and Western European science. The first is the astronomical treatise now known as the Almagest, although it was originally entitled the Mathematical Treatise and then known as The Great Treatise. The second is the Geography, which is a thorough discussion of the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This is sometimes known as the Apotelesmatiká (Ἀποτελεσματικά) but more commonly known as the Tetrábiblos from the Koine Greek (Τετράβιβλος) meaning "Four Books" or by the Latin Quadripartitum.
A geographic coordinate system is a coordinate system that enables every location on Earth to be specified by a set of numbers, letters or symbols. The coordinates are often chosen such that one of the numbers represents a vertical position and two or three of the numbers represent a horizontal position; alternatively, a geographic position may be expressed in a combined three-dimensional Cartesian vector. A common choice of coordinates is latitude, longitude and elevation. To specify a location on a plane requires a map projection.
An astrolabe is an elaborate inclinometer, and can be considered an analog calculator capable of working out several different kinds of problems in astronomy. Historically used by astronomers and navigators to measure the altitude above the horizon of a celestial body, day or night, it can be used to identify stars or planets, to determine local latitude given local time, to survey, or to triangulate. It was used in classical antiquity, the Islamic Golden Age, the European Middle Ages and the Age of Discovery for all these purposes.
Herman of Carinthia, also nicknamed Hermannus Dalmata, Sclavus or Secundus, was a Medieval Carinthian Slavic philosopher, astronomer, astrologer, mathematician, translator and author.
In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane. The projection is defined on the entire sphere, except at one point: the projection point. Where it is defined, the mapping is smooth and bijective. It is conformal, meaning that it preserves angles at which curves meet. It is neither isometric nor area-preserving: that is, it preserves neither distances nor the areas of figures.
The Almagest is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy. One of the most influential scientific texts of all time, it canonized a geocentric model of the Universe that was accepted for more than 1200 years from its origin in Hellenistic Alexandria, in the medieval Byzantine and Islamic worlds, and in Western Europe through the Middle Ages and early Renaissance until Copernicus. It is also a key source of information about ancient Greek astronomy.
Theon of Alexandria was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's Elements and wrote commentaries on works by Euclid and Ptolemy. His daughter Hypatia also won fame as a mathematician.
In astronomy, a planisphere is a star chart analog computing instrument in the form of two adjustable disks that rotate on a common pivot. It can be adjusted to display the visible stars for any time and date. It is an instrument to assist in learning how to recognize stars and constellations. The astrolabe, an instrument that has its origins in Hellenistic astronomy, is a predecessor of the modern planisphere. The term planisphere contrasts with armillary sphere, where the celestial sphere is represented by a three-dimensional framework of rings.
Autolycus of Pitane was a Greek astronomer, mathematician, and geographer. The lunar crater Autolycus was named in his honour.
On the Heavens is Aristotle's chief cosmological treatise: written in 350 BC it contains his astronomical theory and his ideas on the concrete workings of the terrestrial world. It should not be confused with the spurious work On the Universe.
Abū’l-‘Abbās al-Faḍl ibn Ḥātim al-Nairīzī was a Persian mathematician and astronomer from Nayriz, Fars Province, Iran.
Islamic astronomy comprises the astronomical developments made in the Islamic world, particularly during the Islamic Golden Age, and mostly written in the Arabic language. These developments mostly took place in the Middle East, Central Asia, Al-Andalus, and North Africa, and later in the Far East and India. It closely parallels the genesis of other Islamic sciences in its assimilation of foreign material and the amalgamation of the disparate elements of that material to create a science with Islamic characteristics. These included Greek, Sassanid, and Indian works in particular, which were translated and built upon.
Jordanus de Nemore, also known as Jordanus Nemorarius and Giordano of Nemi, was a thirteenth-century European mathematician and scientist. The literal translation of Jordanus de Nemore would indicate that he was an Italian. He wrote treatises on at least 6 different important mathematical subjects: the science of weights; “algorismi” treatises on practical arithmetic; pure arithmetic; algebra; geometry; and stereographic projection. Most of these treatises exist in several versions or reworkings from the Middle Ages. We know nothing about him personally, other than the approximate date of his work.
The Toledo School of Translators is the group of scholars who worked together in the city of Toledo during the 12th and 13th centuries, to translate many of the philosophical and scientific works from Classical Arabic.
An equatorium is an astronomical calculating instrument. It can be used for finding the positions of the Moon, Sun, and planets without calculation, using a geometrical model to represent the position of a given celestial body.
Qusta ibn Luqa (820–912) was a Syrian Melkite Christian physician, philosopher, astronomer, mathematician and translator. He was born in Baalbek. Travelling to parts of the Byzantine Empire, he brought back Greek texts and translated them into Arabic.
Rudolf (Rudolph) of Bruges was a Flemish translator from Arabic into Latin active in the twelfth century who worked at the Toledo School of Translators.
Medieval Islamic geography and cartography refer to the study of geography and cartography in the Muslim world during the Islamic Golden Age. Muslim scholars made advances to the map-making traditions of earlier cultures, particularly the Hellenistic geographers Ptolemy and Marinus of Tyre, combined with what explorers and merchants learned in their travels across the Old World (Afro-Eurasia). Islamic geography had three major fields: exploration and navigation, physical geography, and cartography and mathematical geography. Islamic geography reached its apex with Muhammad al-Idrisi in the 12th century.
A quadrant is an instrument that is used to measure angles up to 90°. Different versions of this instrument could be used to calculate various readings, such as longitude, latitude, and time of day. It was originally proposed by Ptolemy as a better kind of astrolabe. Several different variations of the instrument were later produced by medieval Muslim astronomers.
The stereographic projection, also known as the planisphere projection or the azimuthal conformal projection, is a conformal map projection whose use dates back to antiquity. Like the orthographic projection and gnomonic projection, the stereographic projection is an azimuthal projection, and when on a sphere, also a perspective projection.
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