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Ptolemy
Claudius Ptolemy (; , ; ; – 160s/170s AD) was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine science, Byzantine, Islamic science, Islamic, and Science in the Renaissance, Western European science. The first was his astronomical treatise now known as the ''Almagest'', originally entitled ' (, ', ). The second is the ''Geography (Ptolemy), Geography'', which is a thorough discussion on maps and 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 physics, Aristotelian natural philosophy of his day. This is sometimes known as the ' (, 'On the Effects') but more commonly known as the ' (from the Koine Greek meaning 'four books'; ). The Catholic Church promoted his work, which included the only mathematically sound geocentric model of the Sola ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geography (Ptolemy)
The ''Geography'' (, , "Geographical Guidance"), also known by its Latin names as the ' and the ', is a gazetteer, an atlas (book), atlas, and a treatise on cartography, compiling the geographical knowledge of the 2nd-century Roman Empire. Originally written by Claudius Ptolemy in Ancient Greek, Greek at Alexandria around 150 AD, the work was a revision of a now-lost atlas by Marinus of Tyre using additional Roman and Parthian Empire, Persian gazetteers and new principles. Its translation – Al-Khwarizmi#Geography, Kitab Surat al-Ard – into Classical Arabic, Arabic by Al-Khwarizmi, Al-Khwarismi in the 9th century was highly influential on the geographical knowledge and cartographic traditions of the Geography and cartography in medieval Islam, Islamic world. Alongside the works of Islamic scholars – and the commentary containing revised and more accurate data by Alfraganus – Ptolemy's work was subsequently highly influential on Middle Ages, Medieval and Renaissanc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Almagest
The ''Almagest'' ( ) is a 2nd-century Greek mathematics, mathematical and Greek astronomy, astronomical treatise on the apparent motions of the stars and planetary paths, written by Ptolemy, Claudius Ptolemy ( ) in Koine Greek. One of the most influential scientific texts in history, it canonized a geocentric model of the Universe that was accepted for more than 1,200 years from its origin in Hellenistic Roman-era Alexandria, Alexandria, in the medieval Byzantine and Islamic Golden Age, 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. Ptolemy set up a public inscription at Canopus, Egypt, in 147 or 148. Norman T. Hamilton found that the version of Ptolemy's models set out in the ''Canopic Inscription'' was earlier than the version in the ''Almagest''. Hence the ''Almagest'' could not have been completed before about 150, a quarter-century after Ptolemy began ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptolemy's Theorem
In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). The theorem is named after the Greek astronomer and mathematician Ptolemy (Claudius Ptolemaeus). Ptolemy used the theorem as an aid to creating his table of chords, a trigonometric table that he applied to astronomy. If the vertices of the cyclic quadrilateral are ''A'', ''B'', ''C'', and ''D'' in order, then the theorem states that: : AC\cdot BD = AB\cdot CD+BC\cdot AD This relation may be verbally expressed as follows: :''If a quadrilateral is cyclic then the product of the lengths of its diagonals is equal to the sum of the products of the lengths of the pairs of opposite sides.'' Moreover, the converse of Ptolemy's theorem is also true: :''In a quadrilateral, if the sum of the products of the lengths of its two pairs of opposite sides is equal to the product of the lengths of its diagonals, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptolemy's Inequality
In Euclidean geometry, Ptolemy's inequality relates the six distances determined by four points in the plane or in a higher-dimensional space. It states that, for any four points , , , and , the following inequality holds: :\overline\cdot \overline+\overline\cdot \overline \ge \overline\cdot \overline. It is named after the Greek astronomer and mathematician Ptolemy. The four points can be ordered in any of three distinct ways (counting reversals as not distinct) to form three different quadrilaterals, for each of which the sum of the products of opposite sides is at least as large as the product of the diagonals. Thus, the three product terms in the inequality can be additively permuted to put any one of them on the right side of the inequality, so the three products of opposite sides or of diagonals of any one of the quadrilaterals must obey the triangle inequality.. As a special case, Ptolemy's theorem states that the inequality becomes an equality when the four points lie i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptolemaic Universe
In astronomy, the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a superseded description of the Universe with Earth at the center. Under most geocentric models, the Sun, Moon, stars, and planets all orbit Earth. The geocentric model was the predominant description of the cosmos in many European ancient civilizations, such as those of Aristotle in Classical Greece and Ptolemy in Roman Egypt, as well as during the Islamic Golden Age. Two observations supported the idea that Earth was the center of the Universe. First, from anywhere on Earth, the Sun appears to revolve around Earth once per day. While the Moon and the planets have their own motions, they also appear to revolve around Earth about once per day. The stars appeared to be fixed on a celestial sphere rotating once each day about an axis through the geographic poles of Earth. Second, Earth seems to be unmoving from the perspective of an earthbound observer; it f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 different stages of the planetary 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. Ptolemy does not have a word for the equant – he used expressions such as "the eccentre producing the mean motion". Placement The equant point (shown in the diagram by the large • ), is placed so that it is directly opposite to Earth from the deferent's center, known as the ''eccentric'' (represented by the × ). A planet or the center of an epicycle (a smaller circle carrying the planet) was conceived to move at a constant angular speed with respect to the equant. To a hypothetical observer placed at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptolemy's World Map
The Ptolemy world map is a map of the world known to Greco-Roman societies in the 2nd century. It is based on the description contained in Ptolemy's book ''Geography'', written . Based on an inscription in several of the earliest surviving manuscripts, it is traditionally credited to Agathodaemon of Alexandria. Notable features of Ptolemy's map is the first use of longitudinal and latitudinal lines as well as specifying terrestrial locations by celestial observations. The ''Geography'' was translated from Greek into Arabic in the 9th century and played a role in the work of al-Khwārizmī before lapsing into obscurity. The idea of a global coordinate system revolutionized European geographical thought, however, and inspired more mathematical treatment of cartography. Ptolemy's work probably originally came with maps, but none have been discovered. Instead, the present form of the map was reconstructed from Ptolemy's coordinates by Byzantine monks under the direction of Maximus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptolemy's Table Of Chords
The table of chords, created by the Greece, Greek astronomer, geometer, and geographer Ptolemy in Egypt during the 2nd century AD, is a trigonometric table in Book I, chapter 11 of Ptolemy's ''Almagest'', a treatise on mathematical astronomy. It is essentially equivalent to a table of values of the sine function. It was the earliest trigonometric table extensive enough for many practical purposes, including those of astronomy (an earlier table of chords by Hipparchus gave chords only for arcs that were multiples of ). Since the 8th and 9th centuries, the sine and other trigonometric functions have been used in Islamic mathematics and astronomy, reforming the production of sine tables. Muhammad ibn Musa al-Khwarizmi, Khwarizmi and Habash al-Hasib al-Marwazi, Habash al-Hasib later produced a set of trigonometric tables. The chord function and the table A chord (geometry), chord of a circle is a line segment whose endpoints are on the circle. Ptolemy used a circle wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexandria
Alexandria ( ; ) is the List of cities and towns in Egypt#Largest cities, second largest city in Egypt and the List of coastal settlements of the Mediterranean Sea, largest city on the Mediterranean coast. It lies at the western edge of the Nile Delta, Nile River delta. Founded in 331 BC by Alexander the Great, Alexandria grew rapidly and became a major centre of Hellenic civilisation, eventually replacing Memphis, Egypt, Memphis, in present-day Greater Cairo, as Egypt's capital. Called the "Bride of the Mediterranean" and "Pearl of the Mediterranean Coast" internationally, Alexandria is a popular tourist destination and an important industrial centre due to its natural gas and petroleum, oil pipeline transport, pipelines from Suez. The city extends about along the northern coast of Egypt and is the largest city on the Mediterranean, the List of cities and towns in Egypt#Largest cities, second-largest in Egypt (after Cairo), the List of largest cities in the Arab world, fourth- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science In The Renaissance
During the Renaissance, great advances occurred in geography, astronomy, chemistry, physics, mathematics, manufacturing, anatomy and engineering. The collection of ancient scientific texts began in earnest at the start of the 15th century and continued up to the Fall of Constantinople in 1453, and the invention of printing allowed a faster propagation of new ideas. Nevertheless, some have seen the Renaissance, at least in its initial period, as one of scientific backwardness. Historians like George Sarton and Lynn Thorndike criticized how the Renaissance affected science, arguing that progress was slowed for some amount of time. Humanists favored human-centered subjects like politics and history over study of natural philosophy or applied mathematics. More recently, however, scholars have acknowledged the positive influence of the Renaissance on mathematics and science, pointing to factors like the rediscovery of lost or obscure texts and the increased emphasis on the study of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptolemy's Intense Diatonic Scale
Ptolemy's intense diatonic scale, also known as the Ptolemaic sequence, justly tuned major scale, Ptolemy's tense diatonic scale, or the syntonous (or syntonic) diatonic scale, is a tuning for the diatonic scale proposed by Ptolemy, and corresponding with modern 5-limit just intonation.Chisholm, Hugh (1911). The Encyclopædia Britannica', Vol.28, p. 961. The Encyclopædia Britannica Company. While Ptolemy is famous for this version of just intonation, it is important to realize this was only one of several genera of just, diatonic intonations he describes. He also describes 7-limit "soft" diatonics and an 11-limit "even" diatonic. This tuning was declared by Zarlino to be the only tuning that could be reasonably sung, it was also supported by Giuseppe Tartini, and is equivalent to Indian Gandhar tuning which features exactly the same intervals. It is produced through a tetrachord consisting of a greater tone (9:8), lesser tone (10:9), and just diatonic semitone (16:15) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astrologer
Astrology is a range of Divination, divinatory practices, recognized as pseudoscientific since the 18th century, that propose that information about human affairs and terrestrial events may be discerned by studying the apparent positions of Celestial objects in astrology, celestial objects. Different cultures have employed forms of astrology since at least the 2nd millennium BCE, these practices having originated in Calendrical calculation, calendrical systems used to predict seasonal shifts and to interpret celestial cycles as signs of divine communications. Most, if not all, cultures have attached importance to what they observed in the sky, and some—such as the Hindu astrology, Hindus, Chinese astrology, Chinese, and the Maya civilization, Maya—developed elaborate systems for predicting terrestrial events from celestial observations. Western astrology, one of the oldest astrological systems still in use, can trace its roots to 19th–17th century BCE Mesopotamia, fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
