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Ptolemy
Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen 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 ''Mathēmatikē Syntaxis'' or ''Mathematical Treatise'', and later known as ''The Greatest Treatise''. The second is the ''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 natural philosophy of his day. This is sometimes known as the ''Apotelesmatika'' (lit. "On the Effects") but more commonly known as the '' Tetrábiblos'', from the Koine Greek meaning "Four Books", or by its Latin equivalent ''Quadripa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hipparchus
Hipparchus (; el, Ἵππαρχος, ''Hipparkhos''; BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equinoxes. 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. Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity. 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. He developed trigonometry and constructed trigonometric tables, and he solved ... [...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: : , \overline, \cdot , \overline, =, \overline, \cdot , \overline, +, \overline, \cdot , \overline, where the vertical lines denote the lengths of the line segments between the named vertices. This relation may be verbally expressed as follows: :''If a quadrilateral is inscribable in a circle 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 theo ... [...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 l ... [...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. 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 feels solid, stable, and stationary. ... [...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. 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. In other words, to a hypothetical observer placed at the equant point, the epicycle's center (indicated by the small · ) would appear to move 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 Max ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexandria
Alexandria ( or ; ar, ٱلْإِسْكَنْدَرِيَّةُ ; grc-gre, Αλεξάνδρεια, Alexándria) is the second largest city in Egypt, and the largest city on the Mediterranean coast. Founded in by Alexander the Great, Alexandria grew rapidly and became a major centre of Hellenic civilisation, eventually replacing Memphis, in present-day Greater Cairo, as Egypt's capital. During the Hellenistic period, it was home to the Lighthouse of Alexandria, which ranked among the Seven Wonders of the Ancient World, as well as the storied Library of Alexandria. Today, the library is reincarnated in the disc-shaped, ultramodern Bibliotheca Alexandrina. Its 15th-century seafront Qaitbay Citadel is now a museum. Called the "Bride of the Mediterranean" by locals, Alexandria is a popular tourist destination and an important industrial centre due to its natural gas and oil pipelines from Suez. The city extends about along the northern coast of Egypt, and is the larges ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theon Of Alexandria
Theon of Alexandria (; grc, Θέων ὁ Ἀλεξανδρεύς; 335 – c. 405) 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. Life Little is known about the life of Theon. He made predictions and observations of solar and lunar eclipses in 364 which show he was active at that time, and he is said to have lived during the reign of Theodosius I (379–395). The '' Suda'', a tenth-century Byzantine encyclopedia, calls Theon a "man of the Mouseion".SudaTheon θ205/ref> However, both the Library of Alexandria and the original Mouseion were destroyed in the first century BC and according to classical historian Edward J. Watts, Theon was probably the head of a school called the "Mouseion", which was named in emulation of the Hellenistic Mouseion that had once included the Librar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptolemy's Table Of Chords
The table of chords, created by the 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 ). Centuries passed before more extensive trigonometric tables were created. One such table is the '' Canon Sinuum'' created at the end of the 16th century. The chord function and the table A chord of a circle is a line segment whose endpoints are on the circle. Ptolemy used a circle whose diameter is 120 parts. He tabulated the length of a chord whose endpoints are separated by an arc of ''n'' degrees, for ''n'' ranging from to 180 by increments o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greeks In Egypt
The Egyptiotes, also known as Egyptian Greeks ( el, Αιγυπτιώτες), have existed from the Hellenistic period until the aftermath of the Egyptian revolution of 1952, when most were forced to leave. Antiquity Greeks have been present in Egypt since at least the 7th century BC. Herodotus visited ancient Egypt in the 5th century BC and claimed that the Greeks were one of the first groups of foreigners that ever lived there. Diodorus Siculus claimed that Rhodes, Rhodian Actis (mythology), Actis, one of the Heliadae, built the city of Heliopolis (Ancient Egypt), Heliopolis before the Deluge (mythology), cataclysm; likewise the Athenians built Sais. Siculus reports that all the Greek cities were destroyed during the cataclysm, but the Egyptian cities including Heliopolis and Sais survived. First historical colonies According to Herodotus (ii. 154), King Psammetichus I (664–610 BC) established a garrison of foreign mercenaries at Daphnae, mostly Carians and Ionians, Ionian Gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicolaus Copernicus
Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulated a model of the universe that placed the Sun rather than Earth at its center. In all likelihood, Copernicus developed his model independently of Aristarchus of Samos, an ancient Greek astronomer who had formulated such a model some eighteen centuries earlier. The publication of Copernicus's model in his book ' (''On the Revolutions of the Celestial Spheres''), just before his death in 1543, was a major event in the history of science, triggering the Copernican Revolution and making a pioneering contribution to the Scientific Revolution. Copernicus was born and died in Royal Prussia, a region that had been part of the Kingdom of Poland since 1466. A polyglot and polymath, he obtained a doctorate in canon law and was a mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for by using the classical electromagnetic description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice. Practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines and bend when they pass through or reflect from surfaces. Physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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