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Tusi Couple
The Tusi couple is a mathematical device in which a small circle rotates inside a larger circle twice the diameter of the smaller circle. Rotations of the circles cause a point on the circumference of the smaller circle to oscillate back and forth in linear motion along a diameter of the larger circle. The Tusi couple is a 2-cusped hypocycloid. The couple was first proposed by the 13th-century Persian astronomer and mathematician Nasir al-Din al-Tusi in his 1247 ''Tahrir al-Majisti (Commentary on the Almagest)'' as a solution for the latitudinal motion of the inferior planets, and later used extensively as a substitute for the equant introduced over a thousand years earlier in Ptolemy's ''Almagest''. Original description The translation of the copy of Tusi's original description of his geometrical model alludes to at least one inversion of the model to be seen in the diagrams: :If two coplanar circles, the diameter of one of which is equal to half the diameter of the othe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roulette (curve)
In the differential geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, epitrochoids, hypotrochoids, and involutes. Definition Informal definition Roughly speaking, a roulette is the curve described by a point (called the ''generator'' or ''pole'') attached to a given curve as that curve rolls without slipping, along a second given curve that is fixed. More precisely, given a curve attached to a plane which is moving so that the curve rolls, without slipping, along a given curve attached to a fixed plane occupying the same space, then a point attached to the moving plane describes a curve, in the fixed plane called a roulette. Special cases and related concepts In the case where the rolling curve is a line and the generator is a point on the line, the roulette is called an involute of the fixed curve. If the rolling curve is a circle and the fixed curve is a line then the roulette is a trochoid. If, in this case, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid's Elements
The ''Elements'' ( grc, Στοιχεῖα ''Stoikheîa'') is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. ''Elements'' is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century. Euclid's ''Elements'' has been referred to as the most successful and influential textbook ever written. It was one of the very earliest mathematical works to be printed after the invention of the printing press and has been estimated to be second only to the Bible in the number of editions published since the first printing i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proclus
Proclus Lycius (; 8 February 412 – 17 April 485), called Proclus the Successor ( grc-gre, Πρόκλος ὁ Διάδοχος, ''Próklos ho Diádokhos''), was a Greek Neoplatonist philosopher, one of the last major classical philosophers of late antiquity. He set forth one of the most elaborate and fully developed systems of Neoplatonism and, through later interpreters and translators, exerted an influence on Byzantine philosophy, Early Islamic philosophy, and Scholastic philosophy. Biography The primary source for the life of Proclus is the eulogy ''Proclus, or On Happiness'' that was written for him upon his death by his successor, Marinus, Marinus' biography set out to prove that Proclus reached the peak of virtue and attained eudaimonia. There are also a few details about the time in which he lived in the similarly structured ''Life of Isidore'' written by the philosopher Damascius in the following century. According to Marinus, Proclus was born in 412 AD in Cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Medieval Greek
Medieval Greek (also known as Middle Greek, Byzantine Greek, or Romaic) is the stage of the Greek language between the end of classical antiquity in the 5th–6th centuries and the end of the Middle Ages, conventionally dated to the Ottoman conquest of Constantinople in 1453. From the 7th century onwards, Greek was the only language of administration and government in the Byzantine Empire. This stage of language is thus described as Byzantine Greek. The study of the Medieval Greek language and literature is a branch of Byzantine studies, the study of the history and culture of the Byzantine Empire. The beginning of Medieval Greek is occasionally dated back to as early as the 4th century, either to 330 AD, when the political centre of the Roman Empire was moved to Constantinople, or to 395 AD, the division of the empire. However, this approach is rather arbitrary as it is more an assumption of political, as opposed to cultural and linguistic, developments. Indeed, by this time ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gregory Chioniades
Gregory Chioniades ( el, Γρηγόριος Χιονιάδης, Grēgorios Chioniadēs; c. 1240 – c. 1320) was a Byzantine Greek astronomer. He traveled to Persia, where he learned Persian mathematical and astronomical science, which he introduced into Byzantium upon his return from Persia and founded an astronomical academy at Trebizond. Choniades also served as Orthodox bishop in Tabriz. Biography Information about Chioniades survives from some contemporary sources. In 1347, George Chrysokokkes wrote that He was born in Constantinople, probably around 1240, and was originally named George. Sixteen of Chioniades' letters have survived, which confirm that he received assistance from Alexios II and traveled to Persia. Chioniades translated a number of Arabic and Persian works on mathematics and astronomy, including the astronomical tables of his teacher Shams al-Din al-Bukhari, who had worked at the famous Maragheh observatory under the polymath Nasir al-Din al-Tusi. Chioniades ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Byzantine Science
Byzantine science played an important role in the transmission of classical knowledge to the Islamic world and to Renaissance Italy, and also in the transmission of Islamic science to Renaissance Italy. Its rich historiographical tradition preserved ancient knowledge upon which splendid art, architecture, literature and technological achievements were built. Byzantines stood behind several technological advancements. Classical and ecclesiastical studies Byzantine science was essentially classical science. Therefore, Byzantine science was in every period closely connected with ancient-pagan philosophy and metaphysics. Despite some opposition to pagan learning, many of the most distinguished classical scholars held high office in the Church. The writings of antiquity never ceased to be cultivated in the Byzantine Empire because of the impetus given to classical studies by the Academy of Athens in the 4th and 5th centuries, the vigor of the philosophical academy of Alexandria, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Saliba
George Saliba (Arabic: جورج صليبا) is a Lebanese-American Professor of Arabic and Islamic Science at the Department of Middle Eastern, South Asian, and African Studies, Columbia University, New York, USA, where he has been since 1979. Saliba is currently the founding director of the Farouk Jabre Center for Arabic & Islamic Science & Philosophy and the Jabre-Khwarizmi Chair in the History Department. Career Saliba has been at Columbia University since 1979. He received a bachelors and master's degree in mathematics from the American University of Beirut. After, he received a master of science degree in Semitic languages and a doctorate in Islamic sciences from the University of California at Berkeley. He has won the History of Science Prize given by the Third World Academy of Science in 1993, and the History of Astronomy Prize in 1996 from the Kuwait Foundation for the Advancement of Science. In 2005 he was named as a Senior Distinguished Scholar at the John W. Kluge C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guillaume Postel
Guillaume Postel (25 March 1510 – 6 September 1581) was a French people, French linguist, astronomer, Christian Kabbalah, Christian Kabbalist, diplomat, polyglot, professor, Religious universalism, religious universalist, and writer. Born in the village of Barenton in Normandy, Postel made his way to Paris to further his education. While studying at the Collège Sainte-Barbe, he became acquainted with Ignatius of Loyola and many of the men who would become the founders of the Society of Jesus, retaining a lifelong affiliation with them. He entered Rome in the novitiate of the Jesuits in March 1544, but left on December 9, 1545 before making religious vows. Diplomacy and scholarship Postel was adept at Arabic language, Arabic, Hebrew language, Hebrew, and Syriac language, Syriac and other Semitic languages, as well as the Classical languages of Ancient Greek and Latin, and soon came to the attention of the Kingdom of France (1498-1791), French court. Travel to the Ottoman Empi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trepidation
Trepidation (from Lat. ''trepidus'', "trepidatious"), in now-obsolete medieval theories of astronomy, refers to hypothetical oscillation in the precession of the equinoxes. The theory was popular from the 9th to the 16th centuries. The origin of the theory of trepidation comes from the ''Small Commentary to the Handy Tables'' written by Theon of Alexandria in the 4th century CE. In precession, the equinoxes appear to move slowly through the ecliptic, completing a revolution in approximately 25,800 years (according to modern astronomers). Theon states that certain (unnamed) ancient astrologers believed that the precession, rather than being a steady unending motion, instead reverses direction every 640 years. The equinoxes, in this theory, move through the ecliptic at the rate of 1 degree in 80 years over a span of 8 degrees, after which they suddenly reverse direction and travel back over the same 8 degrees. Theon describes but did not endorse this theory. A more sophisticated v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mercury (planet)
Mercury is the smallest planet in the Solar System and the closest to the Sun. Its orbit around the Sun takes 87.97 Earth days, the shortest of all the Sun's planets. It is named after the Roman god ' ( Mercury), god of commerce, messenger of the gods, and mediator between gods and mortals, corresponding to the Greek god Hermes (). Like Venus, Mercury orbits the Sun within Earth's orbit as an inferior planet, and its apparent distance from the Sun as viewed from Earth never exceeds 28°. This proximity to the Sun means the planet can only be seen near the western horizon after sunset or the eastern horizon before sunrise, usually in twilight. At this time, it may appear as a bright star-like object, but is more difficult to observe than Venus. From Earth, the planet telescopically displays the complete range of phases, similar to Venus and the Moon, which recurs over its synodic period of approximately 116 days. The synodic proximity of Mercury to Earth makes Mercury most ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Revolutionibus Orbium Coelestium
''De revolutionibus orbium coelestium'' (English translation: ''On the Revolutions of the Heavenly Spheres'') is the seminal work on the heliocentric theory of the astronomer Nicolaus Copernicus (1473–1543) of the Polish Renaissance. The book, first printed in 1543 in Nuremberg, Holy Roman Empire, offered an alternative model of the universe to Ptolemy's geocentric system, which had been widely accepted since ancient times. History Copernicus initially outlined his system in a short, untitled, anonymous manuscript that he distributed to several friends, referred to as the ''Commentariolus''. A physician's library list dating to 1514 includes a manuscript whose description matches the ''Commentariolus'', so Copernicus must have begun work on his new system by that time. Most historians believe that he wrote the ''Commentariolus'' after his return from Italy, possibly only after 1510. At this time, Copernicus anticipated that he could reconcile the motion of the Earth with the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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