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Theodosius' Spherics
The ''Spherics'' (Ancient Greek, Greek: , ) is a three-volume treatise on spherical geometry written by the Greek mathematics, Hellenistic mathematician Theodosius of Bithynia in the 2nd or 1st century BC. Book I and the first half of Book II establish basic geometric constructions needed for spherical geometry using the tools of Euclidean geometry, Euclidean solid geometry, while the second half of Book II and Book III contain propositions relevant to astronomy as modeled by the celestial sphere. Primarily consisting of theorems which were known at least informally a couple centuries earlier, the ''Spherics'' was a foundational treatise for geometers and astronomers from its origin until the 19th century. It was continuously studied and copied in Greek manuscript for more than a millennium. It was translated into Arabic in the 9th century during the Islamic Golden Age, and thence translated into Neo Latin, Latin Latin translations of the 12th century, in 12th century Iberia, tho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greek
Ancient Greek (, ; ) includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Greek Dark Ages, Dark Ages (), the Archaic Greece, Archaic or Homeric Greek, Homeric period (), and the Classical Greece, Classical period (). Ancient Greek was the language of Homer and of fifth-century Athens, fifth-century Athenian historians, playwrights, and Ancient Greek philosophy, philosophers. It has contributed many words to English vocabulary and has been a standard subject of study in educational institutions of the Western world since the Renaissance. This article primarily contains information about the Homeric Greek, Epic and Classical periods of the language, which are the best-attested periods and considered most typical of Ancient Greek. From the Hellenistic period (), Ancient Greek was followed by Koine Greek, which is regar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eudoxus Of Cnidus
Eudoxus of Cnidus (; , ''Eúdoxos ho Knídios''; ) was an Ancient Greece, ancient Greek Ancient Greek astronomy, astronomer, Greek mathematics, mathematician, doctor, and lawmaker. He was a student of Archytas and Plato. All of his original works are lost, though some fragments are preserved in Hipparchus' ''Commentaries on the Phenomena of Aratus and Eudoxus''. ''Theodosius' Spherics, Spherics'' by Theodosius of Bithynia may be based on a work by Eudoxus. Life Eudoxus, son of Aeschines, was born and died in Cnidus (also transliterated Knidos), a city on the southwest coast of Anatolia. The years of Eudoxus' birth and death are not fully known but Diogenes Laertius, Diogenes Laërtius gave several biographical details, mentioned that Apollodorus of Athens, Apollodorus said he reached his wikt:acme#English, acme in the 103rd Olympiad (368–), and claimed he died in his 53rd year. From this 19th century mathematical historians reconstructed dates of 408–, but 20th century schola ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
On The Sizes And Distances (Aristarchus)
''On the Sizes and Distances (of the Sun and Moon)'' () is widely accepted as the only extant work written by Aristarchus of Samos, an ancient Greek astronomer who lived circa 310–230 BCE. This work calculates the sizes of the Sun and Moon, as well as their distances from the Earth in terms of Earth's radius. The book was presumably preserved by students of Pappus of Alexandria's course in mathematics, although there is no evidence of this. The ''editio princeps'' was published by John Wallis in 1688, using several medieval manuscripts compiled by Sir Henry Savile. The earliest Latin translation was made by Giorgio Valla in 1488. There is also 1572 Latin translation and commentaryby Frederico Commandino. Symbols The work's method relied on several observations: * The apparent size of the Sun and the Moon in the sky. * The size of the Earth's shadow in relation to the Moon during a lunar eclipse * The angle between the Sun and Moon during a half moon is 90°. The rest of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aristarchus Of Samos
Aristarchus of Samos (; , ; ) was an ancient Greek astronomer and mathematician who presented the first known heliocentric model that placed the Sun at the center of the universe, with the Earth revolving around the Sun once a year and rotating about its axis once a day. He also supported the theory of Anaxagoras according to which the Sun was just another star. He likely moved to Alexandria, and he was a student of Strato of Lampsacus, who later became the third head of the Peripatetic school in Greece. According to Ptolemy, he observed the summer solstice of 280 BC. Along with his contributions to the heliocentric model, as reported by Vitruvius, he created two separate sundials: one that is a flat disc; and one hemispherical. Aristarchus estimated the sizes of the Sun and Moon as compared to Earth's size. He also estimated the distances from the Earth to the Sun and Moon. His estimate that the Sun was 7 times larger than Earth (while inaccurate by an order of magnitu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Little Astronomy
''Little Astronomy'' ( ) is a collection of minor works in Ancient Greek mathematics and astronomy dating from the 4th to 2nd century BCE that were probably used as an astronomical curriculum starting around the 2nd century CE. In the astronomy of the medieval Islamic world, with a few additions, the collection became known as the ''Middle Books'' ( ), mathematical preparation for Claudius Ptolemy's ''Almagest'', intended for students who had already studied Euclid's ''Elements''. Works in the collection The works contained in the collection are: * '' Spherics'' by Theodosius of Bithynia: On spherical geometry, in the style of the ''Elements''. * '' On the Moving Sphere'' by Autolycus of Pitane: On the movements of points and arcs on a sphere as it rotates on its axis. * ''Optics'' by Euclid: On various effects involving propagation of light, including shadows, parallax, and perspective. * '' Phaenomena'' by Euclid: A treatise in 18 propositions, each dealing with important ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Late Antiquity
Late antiquity marks the period that comes after the end of classical antiquity and stretches into the onset of the Early Middle Ages. Late antiquity as a period was popularized by Peter Brown (historian), Peter Brown in 1971, and this periodization has since been widely accepted. Late antiquity represents a cultural sphere that covered much of the Mediterranean world, including parts of Europe and the Near East.Brown, Peter (1971), ''The World of Late Antiquity (1971), The World of Late Antiquity, AD 150-750''Introduction Late antiquity was an era of massive political and religious transformation. It marked the origins or ascendance of the three major monotheistic religions: Christianity, rabbinic Judaism, and Islam. It also marked the ends of both the Western Roman Empire and the Sasanian Empire, the last Persian empire of antiquity, and the beginning of the early Muslim conquests, Arab conquests. Meanwhile, the Byzantine Empire, Byzantine (Eastern Roman) Empire became a milit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Menelaus Of Alexandria
Menelaus of Alexandria (; , ''Menelaos ho Alexandreus''; c. 70 – 140 CE) was a Greek mathematician and astronomer, the first to recognize geodesics on a curved surface as natural analogs of straight lines. Life and works Although very little is known about Menelaus's life, it is supposed that he lived in Rome, where he probably moved after having spent his youth in Alexandria. He was called ''Menelaus of Alexandria'' by both Pappus of Alexandria and Proclus, and a conversation of his with Lucius, held in Rome, is recorded by Plutarch. Ptolemy (2nd century CE) also mentions, in his work ''Almagest'' (VII.3), two astronomical observations made by Menelaus in Rome in January of the year 98. These were occultations of the stars Spica and Beta Scorpii by the moon, a few nights apart. Ptolemy used these observations to confirm precession of the equinoxes, a phenomenon that had been discovered by Hipparchus in the 2nd century BCE. In the 10th-century '' Kitāb al-F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hipparchus
Hipparchus (; , ; BC) was a Ancient Greek astronomy, 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 classical antiquity, 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 se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stereographic Projection
In mathematics, a stereographic projection is a perspective transform, perspective projection of the sphere, through a specific point (geometry), point on the sphere (the ''pole'' or ''center of projection''), onto a plane (geometry), plane (the ''projection plane'') perpendicular to the diameter through the point. It is a smooth function, smooth, bijection, bijective function (mathematics), function from the entire sphere except the center of projection to the entire plane. It maps circle of a sphere, circles on the sphere to generalised circle, circles or lines on the plane, and is conformal map, conformal, meaning that it preserves angles at which curves meet and thus Local property, locally approximately preserves similarity (geometry), shapes. It is neither isometry, isometric (distance preserving) nor Equiareal map, equiareal (area preserving). The stereographic projection gives a way to representation (mathematics), represent a sphere by a plane. The metric tensor, metric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthographic Projection
Orthographic projection (also orthogonal projection and analemma) is a means of representing Three-dimensional space, three-dimensional objects in Plane (mathematics), two dimensions. Orthographic projection is a form of parallel projection in which all the projection lines are orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation on the viewing surface. The obverse of an orthographic projection is an oblique projection, which is a parallel projection in which the projection lines are ''not'' orthogonal to the projection plane. The term ''orthographic'' sometimes means a technique in multiview projection in which principal axes or the planes of the subject are also parallel with the projection plane to create the ''primary views''. If the principal planes or axes of an object in an orthographic projection are ''not'' parallel with the projection plane, the depiction is called ''axonometric'' or an ''auxiliary views''. (''Ax ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trigonometry
Trigonometry () is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine. Throughout history, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation. Trigonometry is known for its many identities. These trigonometric identities are commonly used for rewriting trigonometrical expressions with the aim to simplify an expression, to find a more useful form of an expression, or to solve an equation. History Sumerian astronomers studied angle me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angle Measure
In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight lines at a point. Formally, an angle is a figure lying in a plane formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the '' vertex'' of the angle. More generally angles are also formed wherever two lines, rays or line segments come together, such as at the corners of triangles and other polygons. An angle can be considered as the region of the plane bounded by the sides. Angles can also be formed by the intersection of two planes or by two intersecting curves, in which case the rays lying tangent to each curve at the point of intersection define the angle. The term ''angle'' is also used for the size, magnitude or quantity of these types of geometric figures and in this context an angle consists of a number and unit of measurement. Angular measure or measure of angle are sometimes used to distinguish between the measurement an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
