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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] |
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] |
On Habitations
Theodosius of Bithynia ( ; 2nd–1st century BC) was a Hellenistic astronomer and mathematician from Bithynia who wrote the ''Spherics'', a treatise about spherical geometry, as well as several other books on mathematics and astronomy, of which two survive, ''On Habitations'' and ''On Days and Nights''. Life Little is known about Theodosius' life. The ''Suda'' (10th-century Byzantine encyclopedia) mentioned him writing a commentary on Archimedes' ''Method'' (late 3rd century BC), and Strabo's ''Geographica'' mentioned mathematicians Hipparchus ( – ) and "Theodosius and his sons" as among the residents of Bithynia distinguished for their learning. Vitruvius (1st century BC) mentioned a sundial invented by Theodosius. Thus Theodosius lived sometime after Archimedes and before Vitruvius, likely contemporaneously with or after Hipparchus, probably sometime between 200 and 50 BC. Historically he was called Theodosius of Tripolis due to a confusing paragraph in the ''Suda'' which proba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pappus Of Alexandria
Pappus of Alexandria (; ; AD) was a Greek mathematics, Greek mathematician of late antiquity known for his ''Synagoge'' (Συναγωγή) or ''Collection'' (), and for Pappus's hexagon theorem in projective geometry. Almost nothing is known about his life except for what can be found in his own writings, many of which are lost. Pappus apparently lived in Alexandria, where he worked as a Mathematics education, mathematics teacher to higher level students, one of whom was named Hermodorus.Pierre Dedron, J. Itard (1959) ''Mathematics And Mathematicians'', Vol. 1, p. 149 (trans. Judith V. Field) (Transworld Student Library, 1974) The ''Collection'', his best-known work, is a compendium of mathematics in eight volumes, the bulk of which survives. It covers a wide range of topics that were part of the ancient mathematics curriculum, including geometry, astronomy, and mechanics. Pappus was active in a period generally considered one of stagnation in mathematical studies, where, to s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Book Of Lemmas
The ''Book of Lemmas'' or ''Book of Assumptions'' (Arabic ''Maʾkhūdhāt Mansūba ilā Arshimīdis'') is a book attributed to Archimedes by Thābit ibn Qurra, though the authorship of the book is questionable. It consists of fifteen propositions ( lemmas) on circles. History Translations The ''Book of Lemmas'' was first introduced in Arabic by Thābit ibn Qurra; he attributed the work to Archimedes. A translation from Arabic into Latin by John Greaves and revised by Samuel Foster (c. 1650) was published in 1659 a''Lemmata Archimedis'' Another Latin translation by Abraham Ecchellensis and edited by Giovanni A. Borelli was published in 1661 under the name ''Liber Assumptorum''. T. L. Heath translated Heiburg's Latin work into English in his ''The Works of Archimedes''. A more recently discovered manuscript copy of Thābit ibn Qurra's Arabic translation was translated into English by Emre Coşkun in 2018. Authorship The original authorship of the ''Book of Lemmas'' has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Measurement Of A Circle
''Measurement of a Circle'' or ''Dimension of the Circle'' ( Greek: , ''Kuklou metrēsis'') is a treatise that consists of three propositions, probably made by Archimedes, ca. 250 BCE. The treatise is only a fraction of what was a longer work. Propositions Proposition one Proposition one states: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle. Any circle with a circumference ''c'' and a radius ''r'' is equal in area with a right triangle with the two legs being ''c'' and ''r''. This proposition is proved by the method of exhaustion. Proposition two Proposition two states: The area of a circle is to the square on its diameter as 11 to 14. This proposition could not have been placed by Archimedes, for it relies on the outcome of the third proposition. Proposition three Proposition three states: The ratio of the circumference of any circle to its ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
On The Sphere And Cylinder
''On the Sphere and Cylinder'' () is a treatise that was published by Archimedes in two volumes . It most notably details how to find the surface area of a sphere and the volume of the contained ball and the analogous values for a cylinder, and was the first to do so. Contents The principal formulae derived in ''On the Sphere and Cylinder'' are those mentioned above: the surface area of the sphere, the volume of the contained ball, and surface area and volume of the cylinder. Let r be the radius of the sphere and cylinder, and h be the height of the cylinder, with the assumption that the cylinder is a right cylinder—the side is perpendicular to both caps. In his work, Archimedes showed that the surface area of a cylinder is equal to: :A_C = 2 \pi r^2 + 2 \pi r h = 2 \pi r ( r + h ).\, and that the volume of the same is: :V_C = \pi r^2 h. \, On the sphere, he showed that the surface area is four times the area of its great circle. In modern terms, this means that the surf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid's Data
''Data'' ( Greek: Δεδομένα, ''Dedomena'') is a work by Euclid. It deals with the nature and implications of "given" information in geometrical problems. The subject matter is closely related to the first four books of Euclid Euclid (; ; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of geometry that largely domina ...'s '' Elements''. Editions and translations ;Greek text *''Data'', ed. H. Menge, in ''Euclidis opera omnia'', vol. 6, Leipzig: Teubner, 1896Google Books ;English versions *Translated by Robert Simson 1821 edition [...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] |
Spherics (Menelaus)
Spherics (sometimes spelled sphaerics or sphaerica) is a term used in the history of mathematics for historical works on spherical geometry, exemplified by the ''Spherics'' ( ), a treatise by the Hellenistic mathematician Theodosius Theodosius ( Latinized from the Greek "Θεοδόσιος", Theodosios, "given by god") is a given name. It may take the form Teodósio, Teodosie, Teodosije etc. Theodosia is a feminine version of the name. Emperors of ancient Rome and Byzantium ... (2nd or early 1st century BC), and another treatise of the same title by Menelaus of Alexandria (). References Spherical geometry Classical geometry Spherical astronomy Greek mathematics {{geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypsicles
Hypsicles (; c. 190 – c. 120 BCE) was an ancient Greek mathematician and astronomer known for authoring ''On Ascensions'' (Ἀναφορικός) and possibly the Book XIV of Euclid's ''Elements''. Hypsicles lived in Alexandria. Life and work Although little is known about the life of Hypsicles, it is believed that he authored the astronomical work ''On Ascensions''. The mathematician Diophantus of Alexandria noted on a definition of polygonal numbers, due to Hypsicles: On Ascensions In ''On Ascensions'' (Ἀναφορικός and sometimes translated ''On Rising Times''), Hypsicles proves a number of propositions on arithmetical progressions and uses the results to calculate approximate values for the times required for the signs of the zodiac to rise above the horizon. It is thought that this is the work from which the division of the circle into 360 parts may have been adopted since it divides the day into 360 parts, a division possibly suggested by Babylonian astronom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
On Risings And Settings
Autolycus of Pitane (; c. 360 – c. 290 BC) was a Greek astronomer, mathematician, and geographer. He is known today for his two surviving works ''On the Moving Sphere'' and ''On Risings and Settings'', both about spherical geometry. Life Autolycus was born in Pitane, a town of Aeolis within Ionia, Asia Minor. Of his personal life nothing is known, although he was a contemporary of Aristotle and his works seem to have been completed in Athens between 335–300 BC. Euclid references some of Autolycus' work, and Autolycus is known to have taught Arcesilaus. The lunar crater Autolycus was named in his honour. Work Autolycus' two surviving works are about spherical geometry with application to astronomy: ''On the Moving Sphere'' and ''On Risings and Settings'' (of stars). In late antiquity, both were part of the "Little Astronomy", a collection of miscellaneous short works about geometry and astronomy which were commonly transmitted together. They were translated into Arabic i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
