41. Apollonius Of Perga Article on apollonius of perga from WorldHistory.com, licensed fromWikipedia, the free encyclopedia. Return Index apollonius of perga. http://www.worldhistory.com/wiki/A/Apollonius-of-Perga.htm

World History (home) Encyclopedia Index Localities Companies Surnames ... This Week in History Apollonius of Perga Apollonius of Perga (c. 262 BC - c. 190 BC ) was a Greek geometer, noted for his writings on conic section s. It was Apollonius who gave the ellipse , the parabola , and the hyperbola the names by which we know them. The hypotheses of eccentric orbits, or equivalently, deferent and epicycle s, to explain the apparent motion of the planets and the varying speed of the Moon, are also attributed to him. See also Descartes' theorem Sponsored Links Advertisements DVD New Releases at Barnes and Noble 12 CDs for 1 at BMG Music Service ... at DVDPlanet.com This article is licensed under the GNU Free Documentation License You may copy and modify it as long as the entire work (including additions) remains under this license. You must provide a link to http://www.gnu.org/copyleft/fdl.html To view or edit this article at Wikipedia, follow this link World History How to cite this page Encyclopedia Index ... Contact Us

42. Allmath.com - Math Site For Kids! Home Of Flashcards, Math Click Here apollonius of perga. apolohnius , known as the Great Geometer(280210 BC ). Greek mathematician, born in Perga, Anatolia. http://www.allmath.com/biosearch.php?QMeth=ID&ID=1490

43. APOLLONIUS Of Perga., Conicorum Lib. V. VI. VII. Paraphraste Abalphato Asphahane Bernard Quaritch Ltd. apollonius of perga. Conicorum Lib. V. VI. VII.paraphraste Abalphato Asphahanensi nunc primum editi. Additus http://www.polybiblio.com/quaritch/Sq3.html

Bernard Quaritch Ltd. APOLLONIUS of Perga. Conicorum Lib. V. VI. VII. paraphraste Abalphato Asphahanensi nunc primum editi. Additus in calce Archimedis assumptorum liber ex codicibus Arabicis Mss ... Abrahamus Ecchellensis Latinos ... reddidit ... Io. Alfonsus Borellus ... notas uberiores in universum opus adiecit. Florence, Joseph Cocchini, 1661. Tall 4to, pp. [xxxvi], 415, title printed in red and black, numerous diagrams throughout; old stamp on title and half-title; attractive Italian 18th century vellum-backed paste-paper boards. A FINE COPY OF THE FIRST EDITION of the Ecchelensis translation, the first published version of Books V - VII of Apollonius' Conics, which only survive in the Arabic version of Abu'l Fath al Isfahani, based on the translation of Thabit ibn Qurra. Apollonius introduced the terms ellipse, parabola and hyperbola. The first four books of the Conics 'probably contain little that was not already known ... Books V - VII seem to contain the discoveries which he himself had made' (Smith, History of mathematics, I, p. 117). These books were presumed lost (the eighth is still lost) until Borelli discovered an Arabic manuscript in the Medici library in Florence. Abraham Ecchelensis was a Maronite, born in Syria, who died in Rome 1664. He was professor of Arabic and Syriac in Rome and Paris. All of Apollonius's other works have been lost with one exception, De sectione rationis, which survives only in an Arabic translation. The text by Archimedes appended here was translated from another Arabic manuscript in the Medici library. As with the Apollonius, the Greek original of this text does not survive.

44. ARCHIMEDES., Opera Asher Rare Books. ARCHIMEDES. Opera WITH apollonius of perga. Conica.WITH THEODOSIUS OF TRIPOLIS. Sphærica. Methodo novo illustrata http://www.polybiblio.com/asher/2302.html

Asher Rare Books ARCHIMEDES. Opera WITH: APOLLONIUS OF PERGA. Conica. WITH: THEODOSIUS OF TRIPOLIS. Sphærica. The first editions of Archimedes, Apollonius and Theodosius to be published in England. The addition of these three classics of mathematics generally and geometry in particular to the more widely available Euclid, showed that English mathematical publishing was coming of age and catching up with that on the continent, twelve years before the publication of Newton's Principia . To Archimedes we owe much of modern analytical geometry, mechanics and hydrostatics, including practical applications to pulleys and levers. Apollonius's conics (the four first books here being all that survived in Greek) recognized that the parabola, ellipse and hyperbola (names coined in this treatise) were all special cases of the conic section. The treatise by Theodosius, inventor of a universal sundial, covers spherical geometry. Barrow's contribution in editing and extensively illustrating these three works should not be underestimated, and with special mathematical signs, Greek, Arabic and the twenty-nine copperplates, they must have challenged the resources of the English printers, still somewhat behind their continental colleagues. With a charming early eighteenth-century(?) armorial bookplate of Herbert Jacob of St. Stephens in Kent, with female figures holding a rolled document and playing a cello, with a true bibliophile's motto: "otium cum libris." Also with early stamps of the Inner Temple Library (one of the Inns of Court) in London. With a tear repaired in the last plate, the paper slightly browned and occasional ink spots and other minor defects, but still generally a good copy. A seminal publication in the history of British mathematics.

45. Conics Sections, Apollonius, Menaechmus And Others It is apollonius of perga (about 262 BC about 190 BC), a Greek geometer, whois usually considered the inventor of the conics sections that leads to the http://www.mlahanas.de/Greeks/Conics.htm

Apollonius and Menaechmus It is Apollonius of Perga (about 262 BC - about 190 BC), a Greek geometer, who is usually considered the inventor of the conics sections that leads to the circle, ellipse, parabola and hyperbola that are the possible trajectories of a body in a gravitational field (At least if we ignore some relativistic effects). Apollonius is known as the "Great Geometer" based on his work Conic Sections , an eight-"book" series on the subject. The first four books have come down to us in the original Ancient Greek, but books V-VII are known only from an Arabic translation, while the eighth book has been lost entirely. The Conics Sections is one of the most difficult and complex known mathematical work of ancient Greek mathematicians. Hilal ibn Hilal al-Himsi translated the first four volumes of the Conic Sections while book V to VII were translated by Thabit ibn Qurrah. The Conic Sections is one of the most important mathematical books ever written! Apollonius wrote many books but only the Conics survived partly. Other books considered that he has written area

46. Apollonius apollonius of perga. Born about 262 BC in Perga about 190 BC in Alexandria,Egypt. apollonius of perga was known as The Great Geometer . http://homepages.compuserve.de/thweidenfeller/mathematiker/Apollonius.htm

Apollonius of Perga Born: about 262 BC in Perga, Pamphylia, Greek Ionia (now Murtina, Antalya, Turkey) Died: about 190 BC in Alexandria, Egypt Apollonius of Perga was known as 'The Great Geometer'. Little is known of his life but his works have had a very great influence on the development of mathematics, in particular his famous book Conics introduced terms which are familiar to us today such as parabola , ellipse and hyperbola Apollonius of Perga should not be confused with other Greek scholars called Apollonius, for it was a common name. In [1] details of others with the name of Apollonius are given: Apollonius of Rhodes, born about 295 BC, a Greek poet and grammarian, a pupil of Callimachus who was a teacher of Eratosthenes ; Apollonius of Tralles, 2nd century BC, a Greek sculptor; Apollonius the Athenian, 1st century BC, a sculptor; Apollonius of Tyana, 1st century AD, a member of the society founded by Pythagoras; Apollonius Dyscolus, 2nd century AD, a Greek grammarian who was reputedly the founder of the systematic study of grammar; and Apollonius of Tyre who is a literary character. The mathematician Apollonius was born in Perga, Pamphylia which today is known as Murtina, or Murtana and is now in Antalya, Turkey. Perga was a centre of culture at this time and it was the place of worship of Queen Artemis, a nature goddess. When he was a young man Apollonius went to Alexandria where he studied under the followers of Euclid

47. Encyclopedia: Apollonius Of Perga 4Reference apollonius of pergaRead about apollonius of perga and thousands of other subjects at4Reference.net. apollonius of perga. apollonius of perga (about http://www.nationmaster.com/encyclopedia/Apollonius-of-Perga

Supporter Benefits Signup Login Sources ... Pies Factoid #17 Senior gentlemen might consider a trip to Russia where there's two over 65 women for every man Interesting Facts Make your own graph: Hold down Control and click on several. Compare All Top 5 Top 10 Top 20 Top 100 Bottom 100 Bottom 20 Bottom 10 Bottom 5 All (desc) in category: Select Category Agriculture Crime Currency Democracy Economy Education Energy Environment Food Geography Government Health Identification Immigration Internet Labor Language Manufacturing Media Military Mortality People Religion Sports Taxation Transportation Welfare with statistic: view: Correlations Printable graph / table Pie chart Scatterplot with ... * Asterisk means graphable. Added May 21 Mortality stats Multi-users ½ price Catholic stats Top Graphs Richest Most Murderous Most Populous Most Militaristic ... More Stats Categories Agriculture Background Crime Currency ... Welfare Updated: May 10, 2004 Encyclopedia : Apollonius of Perga Apollonius of Perga (c. 262 BC - c. 190 BC ) was a Greek geometer, noted for his writings on conic sections. It was Apollonius who gave the ellipse, the parabola, and the hyperbola the names by which we know them. The hypotheses of eccentric orbits, or equivalently, deferent and epicycles, to explain the apparent motion of the planets and the varying speed of the Moon, are also attributed to him. See also Descartes' theorem es:Apolonio de P rgamo The Wikipedia article included on this page is licensed under the GFDL Usage implies agreement with terms

48. Curriculum Vitae 1998). apollonius of perga, Hieronimus of Grimstrup, and Richard ofNew York Gloomy Thoughts on History and Neohistoricism. Max http://www.bgu.ac.il/~mfried/

Dr. Michael N. Fried Office: The Institute for Applied Research Ernst David Bergman Campus P.O.B 653, Beer-Sheva Israel Tel: Fax: (972) 8 6472847 e-mail: mfried@bgumail.bgu.ac.il Home: Kibbutz Revivim D. N. Halutza 85515 e-mail: mfried@revivim.org.il Education B.A St. John’s College Annapolis Maryland - Liberal Arts. M.Sc . 1984 - SUNY at Stony Brook - Applied Mathematics. Ph.D Tel Aviv University (Cohn Institute for the History and Philosophy of Science and Ideas) - History of Mathematics. Synopsis of Research My field of research is mathematics education where my main interest lies in what has been termed ‘humanistic mathematics’. Research connected to ‘humanistic mathematics’ follows two distinct directions, one treating mathematics learning and teaching as genuinely human activities and the other treating the subject of mathematics, what students need to learn and teachers to teach, as itself human activity. Related to the first is my work in the Learners Perspective Study, which is an international effort dedicated to exploring and identifying classroom practices by means of video technology. In the context of that study, I have investigated such subjects as student writing and notebooks and authority relations within the classroom.

49. Great Books Index - Apollonius GREAT BOOKS INDEX. apollonius of perga (about 262about 190BC). An Index to Online Great Books in English Translation. http://books.mirror.org/gb.apollonius.html

GREAT BOOKS INDEX Apollonius of Perga (about 262about 190 BC) An Index to Online Great Books in English Translation AUTHORS/HOME TITLES ABOUT GB INDEX BOOK LINKS Mathematical Writings of Apollonius Links to Information About Apollonius Biography of Apollonius (History of Math Archive) [Back to Top of Page] GREAT BOOKS INDEX MENU Great Books Index Home Page and Author List List of All Works by Author and Title [90KB] About the Great Books Index Links to Other Great Books and Literature Sites ... Literary Cryptograms Support for the Great Books Index web pages is provided by Ken Roberts Computer Consultants Inc URL: http://books.mirror.org/gb.apollonius.html Last revised January 11, 1999 by Ken Roberts e-mail ken@mirror.org

50. Re: FWD: Apollonius's Conics By Antreas P. Hatzipolakis Are there more complete others? Thanks. apollonius of perga (Densmore, Dana(ed.); Donahue, William H.; Flaumenhaft, Harvey) Conics. Books IIII. http://mathforum.org/epigone/math-history-list/shahflechon/v01540b01b60b67c7d370

Re: FWD: Apollonius's Conics by Antreas P. Hatzipolakis reply to this message post a message on a new topic Back to messages on this topic Back to math-history-list Subject: Re: FWD: Apollonius's Conics Author: xpolakis@otenet.gr Date: The Math Forum

51. Math Forum: Apollonius And The Conics (Chameleon Graphing: Plane History) He is sometimes called apollonius of perga because of the place where he wasborn. Apollonius wrote several books including a work called Conics. http://mathforum.org/cgraph/history/apollonius.html

Plane History Chameleon Home Ask Dr. Math Chameleon Home ... For Adults Apollonius and the Conics Apollonius was born around 262 BC in the town of Perga, in what is now Turkey. He is sometimes called Apollonius of Perga because of the place where he was born. Apollonius wrote several books including a work called Conics . This book was about the conic sections , curves that are created by slicing through a double cone with a plane. Here is one example: Conic sections include the parabola , the hyperbola , and the ellipse Apollonius was not the first person to write about conic sections, but he discovered many new things about them. He gave the curves the names we use today, and studied the second branch of the hyperbola. His book was very famous, and people went on studying it for hundreds of years. For example, Hypatia wrote a commentary on the Conics around 400 AD. Apollonius often used reference lines to help study conic sections. For example, he studied ellipses by measuring distances along a diameter and along a tangent to the ellipse perpendicular to the diameter: Apollonius's system of measurements worked a lot like the coordinate plane . But there were several important differences. First, Apollonius's reference lines were not always at right angles. Sometimes they slanted or tilted:

52. Apollonius: Introduction apollonius of perga. Introduction a unified theory of conics. Theonly major work of Greek geometry to survive in written form that http://cerebro.xu.edu/math/math147/02f/apollonius/apollointro.html

Apollonius of Perga Introduction: a unified theory of conics The only major work of Greek geometry to survive in written form that studies the conic sections in detail is the Conics of Apollonius of Perga (262? - 190?BCE). Even so, it survives only partially. We have at present only the first seven of the eight books that Apollonius wrote. As we have seen, the conics were used by Menaechmus in dealing with the problem of the duplication of the cube in around 350BC, and we have references in other works to treatises on the conics written by Aristaeus , a contemporary of Menaechmus, and by Euclid, but these are now lost. In any event, the work by Apollonius was extremely well-received by geometers of the ancient world, so much so that it seems to have displaced all other writings in the subject. As Carl Boyer, a noted historian of mathematics, puts it, "If survival is a measure of quality, the Elements of Euclid and the Conics of Apollonius were clearly the best works in their field." About Apollonius we know very little. He was born in

53. Historical View Of The Conic Sections apollonius of perga, one of the greatest Greek mathematicians of the time (circa200 BC), appears to have been the first to have rigorously studied the conic http://www.krellinst.org/UCES/archive/resources/conics/node5.html

Next: Geometric Origin of the Conic Sections Up: Section 1. General Overview ... Section 1. General Overview Historical View of the Conic Sections In this hypertext, we consider the conic sections , which have been studied for over 2000 years. Many people have contributed to this study, and many historical references and texts exist to document this study. Apollonius of Perga, one of the greatest Greek mathematicians of the time (circa 200 B.C.), appears to have been the first to have rigorously studied the conic sections. He applied his work to his study of planetary motion and used this to aid in the development of Greek astronomy. (Recall that Perga was one of the cities visited by the apostle Paul during his first missionary journey as recorded in Acts 13:13. Paul would have been in Perga less than 300 years after Apollonius' development of the topic of conic sections.) More information on Apollonius, as well as many other mathematicians, is held at the MacTutor History of Mathematics Archive at the University of St. Andrews. You may view pages dealing with Apollonius,

54. Apollonius Of Perga - Information An online Encyclopedia with information and facts apollonius of perga Information,and a wide range of other subjects. apollonius of perga - Information. http://www.book-spot.co.uk/index.php/Apollonius_of_Perga

Apollonius of Perga - Information Home Mathematical and natural sciences Applied arts and sciences Social sciences and philosophy ... Interdisciplinary categories Apollonius of Perga (about 262 BC - about 190 BC ) was a Greek geometer, noted for his writings on conic sections . It was Apollonius who gave the ellipse , the parabola , and the hyperbola the names by which we know them. The hypotheses of eccentric orbits, or equivalently, deferent and epicycles , to explain the apparent motion of the planets and the varying speed of the Moon, are also attributed to him. See also Descartes' theorem All text is available under the terms of the GNU Free Documentation License (see for details). . Wikipedia is powered by MediaWiki , an open source wiki engine.

55. HighBeam Research: ELibrary Search: Results Results per Page 10. 1. apollonius of perga (c. 245c.190 BC) The HutchinsonDictionary of Scientific Biography; January 1, 1998 http://www.highbeam.com/library/search.asp?FN=AO&refid=ency_refd&search_dictiona

56. HighBeam Research: Search Results: Article apollonius of perga (c. 245c.190 BC). The Hutchinson Dictionary ofScientific Biography; 1/1/1998. Read the Full Article, Get a FREE http://www.highbeam.com/library/doc0.asp?DOCID=1P1:28910427&num=19&ctrlInfo=Roun

57. Apollonius' Tangency Problem apollonius of perga (born circa 261 BC) subsequently generalized this by showinghow to find a circle tangent to three objects in the plane, where the objects http://www.mathpages.com/home/kmath113.htm

Apollonius' Tangency Problem Polynomials For Sums of Square Roots , an equation of this form, when cleared of radicals, leads to the polynomial [(K - s1)^2 - 4 s2]^2 - 64 K s3 = (2) where s1=a+b+c, s2=ab+ac+bc, and s3=abc. Since each of a,b,c is a polynomial in the unknown quantity r of degree 2, the resulting polynomial is of degree 8, and it is extremely laborious to actually generate this polynomial, let alone solve it. For example, consider the case of three circles whose centers are separated by distances of 32, 26, and 29 units, and whose radii are 4, 6, and 7 units (opposite the edges, respectively) as shown below. Return to MathPages Main Menu

58. History Of Mathematics: Greece Chrysippus (280206); Conon of Samos (c. 245); apollonius of perga (c. 260-c.185); Nicomedes (c. 240?); Dositheus of Alexandria (fl. c. 230); Perseus (fl. http://aleph0.clarku.edu/~djoyce/mathhist/greece.html

Greece Cities Abdera: Democritus Alexandria : Apollonius, Aristarchus, Diophantus, Eratosthenes, Euclid , Hypatia, Hypsicles, Heron, Menelaus, Pappus, Ptolemy, Theon Amisus: Dionysodorus Antinopolis: Serenus Apameia: Posidonius Athens: Aristotle, Plato, Ptolemy, Socrates, Theaetetus Byzantium (Constantinople): Philon, Proclus Chalcedon: Proclus, Xenocrates Chalcis: Iamblichus Chios: Hippocrates, Oenopides Clazomenae: Anaxagoras Cnidus: Eudoxus Croton: Philolaus, Pythagoras Cyrene: Eratosthenes, Nicoteles, Synesius, Theodorus Cyzicus: Callippus Elea: Parmenides, Zeno Elis: Hippias Gerasa: Nichmachus Larissa: Dominus Miletus: Anaximander, Anaximenes, Isidorus, Thales Nicaea: Hipparchus, Sporus, Theodosius Paros: Thymaridas Perga: Apollonius Pergamum: Apollonius Rhodes: Eudemus, Geminus, Posidonius Rome: Boethius Samos: Aristarchus, Conon, Pythagoras Smyrna: Theon Stagira: Aristotle Syene: Eratosthenes Syracuse: Archimedes Tarentum: Archytas, Pythagoras Thasos: Leodamas Tyre: Marinus, Porphyrius Mathematicians Thales of Miletus (c. 630-c 550)

59. Greek For Euclid: Contents built. Later workers, such as Archimedes (287212 BC), Eratosthenes(b. 284 BC), apollonius of perga (fl. 220 BC), and Ptolemy (fl. http://www.du.edu/~etuttle/classics/nugreek/contents.htm

Reading Euclid This course combines Greek and Geometry to show how to read Euclid's Elements in the original language "I would make them all learn English; and then I would let the clever ones learn Latin as an honour, and Greek as a treat" Sir Winston Churchill Go immediately to Contents Introduction Eu)klei/dou Stoixei~a , Euclid's Elements, the classical textbook in geometry, is easy to read in the original ancient Greek, but its grammar and vocabulary are not those familiar from the usual course in elementary Greek, with peculiarities that make it difficult for the beginner. The text of the Elements that we have is written in the literary koinh/ typical of the 1st century AD. This course concentrates on exactly what is necessary to read Euclid, both in vocabulary and grammar. Its sole aim is to teach how to read this work, and similar texts in Greek mathematics, and not to compose Greek sentences, nor to read the Iliad or Plato. All necessary information is included in the course. A great amount of scholarship has been devoted to Euclid, mainly in Latin or German, and this course may expose some of it to a larger audience, to whom it has been largely inaccessible. For authoritative details, reference must be made to these sources, since the present one claims no expertise. There are many websites with information on Euclid and geometry. For example, look at the link to Euclid in the Seven Wonders website that is referenced in the Classics Index page, under the heading Pharos of Alexandria. As is typical of education on the Internet, many sites are poor, repetitive or childish, however.

60. Apollonius Problem Draw a circle tangent to three given circles. The problem was posed and solvedby one of the greatest Greek geometers, apollonius of perga (ca. http://www.cut-the-knot.org/Curriculum/Geometry/Apollonius.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Apollonius Problem: What is it? A Mathematical Droodle Explanation Alexander Bogomolny Apollonious Problem Draw a circle tangent to three given circles. The problem was posed and solved by one of the greatest Greek geometers, Apollonius of Perga (ca. 260-170 B.C.) However, his original solution that was included in his treatise De Tactionibus has been lost. Nowadays, a multitude of solutions is available with contributions from some very famous mathematicians, like C. F. Gauss J. D. Gergonne Tradionally, the problem covers several special cases. For example, one or more of the given circles may degenerate into a point. (If all 3 do, the problem is then reduced to constructing the circumcircle of a given triangle. Note that if the three points are collinear , the circumcircle degenerates into a straight line. If the given circles touch at the same point, there is an infinitude of solutions. Quite often, especially in Inversive Geometry , straight lines are also considered circles - circles with infinite radius and center at infinity. In particular, if the three sides lines of a triangle are looked at as such circles of infinite radius, the

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