61. Gudrun Wolfschmidt A Historian Looks At Astronomy In The The construction of such sundials was rather complicated and it is not astonishingthat famous mathematicians like apollonius of perga were often among the http://www.math.uni-hamburg.de/math/ign/xyz/ca00-v5.htm

The Uses of History in Science Education The Third International Seminar for the History of Science and Science Education Deutsches Museum, Munich, Germany July 30 - August 4, 2000 Gudrun Wolfschmidt A Historian Looks at Astronomy in the Classroom There are more things in heaven and earth than are dreamt of in your philosophy. Shakespeare: Hamlet Astronomy is the oldest science. Observing the stars and planets has always been important e.g. for time determination or for calendar making. We find great interest in astronomical questions in ancient cultures as well as in more recent centuries. history of astronomy one could present the topics in an even more interesting and motivating way for a broader range of pupils. I think this should start in the beginning years of the 'Gymnasium'. Furthermore, with interdisciplinary teaching one could combine science with cultural history. Here I give a concrete example of a subject which lends itself to such an interdisciplinary approach - sundials. After an introduction dealing with antiquity and the Middle Ages, I shall present three sundial examples drawn essentially from the Early Modern period (roughly 15th-17th centuries). I think it is useful to supplement book-learning with practical work - i.e. making such instruments and learning to use them. This can be rounded out by a visit to a museum to see original instruments or by a walk through town to find sundials.

62. Oxbow Books/David Brown Book Company apollonius of perga's Conica Text, Context, Subtext by Michael N Fried and SabetaiUnguru A detailed and highly specialised analysis of Apollonius' of Perga's http://www.oxbowbooks.com/browse.cfm?&CatID=559

63. The Mathematikos Experiment the name is based on the design itself which is in part inspired by two of historiesgreatest mathematicians , Archimedes of Syracuse and apollonius of perga . http://tatumsworkshop.com/WorkshopV2/mathematikos/mathematikos.htm

A few months ago I decided to begin working on a new design based on my spiral tampers . It took some trial and error and the tampers you see below are the result of those experiments . The shape evolves as my technique moves towards the end product of what I had in mind . The whole process was a learning experience , hence the name of the experiment Mathematikos , Greek for "disposed to learn" . Another reason for the name is based on the design itself which is in part inspired by two of histories greatest mathematicians , Archimedes of Syracuse and Apollonius of Perga . The Spiral design is based loosely on the Archimedian Screw , having four flutes which complete one rotation around the cylinder. My dilemma came when I found that I did not like the flat joint of brass and acrylic, wanting instead a movement of brass into acrylic. Once again I looked to the mathematicians for inspiration and found the works on Conic Sections by Apollonius of Perga . 'Conics' deals with the shapes one acquires when slicing a cone . This work would later be used by Kepler in determining the eliptical orbits of the planets . By cutting a precise cone into the brass base and matching it with a mirror image cone on the acrylic inserted into it I am now able to produce a brass base that flows with the spiral design , as shown in the picture above .

64. Great Books And Classics - Plutarch BC) Aristotle (c. 384322 BC) Epicurus (c. 341-270 BC) Aesop (fl.c. 300 BC) Euclid(fl.c. 300 BC) Archimedes (c. 287-212 BC) apollonius of perga (fl.c. 240 BC), http://www.grtbooks.com/plutarch.asp?idx=0&sub=1

65. Great Books And Classics - Welcome BC) Aristotle (c. 384322 BC) Epicurus (c. 341-270 BC) Aesop (fl.c. 300 BC) Euclid(fl.c. 300 BC) Archimedes (c. 287-212 BC) apollonius of perga (fl.c. 240 BC http://www.grtbooks.com/

Selected Index: Author (by date) Author (A-Z) Title (by date) Title (A-Z) Selected Reading List: All Works [Change] Selected Language: All [Change] Author - Chronological Welcome to Great Books and Classics (Epic of Gilgamesh) (c. 2000?-1400? BC) Hammurabi (fl.c. 1700? BC) (Old Testament) (c. 1400?-300? BC) Homer (fl.c. 850? BC) Hesiod (fl.c. 700? BC) Tyrtaeus (fl.c. 650? BC) Confucius (c. 551-479 BC) Aeschylus (c. 525-456 BC) Pindar (c. 522-446? BC) Lao-Tzu (fl.c. 500? BC) Sophocles (c. 495-406 BC) Euripides (c. 485-406 BC) Herodotus (c. 484-425 BC) Thucydides (c. 460-400 BC) Hippocrates (c. 460-377? BC) Aristophanes (c. 448-380 BC) Plato (c. 427-347 BC) Bhagavad-Gita (c. 400 BC) Sun-Tzu (c. 400?-320? BC) Aristotle (c. 384-322 BC) Epicurus (c. 341-270 BC) Aesop (fl.c. 300 BC) Euclid (fl.c. 300 BC) Archimedes (c. 287-212 BC) Apollonius of Perga (fl.c. 240 BC) Here you will find links to classic works of religion, philosophy, politics, science, history and literature from both East and West, spanning nearly four thousand years of human history. Works are indexed alphabetically by Author or Title, and chronologically by Author (or work, if anonymous). There are also separate indexes for works included in various reading lists, and works which are available in languages other than English. Browse around! Site optimized for Internet Explorer 6.0 at 1024x768 resolution

66. APOLLONIUS (THE EFFEMINATE) See C. Muller, Fragmenta Histor’icorum Graecorum, iii.; E. Schurer, storyof the Jewish People, iii. (Eng. tr. 1886). apollonius of perga. http://64.1911encyclopedia.org/A/AP/APOLLONIUS_THE_EFFEMINATE_.htm

document.write(""); APOLLONIUS (THE EFFEMINATE) )oIIo appears in a form which seeks to combine manhood and ye ~rnal youth. His long hair is usually tied in a large knot above F( forehead. The most famous statue of him is the Apollo th ~lvidere in the Vatican (found at Frascati, 1455), an imitation b) longing to the early imperial period of a bronze statue repre- wi nting him, with aegis in’ his left hand, driving back the Gauls iir~ m his temple at Delphi (279 B.c.), or, according to another wr ~w, fighting with the Pythian dragon. In the Apollo Cithar- de dus or Musagetes in the Vatican, he is crowned with laurel atum and Ancona. ‘Inc ‘Irajan column in the centre of the rum is celebrated as being the first triumphal monument of I kind. On the accession of Hadrian, whom he had offended ridiculing his performances as architect and artist, Apollodorus ~s banished, and, shortly afterwards, being charged with aginary crimes, put to death (Dio Cassius lxix. 4). He also ote a treatise on. Siege Engines (lloXiopepruc~i), which was clicated to Hadrian. ~POLLONIA, the name of more than thirty cities of antiquity.

67. Boing Boing: A Directory Of Wonderful Things moon accurately, using an epicyclic model devised by Hipparchus, and of the planetsMercury and Venus, using an epicyclic model derived by apollonius of perga. http://boingboing.net/2002_09_01_archive.html

A DIRECTORY OF WONDERFUL THINGS suggest a site home archives store ... xeni Monday, September 30, 2002 2000+ year old Greek computer reinterpreted The Antikythera mechanism, recovered off a sunken ship in Greece in 1900, is thought to be a clockwork device to calculate the orbits of the celestial bodies. New analysis of the remaining fragments shows that it was wicked-cool: The Greeks believed in an earth-centric universe and accounted for celestial bodies' motions using elaborate models based on epicycles, in which each body describes a circle (the epicycle) around a point that itself moves in a circle around the earth. Mr Wright found evidence that the Antikythera mechanism would have been able to reproduce the motions of the sun and moon accurately, using an epicyclic model devised by Hipparchus, and of the planets Mercury and Venus, using an epicyclic model derived by Apollonius of Perga. (These models, which predate the mechanism, were subsequently incorporated into the work of Claudius Ptolemy in the second century AD.) A device that just modelled the motions of the sun, moon, Mercury and Venus does not make much sense. But if an upper layer of mechanism had been built, and lost, these extra gears could have modelled the motions of the three other planets known at the time—Mars, Jupiter and Saturn. In other words, the device may have been able to predict the positions of the known celestial bodies for any given date with a respectable degree of accuracy, using bronze pointers on a circular dial with the constellations of the zodiac running round its edge.

68. 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/~jcalvert/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.

69. Xah: Special Plane Curves: What's New A subscription based system should soon come to this site. Much addition is in theplanning.. 200208-08 A new book apollonius of perga; Conics, Books I-III. http://www.xahlee.org/SpecialPlaneCurves_dir/Intro_dir/whatsNew.html

Table of Contents Get the CD-ROM , and get all QuickTime movies. What's New 2002-08-25: The Geometer's Sketch Pad files, Matehmatica notebooks, QuickTime movies files has been added to the following pages now: conic sections cycloid deltoid ellipse A subscription based system should soon come to this site. Much addition is in the planning.. 2002-08-08: A new book: Apollonius of Perga; Conics, Books I-III . Published by Green Lion Press in 1998, edited by Dana Densmore. This one is only $23, much cheaper than the $160 one (C.J. Toomer, 1990, Springer Verlag). 2002-07-28. This site has moved from one machine to another. If you find missing files, please let me know. (write to me at xah@xahlee.org . Thanks.) 2002-05-09: more photos. catenary page has many new photos of the St. Louis Gateway Arch. caustics page has new photos of cups under light. mathematical material will be coming to the inversion page soon. Conic Sections page. 2002-04-21: Few more edits. The sinusoid page has a photo of a form modeled after the surface Sin[x]*Sin[y], as well as a new graphics at the top. The Seashell page is again updated with new photos. A draft of

70. The Great Men Of Croatian Science his mathematical research to the recovery of some lost treatises (On Inclinations, On Contacts) by the Greek mathematician apollonius of perga and studied http://public.srce.hr/zuh/English/velik_e.htm

The Great Men of Croatian Science Complete information is available only in Croatian HERMAN DALMATIN HERMANNUS DALMATA Herman Dalmatin ( Hermannus Dalmata, Sclavus, Secundus, De Carinthia) natural philosopher and translator from the Arabic language (about 1110 - after 1143) is the earliest Croatian scientist and philosopher, and one of the greatest. He was born in central Istria, and studied at the Cathedral School at Chartres and in Paris (1130-1135). After completing his studies he travelled to the Middle East with his friend Robert from Ketton, where both were seriously involved in the study of Arabic science and philosophy. In 1138 we find them in a place along the river Ebro in Spain working on translations. At that time Herman was mostly translating works of astrology. In 1138 he translated the astrological treatise Fatidica , the sixth part of a work in astronomy by a scientist of Jewish origin Sahl ibn Bishr; in 1140 he translated Introductorium in astronomiam by Abu Ma'shar contributing thereby to the spreading of Aristotelian philosophy in western Europe. At the same time Herman wrote the astrological works Liber imbrium and De indagatione cordis , compilations from Indian and Arabic texts. Petrus Venerabilis, the Abbot of Cluny met Herman and Robert in Spain in 1142 and encouraged them to translate the Koran. In Leone Herman finished some shorter texts about Islam

71. Quelques Grands Mathématiciens AC/BL Lycée Adam De Craponne Salon Lycée Adam de CRAPONNE SALON DE PROVENCE apollonius DE perga Il est né à Perge en 262 avant JC. Mathématicien et astronome grec, il a étudié à Alexandrie avec les successeurs de Euclide. http://pedagogie.ac-aix-marseille.fr/etablis/lycees/craponne/maths/apoloniu.htm

Lycée Adam de CRAPONNE SALON DE PROVENCE APOLLONIUS DE PERGA Il est né à Perge en 262 avant JC. Mathématicien et astronome grec, il a étudié à Alexandrie avec les successeurs de Euclide Le livre 3 traite de triangles inscrits, de segments, de polaires et pôles par rapport à une conique. Le livre 6 traite de la recherche d' un cône et d'un plan se coupant suivant une conique donnée. Le livre 7 étudie des aires de parallélogrammes définis par des points de la conique. Les 4 premiers sont écrits en grec, les trois suivants ont été traduits en arabe le dernier a été perdu. Platon Si ABC est un triangle, I le milieu de [BC] alors AB² + AC² = 2 (BI² + IA²) Retour au tableau chronologique

72. Estudo Do Problema De Apollonius apollonius de perga (260 170 AC) foi um ge³metra grego que equacionou e resolveu o problema a que lhe foi atribu­do o nome. A solu§£o original foi escrita no seu Tratado De Tactionibus que infelizmente se perdeu. Nos nossos dias, o problema foi resolvido por v¡rios ilustres matem¡ticos como Fran§ois Vi¨te, C. F. Gauss, J. D. Gergonne. http://planeta.clix.pt/anove/gd/apollonius/

Estudo do problema de Apollonius Apollonius de Perga (260 - 170 AC) foi um geómetra grego que equacionou e resolveu o problema a que lhe foi atribuído o nome. A solução original foi escrita no seu Tratado De Tactionibus que infelizmente se perdeu. Nos nossos dias, o problema foi resolvido por vários ilustres matemáticos como François Viète, C. F. Gauss, J. D. Gergonne. O problema consiste em traçar um elemento geométrico (sejam eles um ponto, uma linha recta ou uma linha de circunferência) que seja tangente a três elementos geométricos, sejam eles o ponto , a linha recta ou a linha de circunferência Para a resolução do problema passamos por definir a equação. Assim, determinamos as combinações possíveis entre os elementos geométricos descritos no parágrafo anterior (tabela 1). Os problemas apresentados nas alíneas a, b, c e d foram resolvidos por Euclides no seu Tratado Elementos, encontramos esses problemas descritos no livro IV. Na restantes alíneas temos que recorrer à Geometria Invertida Combinações dos elementos geométricos a) b) c) d) ... e) O f) O O g) O O O h) O O i) O j) O O Ponto Recta Circunferência Tabela 1 Para ver a solução correspondente a cada uma destas dez combinações clique sobre a letra da combinação na tabela 1.

73. References For Apollonius B Elsner, apollonius Saxonicus Die Restitution eines verlorenen Werkes des apolloniusvon perga durch Joachim Jungius, Woldeck Weland und Johannes Müller http://www-gap.dcs.st-and.ac.uk/~history/References/Apollonius.html

References for Apollonius Biography in Dictionary of Scientific Biography (New York 1970-1990). Biography in Encyclopaedia Britannica. Books: M Chasles, (Paris, 1837). B Elsner, T L Heath, Apollonius of Perga: Treatise on Conic Sections T L Heath, A History of Greek Mathematics (2 vols.) (Oxford, 1921). H Wussing, Apollonius, in H Wussing and W Arnold, Biographien bedeutender Mathematiker (Berlin, 1983). Articles: A Abdurahmanov, New information about the Arabic translation of the 'Conica' of Apollonius of Perga (Russian), Taskent. Gos. Univ. Naucn. Trudy Vyp. 490 Voprosy Matematiki A Bilimovitch, Apollonius theorem on station of the planet (Serbo-Croatian), Glas Srpske Akad. Nauka Od. Prirod.-Mat. Nauka (N.S.) A V Dorofeeva, Apollonius (ca. 260-190 B.C.) (Russian), Mat. v Shkole (5) (1988), i. J P Hogendijk, Desargues' 'Brouillon project' and the 'Conics' of Apollonius, Centaurus J P Hogendijk, Arabic traces of lost works of Apollonius, Arch. Hist. Exact Sci. O Neugebauer, The equivalence of eccentric and epicyclic motion according to Apollonius, Scripta Math.

74. APOLLONIUS DE PERGA, Conicorum Lib. V. VI. VII Translate this page Rodolphe Chamonal. apollonius DE perga Conicorum lib. V. VI. VII Florentiae,Ex Typographia Josephi Cocchini, 1661. in-fol., br., couv. http://www.polybiblio.com/chamonal/8.html

Rodolphe Chamonal APOLLONIUS DE PERGA Conicorum lib. V. VI. VII Florentiae, Ex Typographia Josephi Cocchini, 1661 in-fol., br., couv. muette anc 18 ff.n.ch., et 415 pp., diagrammes dans le texte. Brunet I, col. 348. Première édition des livres 5 à 7 des "Sections coniques" d'Apollonius de Perga, que Sarton considère comme l'un des plus grands livres scientifiques de l'Antiquité. Cette traduction latine a été faite par Abraham Echellensis d'après le manuscrit d'une traduction arabe, retrouvée par le célèbre médecin et physicien italien Alfonse Borelli à la Bibliothèque Medicean de Florence. Le même volume renferme "Archimedis Liber Assumptorum, interprete Thebit Ben Kora, exponente Almochtasso, ex codice Arabico manuscripto Sereniss. Magni Ducis Etruriae, Abrahamus Ecchellensis Latine vertit, Jo. Alfonsus Borellus Notis illustravit" (également en première édition, il occupe les pp. 377 à 413). Bon exemplaire à toutes marges This item is listed on Bibliopoly by Rodolphe Chamonal ; click here for further details.

75. Apollonius Von Perga Translate this page in perga, Pamphylia, Griechenland (nun Murtina, Antalya, Türkei) Gestorben ungefähr190 v in der Schulmathematik ist natürlich 'Der Kreis des apollonius'. http://www.mathematik.ch/mathematiker/apollonius.php

Home Geschichte Mathematiker Zitate ... Suche Apollonios von Perge Geboren: ungefähr 262 v.Chr. in Perga, Pamphylia, Griechenland (nun Murtina, Antalya, Türkei) Gestorben: ungefähr 190 v.Chr.in Alexandria, Ägypten Apollonios von Perge war als 'Der Grosse Geometer' bekannt. Über sein Leben ist wenig bekannt, aber seine Arbeiten hatten grossen Einfluss auf die Entwicklung in Mathematik. Speziell sein berühmtes Buch 'Conica' führt in für uns heute wohlbekannte Terme wie Parabel Ellipse und Hyperbel ein. Der Inhalt des Werkes "Conica" Buch I: Erzeugung des Kegelschnitts und Kreiskegels. Buch II: Achsen und Durchmesser der Kegelschnitte. Buch III: Transversalen der Kegelschnitte, Theorie von Pol und Polare, Brennpunkt von Ellipse und Hyperbel. Buch IV: Untersuchung des Schnittes von Kegelschnitten mit Kreisen. Buch V: Theorie der Normalen und Subnormalen, kürzeste und längste Verbindung mit einem Punkt ausserhalb des Kegels und des Kegelschnitts. Buch VI: Untersuchung gleicher und ähnlicher Kegelschnitte. Buch VII: Sätze über spezielle Eigenschaften von konjugierten Durchmessern.

76. Kegelsneden Deze laatste, apollonius van perga (~262 ~190 vC) studeerde in Alexandrië en gingdaarna naar pergamom, een stad die zich naast Alexandrië tot een centrum http://www.pandd.demon.nl/kegelsneden.htm

Kegelsneden volgens Apollonius Inleiding Cirkel Kegelsneden Ellips ... Geschiedenis Zie ook: Kegelsneden en hun vergelijkingen Zie ook: Ellips-constructies met Cabri Zie ook: Pooltransformaties Zie ook: Bollen van Dandelin 1. Inleiding Na de overwinning van Alexander de Grote op de Perzen in 333 vC ontstond een Grieks wereldrijk met Alexandrië als hoofdstad. Dit was de begintijd van het Hellenisme. Van de geleerden uit die tijd die grote invloed op de ontwikkeling van de exacte wetenschappen hebben gehad, noemen we Euclides , Archimedes, Erathostenes en Apollonius. Deze laatste, Apollonius van Perga (~262 - ~190 vC) studeerde in Alexandrië en ging daarna naar Pergamom, een stad die zich naast Alexandrië tot een centrum van wetenschap ontwikkelde. Apollonius' bekendste werk is een verhandeling over kegelsneden , de zogenoemde Konika Uiteraard kon Apollonius zich alleen beroepen op de tot dan toe bekende methoden in de wiskunde, en deze waren eigenlijk zeer beperkt, doordat het getalbegrip bij de Grieken louter gebaseerd was op de oppervlakterekening (zie bijvoorbeeld Boek VI van de Elementen van Euclides).

77. Raakprobleem 1. Inleiding terug In twee verloren gegane boeken, getiteld De Tactionibus (Overaanrakingen), beschrijft apollonius van perga (~262 ~190 vC) een beroemd http://www.pandd.demon.nl/raakprob.htm

Het raakprobleem van Apollonius Overzicht Inversie Geschiedenis Meetkunde Overzicht Inleiding Overzicht deelproblemen Algemene oplossing 1. Inleiding In twee verloren gegane boeken, getiteld De Tactionibus (Over aanrakingen ), beschrijft Apollonius van Perga (~262 - ~190 vC) een beroemd geworden raakprobleem : Gegeven drie dingen, waarvan elk een punt, een lijn of een cirkel kan zijn. Bepaal een cirkel die door elk der gegeven punten gaat en die de gegeven lijnen of cirkels raakt. Zie figuur 3 Voor een reconstructie van de inhoud van de boeken van Apollonius zie Th. Heath, History of Greek Mathematics I , pg 182 ev. Ook eerdere wiskundigen hebben zich uiteraard met het raakprobleem bezig gehouden; oa. Francois Viete , ook wel Vieta (1540-1603, Frankrijk), heeft getracht het werk van Apollonius te reconstrueren (1600). C.F. Gauss Complete Works , vol. IV, pg 399 J. Gergonne Annales de Mathématiques , vol. IV (De oplossing van het probleem zoals Gergonne dat deed, wordt, met weglating van de vele details, weergegeven in paragraaf 3 J. Petersen

78. Nicomachus Of Gerasa (fl.c. 100 AD) Library Of Congress Translated by Sir Thomas L. Heath On conic sections, by apolloniusof perga. Works. 1955. apollonius, of perga. Keonika. English. 1955. http://www.mala.bc.ca/~mcneil/cit/citlcnico.htm

Nicomachus of Gerasa (fl.c. 100 A.D.) : Library of Congress Citations The Little Search Engine that Could Down to Name Citations LC Online Catalog Amazon Search Book Citations [6 Records] Author: Nicomachus, of Gerasa. Uniform Title: Introductio arithmetica. English Title: Introduction to arithmetic. Translated into English by Martin Luther D'Ooge, with studies in Greek arithmetic by Frank Egleston Robbins and Louis Charles Karpinski. New York, Macmillan, 1926. Published: [New York, Johnson Reprint Corp., 1972] Description: ix, 318 p. illus. 23 cm. LC Call No.: QA31 .N553 1972 Dewey No.: 513 Notes: Original ed. issued as v. 16 of University of Michigan studies. Humanistic series. Bibliography: p. 311-312. Subjects: Mathematics, Greek. Arithmetic Early works to 1900. Series Entry: University of Michigan studies. Humanistic series ; v. 16. Control No.: 73039141 //r934 Author: Nicomachus, of Gerasa. Uniform Title: Introductio arithmetica. French Title: Introduction arithmbetique / Nicomaque de Gberase ; introd., traduction, notes et index par Janine Bertier. Published: Paris : J. Vrin, 1978. Description: 254 p. ; 26 cm. Series: Histoire des doctrines de l'antiquitbe classique ; 2 LC Call No.: QA31 .N554 Dewey No.: 513 ISBN: 75.00F Notes: Translation of Introductio arithmetica. Bibliography: p. [227]-232. Includes index. Subjects: Mathematics, Greek. Arithmetic Early works to 1900. Other authors: Bertier, Janine. Control No.: 79338551 //r933

79. Appolonius De Perga Translate this page apollonius De perga. grec, Perge -262 / Alexandrie -180 env. On doità ce mathématicien et astronome grec un traité complet et http://www.reunion.iufm.fr/recherche/irem/histoire/appolonius_de_perga.htm

Accueil Histoire des mathématiques Philosophie des sciences Axiomatiques ... Informations - Contacts APOLLONIUS De Perga grec, Perge -262 / Alexandrie -180 env. On doit à ce mathématicien et astronome grec un traité complet et de très beaux résultats sur les sections coniques (intersection d'un plan et d'un cône) lors de travaux probablement liés à la recherche d'une courbe auxiliaire dans la résolution du problème de la duplication du cube, déjà étudié par Mé n echme. Les coniques en tant que courbes algébriques - l'appellation est de Leibniz - ne furent introduites qu'au XVII ème s. avec Wallis et Descartes. Apollonius vient étudier à Alexandrie sous la direction du successeur d'E u clide. Il complète ses connaissances à Pergame, attiré par la nouvelle université et la bibliothèque de renommée mondiale. Il retourne vivre à Alexandrie qu'il ne quitte plus. Son traité monumental sur les sections coniques tient en huit volumes. Les quatre premiers nous sont parvenus en grec, les trois suivants grâce à une traduction arabe et le dernier est perdu. Avant lui, on définit les coniques par l'intersection d'un cône avec un plan perpendiculaire à une génératrice, ce qui donne, suivant que l'angle du sommet est égal, inférieur ou supérieur à un droit, une parabole, une ellipse ou une hyperbole. Apollonius, le premier, obtient toutes les coniques avec un unique cône, en faisant varier la direction du plan, et, comme il considère des cônes doubles, il obtient deux branches pour les hyperboles. Il remarque une relation simple entre la projection d'un point sur un axe de symétrie et la distance à un sommet, ce qui revient à donner une équation cartésienne de la conique.

80. Re: [HM] Apollonius' Conics By Antreas P. Hatzipolakis Title apollonius Saxonicus die Restitution eines verlorenen Werkes desapollonius von perga durch Joachim Jungius, Woldeck Weland und Johannes Mu http://mathforum.org/epigone/historia_matematica/swexhomimp/v01540B06630BC49A165

Re: [HM] Apollonius' Conics by Antreas P. Hatzipolakis reply to this message post a message on a new topic Back to messages on this topic Back to Historia-Matematica Discussion Group Subject: Re: [HM] Apollonius' Conics Author: xpolakis@otenet.gr Date: The Math Forum

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