81. Conics Remarks. If the conic is singular this result is Pappus's theorem (namedafter pappus of alexandria (about 300 AD). See Exercises 8 Question 5. http://www.gap-system.org/~john/geometry/Lectures/L24.html

82. NIKAIEÔN COINS Obverse Type Within A Circle, The Laureate Bust about 240 in (possibly) Nicaea (Iznik), Bithynia (Turkey) Died about 300 Sporustaught pappus of alexandria and we know of him only through Pappus's writings. http://www.angelfire.com/ar/atay/NICAEA/MathCoin.html

NIKAIEÔN COINS Obverse Type: Within a circle, the laureate bust of Caracalla, facing right. A countermark with an image of Victoria (Victory) appears in the lower left field. Obverse Legend: A[UT] K M AURÊLIOS ANTÔNINOS AUG (around) Reverse Type: Within a dotted circle sits the emperor. He holds a prize crown in his right hand, and a jug sits on the ground in front of him. Reverse Legend: AGÔN (on the side of the throne); SEOUÊREIA PHILADELPHEIA (around); NIKAIEÔN (in exergue) Obverse Type: Within a dotted circle, the laureate bust of Antoninus Pius, bearded, draped and cuirassed, facing right. Obverse Legend: AUT KAISAR TAIA* aDR ANTÔNIN (around) Reverse Type: Within a dotted circle stands the nude figure of Herakles, leaning on club, in 3/4-view to the right. He holds his hand on his right hip. Reverse Legend: TON KTISTÊ ligature N NIKAIEIS (around) MATHEMATICIANS BORN IN NICAEA Hipparchus Born: 180 BC in Nicaea (Iznik), Bithynia (Turkey) Died: 125 BC in Rhodes, Greece Little is known of Hipparchus's life, but he is known to have worked in Nicaea, Rhodes and Alexandria. worked on trigonometry. He introduced the division of a circle into 360 degrees into Greece and produced a table of chords, an early example of trig tables. He also gave methods for solving spherical triangles and advocated the use of latitude and longitude for position on the Earth. Hipparchus calculated the length of the year to within 6.5 minutes and discovered the precession of the equinoxes. Hipparchus's value of 46" for the annual precession is good compared with the modern value of 50.26" and much better than the figure of 36" the Ptolemy was to obtain nearly 300 years later. His star catalog, containing about 850 stars, lists magnitude with a six point scale similar to that used today. His star catalogue, completed in 129 BC, was used by Ptolemy and its quality was such that it was even used by Halley.

83. History Of Astronomy: Roughly Sorted Links - Biographies (1) Julius) Oberth, Hermann (Julius) Olbers, Wilhelm Oort, Jan Hendrik Öpik, ErnestJulius Oughtred, William Overweg, Adolf pappus of alexandria Paracelsus Pascal http://www.astro.uni-bonn.de/~pbrosche/unsorted/rough_bio_01.html

History of Astronomy Unsorted and roughly sorted links Roughly sorted links - Biographies (1) Please note that the links were found some time ago and may be outdated meanwhile. This list is not a permanent one. Any link may be moved or deleted without special announcement, and also this file may be deleted. Alexander Friedmann Jahrbuch fuer die Fortschritte der Mathematik Dirk Frimout (in German) Dirk Frimout (in French) ... ? Raleigh, Sir Walter navigation Ramsden, Jesse Reber, Grote Regiomontanus Reichenbach, Georg von ... Wolfgang R. Dick . Created: 20 Aug 2001. Latest update: 20 Feb 2002

84. Heron it is reasonable to deduce that he taught at the Museum in alexandria. pappus describesthe contribution of Heron in Book VIII of his Mathematical Collection. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Heron.html

85. TEOREMA DE PAPPUS El teorema de pappus fou demostrat per primera vegada per pappus de alexandria, alvoltant de l´any 300 aC Un enunciat d´aquest teorema pot ser el següent http://www.xtec.es/~jdomen28/teoremadepappus.htm

TEOREMA DE PAPPUS El teorema de Pappus fou demostrat per primera vegada per Pappus de Alexandria, al voltant de l´any 300 a.C. Un enunciat d´aquest teorema pot ser el següent : Si els punts A B i C estan en una recta, els punts A B ' i C ' en una altra i les rectes AB BC ' i CA tallen a les rectes BA CB ' i AC ', aleshores els punts d´intersecció estan alineats. Aquest teorema té unes característiques completament projectives, ja que no parla de distàncies ni d´angles, ni tampoc de cap ordre de punts respecte d´altres punts, només de punts que estan en rectes (incidència). JAUME DOMENECH LARRAZ PROFESSOR DE DIBUIX/VISUAL I PLÀSTICA/TIC info@dibuixtecnic.com

86. Apollonius Of Perga Library Of Congress Citations Geometry, Plane Early works to 1800. Other authors pappus, of alexandria. Otherauthors pappus, of alexandria. Eutocius, of Ascalon. http://www.malaspina.edu/~mcneil/cit/citlcapollonius.htm

Apollonius of Perga : Library of Congress Citations The Little Search Engine that Could Down to Name Citations LC Online Catalog Amazon Search Book Citations (12 Records) Author: Apollonius, of Perga. Uniform Title: Keonika. French. Title: Les coniques d'Apollonius de Perge; 6uvres traduites pour la premiaere fois du grec en franpcais avec une introduction et des notes par Paul ver Eecke. Published: Bruges, Desclbee, de Brouwer et cie, 1923. Description: L p., 1 l., 656 p. front., diagrs. 28 cm. LC Call No.: QA31 .A6 1923 Notes: "Ouvrage publibe sous les auspices de la Fondation universitaire de Belgique." Subjects: Mathematics, Greek. Conic sections. Other authors: Ver Eecke, Paul, 1867- tr. Control No.: 24025507 //r842 Author: Apollonius, of Perga. Uniform Title: Keonika. English Title: Conics. Book I- Translated into English from the Greek by R. Catesby Taliaferro ... Published: [Annapolis, Md.] c1939- Description: v. diagrs. 28 cm. Series: The classics of the St. John's program LC Call No.: QA31 .A5 1939 Dewey No.: 513.22 Notes: At head of title: Apollonius of Perga. Mimeographed. Subjects: Mathematics, Greek. Conic sections. Other authors: Taliaferro, R. Catesby (Robert Catesby), 1907- tr. Control No.: 40008976 //r90 Author: Apollonius, of Perga. Title: Treatise on conic sections [microform] / edited in modern notation, with introductions including an essay on the earlier history of the subject by T.L. Heath. Published: Cambridge : University Press, 1896. Description: clxx, 254 p. : ill. ; 23 cm. LC Call No.: Microfilm 84/6746 (Q) Notes: Contents: Introduction: pt. I. The earlier history of conic sections among the Greeks. pt. II. Introduction to the "Conics" of Apollonius The "Conics" of Apollonius. Call number of original: QA31.A5 1896. Master microform held by: DLC. Microfilm. Washington, D.C. : Library of Congress Photoduplication Service, 1984. 1 microfilm reel ; 35 mm. Control No.: 84196497 //r85

87. Pappus. The Columbia Encyclopedia, Sixth Edition. 2001 2001. pappus. (p p´ s) (KEY) , fl. c.300, Greek mathematician of alexandria. pappus’other works include a commentary on Ptolemy’s Almagest. 1. http://www.bartleby.com/65/pa/Pappus.html

Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia World Factbook Columbia Gazetteer American Heritage Coll. Dictionary Roget's Thesauri Roget's II: Thesaurus Roget's Int'l Thesaurus Quotations Bartlett's Quotations Columbia Quotations Simpson's Quotations English Usage Modern Usage American English Fowler's King's English Strunk's Style Mencken's Language Cambridge History The King James Bible Oxford Shakespeare Gray's Anatomy Farmer's Cookbook Post's Etiquette Bulfinch's Mythology Frazer's Golden Bough All Verse Anthologies Dickinson, E. Eliot, T.S. Frost, R. Hopkins, G.M. Keats, J. Lawrence, D.H. Masters, E.L. Sandburg, C. Sassoon, S. Whitman, W. Wordsworth, W. Yeats, W.B. All Nonfiction Harvard Classics American Essays Einstein's Relativity Grant, U.S. Roosevelt, T. Wells's History Presidential Inaugurals All Fiction Shelf of Fiction Ghost Stories Short Stories Shaw, G.B. Stein, G. Stevenson, R.L. Wells, H.G. Reference Columbia Encyclopedia PREVIOUS NEXT ... BIBLIOGRAPHIC RECORD The Columbia Encyclopedia, Sixth Edition. Pappus (p s) ( KEY ) , fl. c.300, Greek mathematician of Alexandria. He recorded and enlarged on the results of his predecessors, including Euclid and Apollonius of Perga, in his

88. Biography.com Papp, Joe, 1921 1991. Papp, Joseph (b. Papirofsky), 1921 1991. pappus ofAlexandria, c. 350 . Paracelsus, 1493 1541. Parbo, Sir Arvi Hillar, 1926. http://search.biography.com/bio_browse.pl?letter=P&num=100

89. ¼¼°èÀÇ ¼öÇÐÀÚ ? Jean Victor Poncelet. Sir Ronald Aylmer Fisher. ? Pappusof alexandria. Luca Pacioli. Hardy, Godfrey Harold. http://math.dongeui.ac.kr/main/mathman/mathman_main.htm

KAIST ¼öÇаú TEL : (051) 890-1470 FAX : (051) 890-1470 Gauss, Karl Friedrich Goel, Kurt Galois, Evariste Gregory, James ... Christiaan Huygens

90. Encyclopædia Britannica Encyclopædia Britannica, http://www.britannica.com/eb/topic?eu=119063&type=13

91. ¤Hª« The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set. http://www.edp.ust.hk/math/history/3/

ªð¦^¥D­¶ ¼Æ¾Ç¥v¦~ªí ¤¤¥~¼Æ¾Ç¥v ¤Hª« »y¿ý ¾Ç¬ì¥v ¦WD»P²q·Q ÄvÁÉ»P¼ú¶µ µØ»y¤åÄm¯Á¤Þ ¾¥¤l ´f¬I ±i»a ¼BÝõ ... §JµÜ¦] ¡A¢Û¡D¢Û¡D¡]Kline, Morris¡^

92. Matematika - Geometrija U Grckoj The summary for this Macedonian page contains characters that cannot be correctly displayed in this language/character set. http://rastko.8m.net/antika/grckaost.html

Free Web site hosting - Freeservers.com Hippocrates Zeno Eratosthenes Appolonius Hipparchus Heron Dophantus Menelaus Ptolomey Pappus Êëàñè÷íî, èëè "Çëàòíî Äîáà" ð÷êå ¼å ïåðèîä 500-323 ã. ï.í.å. Ïåðèîä èçìåó IV è II âåêà ï.í.å. ïîçíàò ¼å êàî Õåëåíèñòè÷êî Äîáà. (Hippocrates of Chios, fl. 440 BC) ãð÷êè ìàòåìàòè÷àð çàáåëåæåí ïî èçðà÷óíàâàœèìà ôèãóðà êî¼å íàçèâàìî ïîëóìåñåöè. Ïðåòïîñòàâšà ñå äà ¼å äîïðèíåî è ðåøàâàœó ïðîáëåìà óäâîñòðó÷àâàœà êîöêå. (Zeno of Elea, 5th century BC) ¼å àóòîð ÷åòèðè ïàðàäîêñà êî¼è óêàçó¼ó íà òåøêîžå óâåðåœà ó îïøòó áåñêîíà÷íó äåšèâîñò. Íà¼ïîçíàòè¼à ¼å î òðöè áðçîíîãîã Àõèëà è ñïîðå êîðœà÷å ó êî¼î¼ êîðœà÷à èìà ïî÷åòíó ïðåäíîñò. Äà áè ïðåñòèãàî êîðœà÷ó Àõèë ïðâî ìîðà äîžè äî êîðœà÷èíå ñòàðòíå ïîçèöè¼å. Àëè äî òàäà žå êîðœà÷à èçìàžè íàïðåä ó íîâó ïîçèöè¼ó. Äîê Àõèë äîñòèãíå îâó, êîðœà÷à žå ñå îïåò ïîìåðèòè íàïðåä. Ïàðàäîêñ ¼å ó òîìå äà Àõèë íèêàä íå ïðåñòèæå êîðœà÷ó, ìà êàêî áðçî òð÷àî. (Eratosthenes of Cyrene, c. 275-194 BC) áèî ¼å ãð÷êè àñòðîíîì è ìàòåìàòè÷àð êî¼è ¼å èçóìèî íà÷èí íàëàæåœà ïðîñòèõ áðî¼åâà ïîçíàò êàî Åðàòîñòåíîâî ñèòî. Òàêîå ¼å çàïàìžåí ïî ãåíè¼àëíîì îäðåèâàœó îáèìà Çåìšå. Ðà÷óí ¼å çàñíîâàî íà çàïàæàœó äà ó ïîäíå ó Syene-ó (ñàäà Aswan) Ñóíöå ñòî¼è âåðòèêàëíî èçíàä, äîê ó èñòî âðåìå ó Àëåêñàíäðè¼è ñóí÷åâå çðàêå ÷èíå óãàî îä 7,2° ñà âåðòèêàëîì. Ïîìîžó òðà¼àœà ïóòîâàœà íà êàìèëè ¼å ïðîöåíèî óäàšåíîñò èçìåó Ñåíå è Àëåêñàíäðè¼å è íà îñíîâó òîãà èçðà÷óíàî îáèì Çåìšå. Íåèçâåñíî ¼å êîëèêî ¼å òà÷àí œåãîâ ðåçóëòàò ¼åð íå ïîçíà¼åìî âåëè÷èíà ¼åäèíèöå êî¼ó ¼å óïîòðåáèî ( 1 ñòàäè¼óì). Åðàòîñòåí ¼å òàêîå èçìåðèî óãàî íàãèáà åêëèïòèêå.

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