81. Perga - Prolegomena Mathematica From apollonius of perga to Late Neoplatonism With an apollonius of perga Treatise on conic sections with introductions http://perga.idoneos.com/

Homepage Idoneos.com Shop Directory Top RSS news Homepage : Perga - Perga - See Also perga general history mathematics ... kōnika Links perga Bible Dictionary Perga earthy ), a city of Pamphylia, ( acts 13:13) situated on theriver Cestius, at a distance of 60 stadia (7 1/2 miles ) fromits mouth, and celebrated in antiquity for the worship ofArtemis ( diana Web idoneos.com The Thirteen Books of Euclid's Elements, Archimedes, Appollonius of Perga, Nicomachus (Great books of the Western World #11) Published: 1955 Authors: Euclid, Archimedes, and Appollonius ... marketplace, click here... Our price: Collectible price: Buy one from zShops for: Sales rank: 827986 marketplace information. complete product info, click here... Apollonius of Perga's Conica: Text, Context, Subtext (Mnemosyne, Bibliotheca Classica Batava Supplementum) Published: 01 August, 2001 ... marketplace, click here... Our price: Buy one from zShops for: Sales rank: 2132013 marketplace information. complete product info, click here... Prolegomena Mathematica: From Apollonius of Perga to Late Neoplatonism : With an Appendix on Pappus and the History of Platonism (Philosophia Antiqua) Published: 01 September, 1998 ... marketplace, click here... Our price: Buy one from zShops for: Sales rank: 3208326 marketplace information.

82. The Great Men Of Croatian Science He placed himself alongside Apollonius and Viete by saying and thus of Gaul will need the Croatian Apollonius to revive apollonius of perga who was http://pubwww.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

83. The Modern Age - 17th Century On Contacts) by the Greek mathematician apollonius of perga and studied Gaul will need the Croatian Apollonius to revive apollonius of perga who was http://pubwww.srce.hr/zuh/English/nv17_e.htm

The Seventeenth Century Complete information is available only in Croatian Primas of Hungary, then went on to study philosophy and law at Padua. In 1575 he became a member of the Croatian fraternity of Saint Jerome in Rome. After his appointment as secretary to king Rudolph II in 1579, Vranèiæ began a more systematic study of the natural and technical sciences. From 1594 to 1598 he lived in Dalmatia and Italy, working in comparative lexicology and publishing his famous dictionary in five languages (Venice 1595). In 1598 Rudolph II made him a Bishop and royal cousellor for Hungary and Transylvania. He held this post up to 1605, when he left the Court, and entered the order of St Paul (the "Barnabites") in Rome. Returning to Rome, he devoted himself to experimental work with machine construction and architectural problems. After the Barnabite Giovanni Ambrogio Mazente introduced him to Leonardo's technical drawings he was inspired to write his most significant work, Machinae Novae II. Marko Antun de Dominis, Late Renaissance Physicist

84. Annotated Bibliography apollonius of perga, Treatise on Conic Sections , TL Heath, ed., New York Dover, apollonius of perga, On Cutting Off a Ratio,, EM Macierowski,trans; http://www.math.cornell.edu/~dwh/books/eg00/00EG-biblio/

Annotated Bibliography This bibliography consists of books (and other items) that are referenced in this book, books used in the writing this book, or books that I have read that I think readers may be interested in. There is a more complete (and frequently updated) bibliography with more than 300 listings on the web at http://www.math.cornell.edu/~dwh/biblio. The section names below coorespond to a subset of the section names in the bibliography on the web. The annotations in quotes are taken from the introductory matter, cover, or dust jacket of the book being annotated. AT. Ancient Texts al'Khowarizmi, Algebra This is the world's first algebra text. An English translation is contained in : Karpinski, L.C., ed., Robert of Chester's Latin Translation of Al'Khowarizmi's Algebra, New York: Macmillan, 1915. Apollonius of Perga, Treatise on Conic Sections , T.L. Heath, ed., New York: Dover, 1961. This is the standard work on conic sections from the Greek world. Apollonius of Perga, On Cutting Off a Ratio, , E.M. Macierowski,trans; R.H. Schmidt, ed., Fairfield: The Golden Hind Press, 1987.

85. From Euclid To Newton apollonius of perga composed a systematic treatise on conic sections It iswritten by three men Eculid the Elementarist, apollonius of perga, http://www.brown.edu/Facilities/University_Library/exhibits/math/nofr.html

From Euclid to Newton: An Exhibition in Honor of the 1999 Conference of the Mathematical Association of America Math Exhibit Home Exhibits Home Euclid (ca. 326-265 BC) Archimedes (ca. 287-212 BC) Apollonius of Perga (ca. 260-200 BC) Nichomachus of Gerasa (ca. 100) Claudius Ptolemy (ca. 85-165) Diophantus of Alexandria (ca. 200-284) Pappus of Alexandria (ca. 300-350) Proclus (ca. 410-485) Boethius (ca. 480-524) Thomas Bradwardine (ca. 1290-1349) Girolamo Cardano Robert Recorde Johann MŸller of Kšnigsberg called Regiomontanus Franois Vite John Napier Henry Briggs Adriaan Vlacq ... Bonaventura Cavalieri (ca. 1598-1647) Christiaan Huygens RenŽ Descartes Gottfried Wilhem Leibniz Sir Isaac Newton ... Guillaume Franois Antoine l'Hospital, Marquis de Sainte-Mesme TOP Euclid Brown University Library possess a copy of each sixteenth-century translation of Euclid's Elements of Geometry into a modern language. These vernacular editions, grouped around the first Latin edition of 1482, are displayed in chronological sequence, from 1533 (Greek) to 1594 (Arabic). All copies are opened at Book I, proposition 47, "Pythagoras' Theorem," which asserts: "In right-angled triangles the square of the side opposite the right angle is equal to the sum of the squares of the sides containing the right angle." Most of the translations provide proof of this equation (a

86. Gudrun Wolfschmidt A Historian Looks At Astronomy In The Classroom. famous mathematicians like apollonius of perga were often among the makers . promoted the discovery of the conic sections (apollonius of perga).4 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.

87. Apollonius Unguru Sabetai, cohn institute apollonius of perga s Conica Text, Context, Subtext by Michael N.Fried apollonius of perga s Conica Selected Texts in Hellenistic Mathematics http://turnbull.mcs.st-and.ac.uk/~history/Mathematicians/Apollonius.html

Apollonius of Perga Born: about 262 BC in Perga, Pamphylia, Greek Ionia (now Murtina, Antalya, Turkey) Died: about 190 BC in Alexandria, Egypt Click the picture above to see a larger version Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing 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, 2 nd century BC, a Greek sculptor; Apollonius the Athenian, 1 st century BC, a sculptor; Apollonius of Tyana, 1 st century AD, a member of the society founded by Pythagoras; Apollonius Dyscolus, 2

88. CONIC SECTION - LoveToKnow Article On CONIC SECTION all we have is chiefly to be found in the works of apollonius of perga. But the greatest Greek writer on the conic sections was apollonius of perga, http://5.1911encyclopedia.org/C/CO/CONIC_SECTION.htm

CONIC SECTION CONIC SECTION The definitions given above reflect the intimate association of these curves, but it frequently happens that a particular conic is defined by some special property (as the ellipse, which is the locus of a point such that the sum of its distances from two~ fixed points is constant); such definitions and other special properties are treated in the articles ELLIPSE, HYPERBOLA and PARABOLA. In this article we shall consider the historical development of the geometry of conics, and refer the reader to the article GEOMETRY: Analytical and Projective, for the special methods of investigation. But the greatest Greek writer on the conic sections was Apollonius of Perga, and it is to his Conic Sections that we are indebted for a review of the early history of this subject. Of the eight books which made up his original treatise, only seven are certainly known, the first fouI in the original Greek, the next three are found in Arabic translations, and the eighth was restored by Edmund Halley in 1710 from certain introductory lemmas of Pappus. The first four books, of which the first three are dedicated to Eudemus, a pupil of Aristotle and author of the original Eudemian Summary, contain little that is original, and are principally based on the earlier works of Menaechmus, Aristaeus (probably a senior contemporary of Euclid, flourishing about a century later than Menaechmus),Euclid and Archimedes. The remaining books are strikingly original and are to~be regarded as embracing Apolloniuss own researches.

89. Greek For Euclid: Contents 284 BC), apollonius of perga (fl. 220 BC), and Ptolemy (fl. 150) advanced geometryand astronomy greatly. Geometry was still actively pursued in the time of 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.

90. Apollonius Of Perga's Conica Text, Context, Subtext :: Brill :: Editeurs & Colle http://librarius.fr/boutique_librarius/product.php?productid=12414

91. Simon Finch Author apollonius of perga. More Details.. Title Locorum planorum libri II.Restituti a Roberto Simson. Author apollonius of perga. More Details.. http://www.simonfinch.com/pages/alpharesults.php?selLetter=A

92. 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/

93. Apollonius Von Perga Translate this page Berühmte Mathematiker apollonius von perga. Apollonios von Perge apollonius.Geboren ungefähr 262 v.Chr. in perga, Pamphylia, Griechenland (nun http://www.mathematik.ch/mathematiker/apollonius.php

Home Geschichte Mathematiker Zitate ... Abhandlungen Archimedes 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.

94. Biografi: Apollonius apollonius ble født i perga, som var et kulturelt sentrum på denne tiden. Da hanvar ung, Her finner du en biografi på engelsk om apollonius av perga. http://www.matematikk.org/artikkel/vis.php?id=1048

95. Appolonius De Perga Translate this page apollonius De perga. grec, Perge -262 / Alexandrie -180 env. On doit à cemathématicien et astronome grec un traité complet et de très beaux résultats sur http://www.reunion.iufm.fr/recherche/irem/histoire/appolonius_de_perga.htm

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.

96. Kegelsneden Deze laatste, apollonius van perga (~262 ~190 vC) studeerde in Alexandrië enging daarna 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).

97. Maths Title page of apollonius, of perga. Apollonii Pergæi de sectione rationis libriduo ex arabico msto. latine versi. Accedunt ejusdem de sectione spatii http://www.kcl.ac.uk/depsta/iss/library/speccoll/exhibitions/gsci/maths.html

Text only ISS: Information Services and Systems Services Information gateway ... Structure Case 5: Mathematics Exhibition curator: Hugh Cahill Diagram of the Archimedes Screw: Archimedes. Londini : excudebat Guil. Godbid, voeneunt apud Rob. Scott, 1675.[Rare Books Collection QA31.Ar1 B2] Archimedes. Londini : excudebat Guil. Godbid, voeneunt apud Rob. Scott, 1675. Rare Books Collection QA31.Ar1 B2 The mathematician and engineer Archimedes (ca.287-212BC) was one of the greatest minds of antiquity, making important discoveries in geometry, statics, hydrostatics and mechanics. For example, in The measurement of the circle he determined the value of Pi, with great accuracy to be between 223/71 and 220/70 and in The sand reckoner On plane equilibriums , the first extant work on statics, Archimedes discovered fundamental theorems concerning the centre of gravity of figures, such as the parallelogram, the triangle, the trapezium and a segment of a parabola. In On floating bodies he laid down the basic principles of hydrostatics. In this treatise, he determines the positions that various solids will assume when floating in a fluid, according to their shape and the variation in their specific gravities, and also establishes a number of general principles, including what has become known as Archimedes' principle. However, Archimedes was also a practical engineer who constructed war machines and other devices for his patron. He is said to have invented a system of compound pulleys capable of lifting entire ships and their contents in order to demonstrate to King Hieron the principle of mechanical advantage. He is also said to have designed the water pump that we now know as the Archimedes Screw in order to raise water from the hold of another King Hieron's ships.

98. Apollonius Von Perga Translate this page apollonius perga oder Perge (c. 262 BC - c. 190 BC) war von einer griechischen. http://www.yotor.com/wiki/de/ap/Apollonius von Perga.htm

Yotor Facts Yotor faits Yotor Tatsachen Yotor hechos Apollonius von Perga Apollonius Perga oder Perge (c. 262 BC - c. 190 BC) war von einer griechischen Geometers und von des Astronomen, gemerkt für seine Schreiben auf Kegelschnitten. Es war Apollonius, das den Ellipse, die Parabel und die Hyperbel die Namen gab, durch die wir sie kennen. Von die Hypothesen Exzenterbahnen oder gleichwertig, deferent und Epicycles, zu erklären die offensichtliche Bewegung von die Planeten und die unterschiedliche Geschwindigkeit des Mondes, werden auch ihm zugeschrieben. Nur zwei seiner Arbeiten überleben: Ausschnitt- ein Verhältnis (zwei Bücher konserviert in einer arabischen Übersetzung) und das Conics (vier Bücher konserviert in vom ursprünglichen Griechen, in von drei auf Arabisch und in von einem verloren). Seine erfinderische Methodenlehre und Terminologie, besonders auf dem Gebiet von conics, beeinflußten viele neuere Gelehrte einschließlich Ptolemäus, Isaac Newton und René Descartes. Auch sehen Theorem Descartes' English version: Apollonius of Perga Next: Pentaquark Up This article is licensed under the GNU Free Documentation License . It uses material from the Wikipedia article "Apollonius of Perga" Kinoprogramm Tattoo Information Resource Hosting ... Yotor.com

99. Apollonius Of Perga (ca. 262-ca. 190 BC) -- From Eric Weisstein's World Of Scien From AOUM AOUM. Newsgroups sci.math Subject Re Problems from apollonius from perga give us the following beutifull construction to 3. * *A*********************************o***************M http://www.treasure-troves.com/bios/Apollonius.html

Branch of Science Astronomers Branch of Science Mathematicians ... Greek Apollonius of Perga (ca. 262-ca. 190 BC) Greek geometer from the southern coast of Turkey who postulated that the planets revolved around the Sun and the Sun revolves around the Earth Apollonius is believed to be the inventor of the system of epicycles and eccentric circles, used extensively by Hipparchus of Nicaea. He also wrote a monumental treatise on conic sections entitled On Conics. In this treatise, the term ellipse was first used. Additional biographies: MacTutor (St. Andrews) Bonn Greek and Roman Science and Technology References Dunham, W. Journey Through Genius: The Great Theorems of Mathematics. New York: Wiley, pp. 117-118, 1990.

100. Encyclopedia Of Astronomy And Astrophysics » Apollonius [Apollonios] Of Perga ( apollonius Apollonios of perga (200–100 BC). DOI 10.1888/0333750888/3432;Published November 2000. Icon Full text (PDF, 20K) http://eaa.iop.org/index.cfm?action=summary&doc=eaa/3432@eaa-xml

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