41. 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)

42. 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.cs.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

43. Re: 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/geometry-college/senchehbrang/v01540b00b60b64c11dc4

Re: 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 geometry-college Subject: Re: Apollonius's Conics Author: xpolakis@otenet.gr Date: The Math Forum

44. Sir Thomas Little Heath Just click on the books below or their links to go to Amazon's relevantpages. apollonius of perga Sir Thomas Little Heath Published 1896. http://dspace.dial.pipex.com/ashtead.parish/people/tlh.htm

Sir Thomas Little Heath Sir Thomas Little Heath , 5 Oct 1861, Barnetby le Wold, Lincoln, England - 16 March 1940, Ashtead Sir Thomas Little Heath , short article from School of Mathematics and Statistics University of St Andrews, Scotland Civil servant and authority on ancient mathematics; educated at Clifton and Trinity College, Cambridge; first classes, classical tripos, 1881-3; twelfth wrangler, 1882; passed first into Civil Service, 1884; entered Treasury; assistant secretary, 1907; joint permanent secretary, controlling administrative side, 1913; comptroller-general, National Debt Office, 1919-26; KCB, 1909; KCVO, 1916; a leading authority on Greek mathematics; made accessible in modern notation works of Diophantus Apollonius of Perga Archimedes (1897), and Euclid (1908); other publications include A History of Greek Mathematics (2 vols., 1921) and Greek Astronomy (1932); FRS, 1912; FBA, 1932. Source: Concise Dictionary of National Biography English mathematical historian who specialized in ancient Greece. His History of Greek Mathematics 1921 is regarded as the standard work on the subject in the English language. KCB 1909. Heath was born in Lincolnshire, studied at Cambridge and joined the civil service. He rose through the ranks in the Treasury Office; in 1913 he was appointed joint permanent secretary to the Treasury and auditor of the Civil List, and he was comptroller general and secretary to the Commissioners for the Reduction of the National Debt 1919-26. Between 1885 and 1912, Heath edited the works of Greek mathematicians

45. A/AP A PRIORI APACHE APALACHEE APALACHICOLA APAMEA APARRI APATITE OF CARYSTUS APOLLODORUS OF DAMASCUS APOLLONIA APOLLONIUS (THE EFFEMINATE) APOLLONIUS(THE SURLY OR CRABBED) APOLLONIUS MOLON apollonius of perga APOLLONIUS OF http://1911encyclopedia.org/A/AP/

A/AP A PRIORI APACHE APALACHEE APALACHICOLA ... APYREXIA

46. DownloadEssays.com - Essays And Research Papers Available Right Now! apollonius of perga.htm html title apollonius of perga /title pre Apolloniusof Perga Apollonius was a great mathematician, known by his contempories as http://www.downloadessays.com/cgi-bin/nav.cgi?start=50&cat=Biographies

47. Ulearn Today - Magazine apollonius of perga (c. 262 190 BC). Apollonius, along with mathematics.Apollonius was born in Perga (now in Antalya, Turkey). As a http://www.ulearntoday.com/magazine/physics_article1.jsp?FILE=apollonius

48. 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,

49. Unguru Sabetai, Cohn Institute Books 1. apollonius of perga's Conica Text, Context, Subtext by Michael N.FriedSabetai Unguru 2. Witelonis Perspectivae Liber Primus Book I of Vitelo's http://www.tau.ac.il/humanities/cohn/staff/unguru-sabetai.html

Unguru Sabetai, Cohn Institute Short Curriculum Vitae (highlights): Sabetai Unguru was born in Podul-Ilonaiei, Romania on January 1, 1931, and studied philosophy, philology, history and mathematics at the University "Al. I. Cusa" in Jassy. In 1961 he emigrated to Israel, and in 1966 went to the United States where he recieved, in 1970, his Ph.D. in history of science from the University of Wisconsin in Madison. Between 1970-1982 he was an Assistant and Associate Professor in the Department of History at the University of Oklahoma. Coming back to Israel, in 1983 he was appointed Associated Professor at the newly created Institute for the History and Philosophy of Science and Ideas at Tel-Aviv University. Since 1987 he is full Professor at the renamed Cohn Institute for the History and Philosophy of Science and Ideas. Since 1991 he serves as Director of the Institute. He is married to Yocheved Unguru and has two children. Major publications (books and major articles): Books: 1. "Apollonius of Perga's Conica Text, Context, Subtext" by

50. Wilson Stothers' Inversive Geometry And CabriJava Pages apollonius of perga is best remembered for his work on conics (he is responsiblefor the names parabola, ellipse and hyperbola), but he also investigated other http://www.maths.gla.ac.uk/~wws/cabripages/inversive/newapollonius.html

Apollonian Families Apollonius of Perga is best remembered for his work on conics (he is responsible for the names parabola, ellipse and hyperbola), but he also investigated other families of curves. One such family has particular relevance to inversive geometry. Definition If A and B are points in the euclidean plane, and k is a positive constant, then the apollonian curve A k (A,B) is defined as the locus and A (A,B) as the apollonian family A k If we choose k = 1, then we get the perpendicular bisector of AB, i.e. a line. Indeed, for any line L , we can choose A not on L and B the reflection of A in L so L is an apollonian curve. The sketch on the right shows some other possibilities. Observe that the members of an apollonian family are disjoint, for if a point P lies on A k (A,B) and on A k' (A,B), then we have PA = k.PB = k'.PB so k = k'. Apollonius's Theorem A k (A,B) is a line if k is 1, and a circle if k is not 1. If A k (A,B) is the circle C with centre C and radius r, then A, B and C are collinear, with A and B on the same side of C, and CA.CB = r

51. Wilson Stothers' Inversive Geometry And CabriJava Pages The object of these pages is to introduce inversive geometry. Many ofthe results and ideas are Greek, largely due to apollonius of perga http://www.maths.gla.ac.uk/~wws/cabripages/inversive/inversive0.html

The object of these pages is to introduce inversive geometry Many of the results and ideas are Greek, largely due to Apollonius of Perga We shall approach from the Klein viewpoint, that is to say using a group of transformations of a set of points. To motivate the definitions of the set and its transformations, we begin by looking at a classical greek Theorem (Apollonius's Theorem). Whenever it is useful, we give CabriJava (interactive) illustrations. For example, the CabriJava pane on the right shows three touching red circles. The blue and green circles each touch all of the red circles. By dragging A or B, you can change the red circles, but it is always possible to draw the blue and green circles. Why? That's what inversive geometry is about. You can find an inversive proof here table of contents Apollonian Families The basic properties of inversion The extended plane and i-lines The Equal Angles Theorem ... more on orthogonal i-lines related pages the inversive group the fundamental theorem an inversive invariant appendices Stereographic Projection an alternative approach to the point at infinity and i-lines Very simple cabri macros main geometry page

52. 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

53. The Helenistic Period Of Greek Mathematics He also made other trigonometic estimates without trigonometry.ARCHIMEDES. apollonius of perga (ca 262 BC 190 BC). Apollonius http://www.math.tamu.edu/~don.allen/history/helnistc/helnistc.html

Next: About this document Aristarchus of Samos (ca. 310-230 BC) He was very knowledgeable in all sciences, especially astronomy and mathematics. He discovered an improved sundial, with a concave hemispherical circle. He was the first to formulate the Copernican hypotheses and is sometimes called the Ancient Copernican He countered the nonparallax objection by asserting that the stars to be so far distant that parallax was not measurable. Wrote On the Sizes and Distances of the Sun and Moon . In it he observed that when the moon is half full, the angle between the lines of sight to the sun and the moon is less than a right angle by 1/30 of a quadrant. From this he concluded that the distance from the earth to the sun is more than 18 but less than 20 times the distance from the earth to the moon. (Actual ). Without trigonometry he was aware of and used the fact that He also made other trigonometic estimates without trigonometry. ARCHIMEDES Apollonius of Perga (ca 262 BC - 190 BC) Apollonius was born in Perga in Pamphilia (now Turkey), but was possibly educated in Alexandria where he spent some time teaching. Very little is known of his life. He seems to have felt himself a rival of Archimedes. In any event he worked on similar problems. He was known as the ``great geometer" because of his work on conics.

54. Binghamton Univ. Libraries: Remote Storage Q And A Title The thirteen books of Euclid's elements ; The works of Archimedes, includingThe Methods ; On conic sections / by apollonius of perga ; Introduction to http://library.lib.binghamton.edu/webdocs/storage.html

BU Libraries Remote Storage What is the Remote Storage Facility? Where is the Remote Storage Facility? What Materials are Located in the Facility? How Do I Determine That Materials Are in Storage? ... What if I need to browse large quantities of paged materials? Rogers Warehouse Building (BU Libraries storage entrance at right) What is the Remote Storage Facility? Where is the Remote Storage Facility? The facility is located 10 miles from the Binghamton University campus in the Rogers Warehouse Building, Broome Corporate Parkway in Conklin, NY. Initial Shelving Installation at Storage Facility (click to enlarge Remote Storage Facility after the move (click to enlarge What Materials are Located in the Facility? All materials that have been moved have been carefully selected by the Libraries' bibliographers and are low-use, older materials. Pre-1980 journals from the 3d floor of Bartle Library and the Fine Arts Collections Older journals from the Science Library Infrequently used monographic sets from the Bartle and Science Libraries BU honors, masters, and PhD theses completed prior to 1994

55. 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

56. The Alexandria Effect knowledge. Eratosthenes, apollonius of perga, Archimedes, Euclid, andPtolemy are among the scholars that graced this Pierian place. http://www.uea.ac.uk/~j013/wipout/essays/1031sammartino.htm

The Alexandria Effect Ryan T. Sammartino The Library of Alexandria was the ultimate repository of human knowledge in the ancient world. It was the one central place to go for knowledge on any subject, from mathematics to astronomy to philosophy. Having such a central repository proved to be very beneficial for a very long time: if you needed to know anything, Alexandria was the place to go. The huge store of knowledge also served as a jumping off point for even more knowledge, and the library snowballed in this way towards an ever increasing richness and diversity of knowledge. Eratosthenes, Apollonius of Perga, Archimedes, Euclid, and Ptolemy are among the scholars that graced this Pierian place. Unfortunately, having most of all human knowledge in one central place turned out to be disastrous. In the fourth century CE, under the Christian Patriarch Cyril, the library was looted and torched. Seven centuries of human knowledge was lost in one fell swoop; much of the knowledge contained in the volumes at the Library would not be rediscovered for up to 1500 years later. At the beginning of the 21st century CE the beginnings of a new Library began to take shape. The Internet fast became a massive store of knowledge, personal musings, pornography, mundane business dealings, and a host of other documents, the collective writings of millions of people. Off-line, people began writing books and

57. Resources For Study And Research - Integral Liberal Arts - Apollonius Of Perga Saint Mary's College Library, Integral Liberal Arts. apollonius of perga.(fl. 250 BC 195 BC). Conic Sections c.220 bc Additional Texts http://gaelnet.stmarys-ca.edu/study/integral/docs/apollo/

Saint Mary's College Library Integral Liberal Arts Apollonius of Perga (fl. 250 B.C. - 195 B.C.) Conic Sections [c.220 b.c.] Additional Texts On Proportional Section [c. 220 b.c.] Integral Liberal Arts Gaelnet: WWW Resources Library Search ... Br. Richard Lemberg F.S.C. Integral Liberal Arts Librarian, Saint Mary's College Last revised: April, 2002

58. Prolegomena Mathematica: From Apollonius Of Perga To Late Neoplatonism: With An Prolegomena Mathematica From apollonius of perga to Late NeoplatonismWith an Appendix Buy Prolegomena Mathematica From http://www.computerhelpbooks.com/m/Mathematica/Prolegomena_Mathematica_From_Apol

All Products Books Pop Music Classical Music Videos Consumer Electronics Software Kitchen Search by keywords: Search: Auctions The Web Books Music Electronics Forums Hardware Jobs Software Toys Video Games Links Our Online Mall Our Other Sites How To Use This Site ... Privacy Statement Related Sites Digital Cameras Computer Printers Digital Cameras Digital Cameras ... Adapt, Inc. Mathematica Bookstore Prolegomena Mathematica: From Apollonius of Perga to Late Neoplatonism: With an Appendix... by Jaap Mansfeld Sales Rank - 996,309 Jaap Mansfeld MORE INFO by ALPHABETICAL 74 of 100 ITEMS Previous Next by CUSTOMER REVIEW 68 of 100 ITEMS Previous Next by SALES RANK 68 of 100 ITEMS Previous Next More Mathematica Items Related

59. Apollonius apollonius of perga. apollonius of perga studied in Alexandria and he then visitedPergamum where a university and library similar to Alexandria had been built. http://sfabel.tripod.com/mathematik/database/Apollonius.html

Apollonius of Perga Born: about 262 BC in Perga, Greek Ionia (now Turkey) Died: about 190 BC in Alexandria, Egypt Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page Apollonius was known as 'The Great Geometer'. His famous book Conics introduced the terms parabola, ellipse and hyperbola. Apollonius of Perga studied in Alexandria and he then visited Pergamum where a university and library similar to Alexandria had been built. While Apollonius, 'The Great Geometer', was at Pergamum he wrote the first edition of his famous book Conics . In Conics Apollonius introduced for the first time the terms parabola, ellipse and hyperbola which we use so frequently today. Conics consists of 8 books. Books 1 to 4 do not contain original material but introduce basic properties of conics that were known to Euclid Aristaeus and others. Books 5 to 7 are highly original. In these he discusses normals to conics and shows how many can be drawn from a point. He gives propositions determining the centre of curvature which lead immediately to the Cartesian equation of the evolute. Most of his other work is lost. In fact Book 8 of

60. BMCR-L: BMCR 2002.09.34 Fried & Unguru, Apollonius Of Perga's Conica: BMCR 2002.09.34 Fried Unguru, apollonius of perga's Conica http://omega.cohums.ohio-state.edu:8080/hyper-lists/bmcr-l/2002/0308.html

Date view Thread view Subject view Author view Subject: From: owner-bmcr-l@brynmawr.edu Date: Wed Sep 25 2002 - 13:04:28 EDT Next message: owner-bmcr-l@brynmawr.edu: "BMCR 2002.09.33 Klodt, Bescheidene Gro+sse: Die Herrschergestalt," Previous message: owner-bmcr-l@brynmawr.edu: "BMCR 2002.09.35 Colaiaco, Socrates Against Athens: Philosophy on" Michael N. Fried, Sabetai Unguru, Apollonius of Perga's Conica: Text, Context, Subtext. Mnemosyne Supplement no. 222. Leiden: Brill, 2001. Pp. xii, 499. ISBN 90-04-11977-9. Reviewed by Reviel Netz, Stanford Word count: 3042 words This book brings to completion the long-standing research project of the second author delineating the geometrical character of Greek mathematics and showing that a historian of mathematics ought, first and foremost, to be a historian. It is also the first book-length publication by the first author, giving in detail many of his new interpretations of Apollonius' Conics. For both authors this book should be considered a clear success. It effectively makes the case for a geometrical interpretation of Greek mathematics and will be considered the standard work on Apollonius.

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