61. VisitMaldives - Nation Of Islands For example pappus of alexandria (about the end of the 4th century (AD) says, It(Taprobane) is one of the largest islands of the world, being 1,100 miles in http://www.visitmaldives.com/maldives/history2.html

Maldives - Nation of Islands History Early Settlers Conversion to Islam British Protectorate Independence The history of the Maldives is lost in antiquity. Very little information is available on the ancient people and their way of life. The late H.C.P. Bell, a British archeologist states: "Indeed it may be preferable to assign to the original colonization of the group of dates synchronic with that of Ceylon itself (Viz., several centuries before the Christian era)". The Maldives was certainly known among some of the classical writers. For example Pappus of Alexandria (about the end of the 4th century (A.D) says, "It (Taprobane) is one of the largest islands of the world, being 1,100 miles in length by 1,500 miles broad and encompasses 1,370 adjacent islands among its dependencies. About the same time as Pappus of Alexandria, Scholasticu, the Theban who was visiting India in the company of a priest, and reached Muziris (Cranganore) on the Malabar coast, mentioned about a thousand islands, Maniolae and the loadstone rocks that attracted iron-bound vessels to their destruction.

62. University Of Pittsburgh: Department Of Mathematics This ancient proof has been lost, unless it was the proof presented a few centurieslater by pappus of alexandria in the preface to his fifth book. http://www.math.pitt.edu/articles/pappus.html

Table of Contents Fall 2001 Cannonballs and Honeycomb: Pappus R. Weaire was writing a book on sphere packings when I finished the proof of the Kepler conjecture, and we began to correspond. Under his influence, I turned to the planar version of the foam problem. This problem goes back over 2000 years. What is the most efficient partition of the plane into equal areas? The honeycomb conjecture asserts that the answer is the regular hexagonal honeycomb. Pappus Around 36 BC, the Roman scholar Marcus Terentius Varro wrote a book on agriculture in which he discusses the hexagonal form of the bee's honeycomb. There were two competing theories of the hexagonal structure. One theory held that the hexagons better accommodated the bee's six feet. The other theory, supported by the mathematicians of the day, was that the structure was explained by the isoperimetric property of the hexagonal honeycomb. Varro writes, ``Does not the chamber in the comb have six angles

63. Eratosthenes a star catalog. His mathematical work is known principally from thewritings of pappus of alexandria. After study in Alexandria http://zebu.uoregon.edu/~js/glossary/eratosthenes.html

Eratosthenes After study in Alexandria and Athens, Eratosthenes settled in Alexandria about 255 BC and became director of the great library there. He worked out a calendar that included leap years, and he tried to fix the dates of literary and political events since the siege of Troy. His writings include a poem inspired by astronomy, as well as works on the theatre and on ethics. Eratosthenes was afflicted by blindness in his old age, and he is said to have committed suicide by voluntary starvation.

64. Pappus' Theorem Pappus Theorem. pappus of alexandria was a Greek mathematician who lived aroundthe end of the third century AD, although the exact date is uncertain. http://www.mathpages.com/home/kmath542/kmath542.htm

Pappus' Theorem Pappus of Alexandria was a Greek mathematician who lived around the end of the third century AD, although the exact date is uncertain. Theon made a marginal note in one of his manuscripts stating that Pappus wrote during the reign of Roman emperor Diocletian, which places him in the period from 284 to 305 AD, but it also seems from Pappus' commentary on Ptolemy's Almagest that he witnessed a particular solar eclipse that occurred in 320 AD In any case, the "Collection" (Synagoge) of Pappus is an invaluable source of information on Greek mathematics, since it contains summaries and attributions of results based on ancient works that have subsequently been lost. In addition, Pappus gave some apparently original results, such as the proposition that is commonly called "Pappus' Theorem" involving a hexagon inscribed between two lines. Consider two straight lines emanating from point O and containing the points P through P as shown in the figure below. Letting L ij denote the line through points P i and P j , and letting a,b,c denote the points of intersection between the pairs of lines [L ,L ], [L

65. Biography-center - Letter P Pappenheim, Artur www.whonamedit.com/doctor.cfm/1757.html; pappus of alexandria,wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/Pappus.html; http://www.biography-center.com/p.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish P 538 biographies www-history.mcs.st-and.ac.uk/~history/Mathematicians/Peres.html www-history.mcs.st-and.ac.uk/~history/Mathematicians/Peter.html www-history.mcs.st-and.ac.uk/~history/Mathematicians/Polya.html Paar, Jack www.pbs.org/wnet/americanmasters/database/paar_j.html Paavolainen, Olavi www.kirjasto.sci.fi/opaavola.htm pablo, picasso www.time.com/time/time100/artists/profile/picasso.html Pacchia, Girolamo del www.getty.edu/art/collections/bio/a844-1.html Pacchioni, Antonio www.whonamedit.com/doctor.cfm/391.html Pace, Carlos www.grandprix.com/gpe/drv-paccar.html Pacher, Michael www.kfki.hu/~arthp/bio/p/pacher/biograph.html Pacioli, Luca www-history.mcs.st-and.ac.uk/~history/Mathematicians/Pacioli.html Packer, Kerry

66. A Civilization Is Like A Great River Flowing Through Time 2. pappus of alexandria, hurry up, unfortunately the great age ofGreek mathematics is drawing its last breath. Fitzgerald made http://www.usd.edu/~mgamble/math history.htm

A civilization is like a great river flowing through time, nourished and strengthened by many rich tributaries from other cultures. Let us project our imagination backward to a few thousand years. We are invited by the mathematics society of Greece, the birthplace of many mythical gods. We ask them a simple question: "Who created mathematics?" They respond "Mathematics begins with this half-mythical figure of Pythagoras. Science Begins with him. Western philosophy begins with him. He is even the first to use the word mathematike . Before him there was only mathemata, which meant knowledge or learning in general." The question is answered; we may begin our real journey in this never ending rational universe. The only rule shall be the anonymity, no last name will be mentioned, except Pappus of Alexandria. There is no royal road to geometry. The only way to a knowledge of geometry is a set of 13 books, 465 propositions, and 5 postulates. A point is that which has no part. A line is breathless length. A straight line is a line which lies evenly with the point on itself. A unit is that by virtue of which each of the things that exist is called one. A number is a multitude composed of units. Give this person a penny, since he must make a profit out of what he learns.

67. Alexander Jones's Publications pappus of alexandria. Book 7 of the Collection. Articles, ‘pappus of alexandria’,‘Hipparchus’, ‘Ptolemy’, ‘Ptolemaic System’. http://www.chass.utoronto.ca/~ajones/publications/

Alexander Jones Publications Books and Monographs (with J. L. Berggren) Ptolemy's Geography: An Annotated Translation of the Theoretical Chapters. Princeton (Princeton University Press), in press. Astronomical Papyri from Oxyrhynchus Memoirs of the American Philosophical Society. 2 vols. Philadelphia, 1999. (with M. W. Haslam, F. Maltomini, M. L. West, and others) The Oxyrhynchus Papyri Volume LXV. London, 1998. Egypt Exploration Society, Graeco-Roman Memoirs 85. 212 pp. Ptolemy's first commentator . Transactions of the American Philosophical Society, 80.7. Philadelphia, 1990. An Eleventh-century manual of Arabo-Byzantine astronomy . Corpus des astronomes byzantins, 3. Amsterdam (Gieben), 1987. Pappus of Alexandria. Book 7 of the Collection . Edited with translation and commentary by Alexander Jones. Sources in the History of Mathematics and the Physical Sciences, 8. 2 vols. Berlin (Springer Verlag), 1986. Articles The Astrologers of Oxyrhynchus and Their Astronomy. Forthcoming in Oxyrhynchus: A City and its Texts Astronomy after Ptolemy. Forthcoming in

68. Lecture Notes 2 - Math 3210 Lecture Notes 2. pappus of alexandria (340 AD) Pappus Theorem Ifpoints A,B and C are on one line and A , B and C are on another http://www-math.cudenver.edu/~wcherowi/courses/m3210/hg3lc2.html

Lecture Notes 2 Pappus of Alexandria (340 A.D.) Pappus' Theorem: If points A,B and C are on one line and A', B' and C' are on another line then the points of intersection of the lines AC' and CA', AB' and BA', and BC' and CB' lie on a common line called the Pappus line of the configuration. Axioms for the Finite Geometry of Pappus There exists at least one line. Every line has exactly three points. Not all lines are on the same point. [N.B. Change from the text] If a point is not on a given line, then there exists exactly one line on the point that is parallel to the given line. If P is a point not on a line, there exists exactly one point P' on the line such that no line joins P and P'. With the exception in Axiom 5, if P and Q are distinct points, then exactly one line contains both of them. Theorem 1.10 Each point in the geometry of Pappus lies on exactly three lines. Pf . Let X be any point. By corrected axiom 3, there is a line not containing X. This line contains points A,B,C [Axiom 2]. X lies on lines meeting two of these points, say B and C [Axiom 5]. There is exactly one line through X parallel to BC [Axiom 4]. There can be no other line through X since by Axiom 4 it would have to meet BC at a point other than A, B or C [Axioms 6 and 5], and this would contradict Axiom 2. Pappus geometry has 9 points and 9 lines.

69. Eratosthenes Of Cyrene great accuracy and compiled a star catalog. His mathematical workis known principally from the writings of pappus of alexandria. http://www.kat.gr/kat/history/Greek/Sc/Eratosthenes.htm

Eratosthenes Of Cyrene b. c. 276 BC, Cyrene, Libya d. c. 194, Alexandria, Egypt Greek scientific writer, astronomer, and poet, the first man known to have calculated the Earth's circumference. At Syene (now Aswan), some 800 km (500 miles) southeast of Alexandria in Egypt, the Sun's rays fall vertically at noon at the summer solstice. Eratosthenes noted that at Alexandria, at the same date and time, sunlight fell at an angle of about 7 from the vertical. He correctly assumed the Sun's distance to be very great; its rays therefore are practically parallel when they reach the Earth. Given estimates of the distance between the two cities, he was able to calculate the circumference of the Earth. The exact length of the units (stadia) he used is doubtful, and the accuracy of his result is therefore uncertain; it may have varied by 0.5 to 17 percent from the value accepted by modern astronomers. He also measured the degree of obliquity of the ecliptic (in effect, the tilt of the Earth's axis) with great accuracy and compiled a star catalog. His mathematical work is known principally from the writings of Pappus of Alexandria. After study in Alexandria and Athens, Eratosthenes settled in Alexandria about 255 Bc and became director of the great library there. He worked out a calendar that included leap years, and he tried to fix the dates of literary and political events since the siege of Troy. His writings include a poem inspired by astronomy, as well as works on the theatre and on ethics. Eratosthenes was afflicted by blindness in his old age, and he is said to have committed suicide by voluntary starvation.

70. Euclid In ancient times, commentaries were written by Hero of Alexandria (fl. c. AD 62),pappus of alexandria (fl. c. AD 320), Proclus, and Simplicius of Cilicia (fl. http://www.kat.gr/kat/history/Greek/Tc/Euclid.htm

Euclid flourished c. 300 BC , Alexandria, Egypt Greek Eukleides the most prominent mathematician of Greco-Roman antiquity, best known for his treatise on geometry, the Elements Life Of Euclid's life nothing is known except what the Greek philosopher Proclus (c. AD BC Elements BC Sources and contents of the Elements Euclid compiled his Elements from a number of works of earlier men. Among these are Hippocrates of Chios (fl. c. 460 BC BC BC ). The older elements were at once superseded by Euclid's and then forgotten. For his subject matter Euclid doubtless drew upon all his predecessors, but it is clear that the whole design of his work was his own, culminating in the construction of the five regular solids, now known as the Platonic solids. A brief survey of the Elements BC ). While Book V can be read independently of the rest of the Elements arithmos antanaresis (now known as the Euclidean algorithm), for finding the greatest common divisor of two or more numbers; Book VIII examines numbers in continued proportions, now known as geometric sequences (such as a x a x a x a x ); and Book IX proves that there are an infinite number of primes.

71. 3960. Archimedes. The Columbia World Of Quotations. 1996 Quoted in Mathematical Collection, book VIII, proposition 10, section 11,pappus of alexandria (date unknown); translated into Latin (1588). http://www.bartleby.com/66/60/3960.html

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72. LookSmart - Directory - Ancient Mathematics History of Mathematics pappus of alexandria Find a biographical sketch of Pappus,a 4th-century mathematician and author of the geometry treatise, The http://search.looksmart.com/p/browse/us1/us317914/us328800/us4231786/us10026157/

@import url(/css/us/style.css); @import url(/css/us/searchResult1.css); Home IN the directory this category YOU ARE HERE Home Sciences Mathematics History Ancient Mathematics - Discover articles on the art of mathematics in ancient times, and biographies of ancient mathematicians. Directory Listings About allRefer Reference - Pythagoras Get acquainted with details on the life, works, contributions, and philosophy of the pre-Socratic Greek philosopher who founded the Pythagorean school. General View of Mathematics Before 1000 B.C. Review evidence from India, Egypt, Mesopotamia, and China that reveals the existence of mathematical thought beyond counting before 1000 B.C. Hist. of Math - Hellenistic Period of Greek Mathematics Meet the mathematicians of the Hellenistic Period, including Aristarchus of Samos, Apollonius of Perga, Hipparchus, and Cladius Ptolemy. Historical Tidbits Information on the life and work of famous mathematicians including Abel, Archimedes, Bolzano, Cantor, Euclid, Weierstrass, and Zeno of Elea. History of Math - Anaxagoras of Clazomenae Find a biography of the Athenian philosopher interested in squaring the circle, notable because of the purely mathematical nature of the problem.

73. 285 A.D. The only mathematician of any importance alive, Sporus of Nicaea, isbest know for being a teacher of pappus of alexandria. Sporus http://faculty.oxy.edu/jquinn/home/Math490/Timeline/285AD.html

285 A.D. In the year 285 B.C., there was not much work done in mathematics. The only mathematician of any importance alive, Sporus of Nicaea, is best know for being a teacher of Pappus of Alexandria. Sporus was about forty-five years old at the time, and would die fifteen years later. All that is known about Sporus comes from the writings of Pappus. He was a professor at the University of Alexandria and his primary interest was solving the problems of the duplication of the cube and the quadrature of the circle. Some of the methods that Sporus used resemble the theory behind integration. Sporus also wrote critiques of other mathematician’s works on these problems. Astronomy was another science that caught Sporus’ attention and he worked on calculating the size on the sun and various comets. Because of his teaching ability and work on these problems, Pappus held Sporus in high esteem and described him as having an excellent reputation among his colleagues. Author : Tim Lucas References: Mac Tutor History of Mathematics Archive http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Sporus.html

74. Bryn Mawr Classical Review 2002.03.31 Serafina Cuomo, pappus of alexandria and the Mathematics of Late Antiquity. SerafinaCuomo, pappus of alexandria and the Mathematics of Late Antiquity. http://ccat.sas.upenn.edu/bmcr/2002/2002-03-31.html

Bryn Mawr Classical Review 2002.03.31 Serafina Cuomo, Pappus of Alexandria and the Mathematics of Late Antiquity . Cambridge: Cambridge University Press, 2000. Pp. x + 234. ISBN 0-521-64211-6. $59.95. Reviewed by Alan C. Bowen, Institute for Research in Classical Philosophy and Science, Princeton (acbowen@Princeton.edu) Word count: 1922 words As it is typically practiced today, the history of ancient Greek mathematics is a history of results and the resources or techniques used to get them, and, when its practitioners do attempt to write about the historical circumstances of the ideas they study, too often they fallaciously confuse their logical reconstructions with past realia . The reason for this, I suspect, is not just that many of the source materials available lack any information about their authors and settingsand so by their nature would seem to direct our attention to results and deductive structure alonebut that many historians of mathematics have not fully separated their subject from mathematics proper. Fortunately, there are recent signs of a major change in how the history of Greek mathematics is to be written. Reviel Netz, for instance, has brought to light valuable information about the cognitive practices constituting what it meant to do mathematics in antiquity by paying close attention to the language in which ancient mathematical argumentation is expressed and the role of diagrams. Serafina Cuomo would have us move even farther from previous work in the field by interpreting ancient mathematical output as a product of human activity with intellectual and social agendas and contexts. The work she analyzes in her excellent book is the

75. Who Was Who In Roman Times: Data On Persons: Pappus Of Alexandria Sponsored links Data on Persons. pappus of alexandria. Function Scientist Sex Male, Synonym(s) Pappus. No parents found. No spouse/wife/partner found. http://www.romansonline.com/Persns.asp?IntID=565&Ename=Pappus of Alexandria

76. The Beginnings Of Trigonometry pappus of alexandria, who was a teacher of mathema tics in the fourth century, observedthat Hipparchus in his book on the rising of the twelve signs of the http://www.math.rutgers.edu/~cherlin/History/Papers2000/hunt.html

The Beginnings of Trigonometry Joseph Hunt History of Mathematics Rutgers, Spring 2000 The ancient Greeks transformed trigonometry into an ordered science. Astronomy was the driving force behind advancements in trigonometry. Most of the early advancements in trigonometry were in spherical trigonometry mostly because of its application to astronomy. The three main figures that we know of in the development of Greek trigonometry are Hipparchus, Menelaus, and Ptolomy. There were likely other contributors but over time their works have been loss and their names have been forgotten. "Even if he did not invent it, Hipparchus is the first person of whose systematic use of trigonometry we have documentary evidence." (Heath 257) Some historians go as far as to say that he invented trigonometry. Not much is known about the life of Hipp archus. It is believed that he was born at Nicaea in Bithynia. (Sarton 285) The town of Nicaea is now called Iznik and is situated in northwestern Turkey. Founded in the 4th century BC, Nicaea lies on the eastern shore of Lake Iznik. He is one of the g reatest astronomers of all time. We know from Ptolemy's references that he made astronomical observations from 161 to 127 BC. (Sarton 285) Unfortunately, nearly all of his works are lost, and all that remains is his commentary on the Phainomena of Eudoxos of Cnidos, and a commentary on an astronomical poem by Aratos of Soloi. (Sarton 285) Most of what we know about Hipparchus comes from Ptolemy's

77. The Great Library Of Alexandria pappus of alexandria, who lived around the time of Roman emperor Theodosius, wasthe last of the great Greek geometers and one of his theorems is cited as the http://www.geocities.com/apollonius_theocritos/page04.html

Hellenism and Multiculturalism G reek was the official language of Ptolemaic Egypt and though Egyptians continued to form the overwhelming majority of the population of the countryside, Alexandria was different. Peoples from many lands settled there and most newcomers eventually adopted Greek, the lingua franca of the whole eastern Mediterranean and beyond. Even those groups known for the conservative retention of other aspects of their culture, notably the Jews, forgot their native tongues and learned Greek. A t the Great Library Greek translations were commissioned as a matter of course. Aristeas, writing one hundred years after the Library's inception, records that Ptolemy I Soter handed over to Demetrius of Phaleron, a former pupil of Aristotle, the job of gathering books and scrolls, as well as letting him supervise a massive effort to translate the most important works of other cultures into Greek. This process began with the translation of Old Testament, for which project the library hired and housed seventy-two rabbis to produce its famous namesake, the Septuagint.

78. Religion Detoxification Web Guide Some notable Egyptians in the field were Paul of Alexandria; Hephaestionof Thebes; Palchus; pappus of alexandria; Theon of Alexandria; http://www.artdsm.com/religiondetoxification/the_jesus_story9.html

The Jesus Story To Water instead of Blood: The Story of Serapis to Jesus CHAPTER FIVE of TWELVE God Parts in (Above) ChristLand 17 CE - Egyptian "Zodiac" is erected at Dendera Temple ("Hathor" goddess of love). "Hathor," Goddess of Love, Music, and Beauty She was the celestial cow or sky goddess; patron of sky, sun, music, dance, art, and the mother-goddess of the whole world. She was worshipped throughout all of Egypt. Her philosophical teaching center was at Dendera in Upper Egypt. Her name means "House of Horus." When you read about Origen of Alexandria later on, you should also be aware that his name, Origen, means "born of Horus." In Hathor's temple, a large hypostyle hall was added in the 1st century CE by the Roman Emperor Tiberius. The ceiling of the hall, which retains much of its original color, is decorated as a complex and carefully aligned symbolic chart divided into seven bands of the heavens including "Signs" of the Zodiac; which were introduced by the Romans. The walls of this hall are adorned with scenes of Roman emperors (as pharaohs) making offerings to Hathor.

79. Introductory Essay 3 vols. Berlin, 18761878. Jones pappus of alexandria. Book 7 of the Collection.Ed. and trans. Alexander Jones. 2 vols. New York Springer, 1986. http://wwwhs.cias.osakafu-u.ac.jp/~ksaito/Pidx_bib.html

Index of the Propositions Used in Book 7 of Pappus' Collection Ken SAITO (This article was originally printed in Jinbun Kenkyu: The Journal of Humanities, No.26(1997), Faculty of Letters, Chiba University pp. 155-188. For this printed version, write to the author Home Introductory Essay. Part 1-1: Symbols for Propositions in Part 1. ... Part 3. Index in the order of Pappus' text. Bibliography and Acknowledgements (this file) Bibliography and Acknowledgements Bibliography [Eecke] Pappus d'Alexandrie. tr. Paul Ver Eecke. 2 vols. (consecutive pagination). Paris, 1933. Reprint, Paris: Blanchard, 1982. [Gardies 1991] Gardies, J.-L. "La proposition 14 du livre V dans l'économie des Eléments d'Euclide." Revue d'histoire des sciences [Hultsch] Pappus. Pappi Alexandrini Collectionis quae supersunt. ed. and trans. F. Hultsch. 3 vols. Berlin, 1876-1878. [Jones] Pappus of Alexandria. Book 7 of the Collection. Ed. and trans. Alexander Jones. 2 vols. New York: Springer, 1986. [Mueller 1981]Mueller, Ian. Philosophy of Mathematics and Deductive Structure in Euclid's `Elements' . Cambridge, Mass.:The MIT Press.

80. Sciences Et Techniques - Astronomie, Cosmologie, Astrologie, Mathématiques Translate this page New York, 1960. Cuomo S., pappus of alexandria and the Mathematics of Late Antiquity,Cambridge UP, 2000, 234 p. (Cambridge Classical Studies). CR BMCR. http://bcs.fltr.ucl.ac.be/ScTech2.html

Bibliotheca Classica Selecta Bibliographie d'orientation Sciences et techniques MOTEUR DE RECHERCHE DANS LA BCS Sciences et techniques Plan Sur la Toile Dictionnaire Revue Monde antique ... Monde romain Voir aussi la rubrique Magie Sur la Toile Science, Technology, Engineering, Medicine On verra avant tout la section Science, Technology, Engineering, Medicine des RomanSites Ancient Astrology and Divination on the Web Archimedes Episteme ... Histoire de l'astrologie occidentale: bibliographie Dans l' imposante bibliographie Hypatia of Alexandria Star Myths and Constellation Lore ci-dessous Plan de cette section ... Bibliographie d'orientation Dictionnaire Montero S., Plan de cette section Sciences et techniques Bibliographie d'orientation Revue Condos Th., Star Myths of the Greeks and Romans: A Sourcebook containing the Constellations of Pseudo-Eratosthenes and the Poetic Astronomy of Hyginus, Astronomie Star Myths and Constellation Lore Monde antique Aujac G., Barton T., Ancient Astrology, Bezza G., Arcana Mundi, Antologia del pensiero astrologico antico

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