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Pappus Of Alexandria: more detail

Pappus of Alexandria - Book 7 of the Collection by Alexander Jones, 1986-12-31

Pappus of Alexandria and the Mathematics of Late Antiquity (Cambridge Classical Studies) by Serafina Cuomo, 2007-06-21

Selections Illustrating The History Of Greek Mathematical Works..2 Volume Set..Vol. 1:Thales To Euclid:Vol.2:Aristarchus To Pappus Of Alexandria...Loeb Classical Library

Pappus of Alexandria: Book 7 of the Collection by Pappus, 1985

Pappus of Alexandria Book 7 Part 2 Only by Alexander Jones, 1986

On the duplication of the cube in Pappus of Alexandria (IIIrd century A.D.) (Rapport / SeÌminaires de matheÌmatique pure) by E EÌtienne, 1978

The Commentary of Pappus on Book X of Euclid's Elements: Arabic Text and Translation by Pappus of Alexandria & William Thomson, 1930

lists with details

Centre For The History Of Science Technology And Medicine
Her publications so far include a book on pappus of alexandria and the mathematicsof late antiquity, and articles on Roman landsurveying, ancient military
http://www.hstm.ic.ac.uk/staff/cuomo.htm

Extractions: Serafina Cuomo works on the history of science and technology in Greek and Roman antiquity, and on the history of early modern mathematics and mechanics. Her publications so far include a book on Pappus of Alexandria and the mathematics of late antiquity, and articles on Roman land-surveying, ancient military technology and the sixteenth-century mathematician Niccolo Tartaglia. She has just completed a general book on ancient mathematics, to be published in 2001, and is currently working on a book on ancient Greek and Roman technical knowledge for Cambridge University Press.
Pappus' Theorem
The applet below illustrates one of the most surprising geometric results probablydiscovered by pappus of alexandria (3 rd century AD) who is considered to be
http://www.cut-the-knot.com/pythagoras/Pappus.shtml

Extractions: Recommend this site The word Geometry is of the Greek and Latin origin. In Latin, geo- ge- means earth, while metron is measure. Originally, the subject of Geometry was earth measurement. With time, however, both the subject and the method of geometry have changed. From the time of Euclid's Elements rd century B.C.), Geometry was considered as the epitome of the axiomatic method which itself underwent a fundamental revolution in the 19 th century. Revolutionary in many other aspects, the 19th century also witnessed metamorphosis of a single science - Geometry - into several related disciplines The subject of Projective Geometry , for one, is the incidence of geometric objects : points, lines, planes. Incidence (a point on aline, a line through a point) is preserved by projective transformations, but measurements are not. Thus in Projective Geometry, the notion of measurement is completely avoided, which makes the term - Projective Geometry - an oxymoron. In Projective Geometry
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

Extractions: 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
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://www.fusl.ac.be/Files/General/BCS/ScTech2.html

Extractions: Bibliotheca Classica Selecta Bibliographie d'orientation Sciences et techniques MOTEUR DE RECHERCHE DANS LA BCS Plan Voir aussi la rubrique Magie Plan de cette section ... Bibliographie d'orientation Plan de cette section Sciences et techniques Bibliographie d'orientation Aujac G., Barton T., Ancient Astrology, Bezza G., Arcana Mundi, Antologia del pensiero astrologico antico
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

Extractions: 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.
Mig51 's Home Page
GeoGuide AD Pappus's Theorem. pappus of alexandria was born around 290in Alexandria, Egypt, and died around 350. Pappus is considered
http://www.geocities.com/CollegePark/Residence/1629/
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

Extractions: 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.
Archimedes' Lever
A remark of Archimedes quoted by pappus of alexandria in his Collection (Synagoge, Book VIII, c. AD 340 ed. Hultsch, Berlin 1878, p. 1060).
http://www.mcs.drexel.edu/~crorres/Archimedes/Lever/LeverIntro.html

Extractions: Following are some variations of the translation of Pappus' Greek text into English . . . "Give me a place to stand on, and I can move the earth." The Works of Archimedes with the Method of Archimedes, edited by T. L. Heath, Dover Publications, Inc., New York, 1953, p. xix. "Give me a place to stand on, and I will move the earth." Archimedes, by E.J. Dijksterhuis, (translated from the Dutch by C. Dikshoorn), Princeton University Press, Princeton, 1987, p. 15. "Give me somewhere to stand and I will move the earth." Greek Mathematical Works
Spheres And Planetaria (Introduction)
The Greek mathematician pappus of alexandria, who lived in the fourth century AD,writes that Archimedes wrote a nowlost manuscript entitled On Sphere-making.
http://www.mcs.drexel.edu/~crorres/Archimedes/Sphere/SphereIntro.html

Extractions: I n the first century BC Cicero wrote of two "spheres" built by Archimedes that Marcellus, the Roman consul who conquered Syracuse in 212 BC , looted from Syracuse and brought to Rome. One was a solid sphere on which were engraved or painted the stars and constellations, which Marcellus placed in the Temple of Virtue. Such celestial globes predate Archimedes by several hundred years and Cicero credits the famed geometers Thales and Eudoxos with first constructing them. The second sphere, which Marcellus kept for himself, was much more ingenious and original. It was a planetarium: a mechanical model which shows the motions of the sun, moon, and planets as viewed from the earth. Cicero writes that Archimedes must have been "endowed with greater genius that one would imagine it possible for a human being to possess" to be able to build such an unprecedented device. M any other ancient writers also refer to Archimedes' planetarium in prose and in verse. Several viewed it as proof that the cosmos must have had a divine creator: for just as Archimedes' planetarium required a creator, so then must the cosmos itself have required a creator. Cicero reverses the argument to contend that since the cosmos had a divine creator, so then must Archimedes be divine to be able to imitate its motions.
Free Papers - Free Essays, Free Papers, Free Term Papers, Free Book Reports, Fre
pappus of alexandria. Pappus was born in approximately 920 in Alexandria,Egypt. He was the last of the great Greek geometers and
http://www.freepapers.net/essays/Pappus_of_Alexandria.history.shtml

Extractions: Home New to Site? FAQ Essays Links ... Contact Us Pappus was born in approximately 920 in Alexandria, Egypt. He was the last of the great Greek geometers and one of his major theorems is considered to be the basis of modern projective geometry ("Pappus"). Pappus flourished in the fourth century, writing his key work, the Mathematical Collection, as a guide to Greek geometry ("Biography"). In this work, Pappus discusses theorems and constructions of over thirty mathematicians including Euclid, Archimedes and Ptolemy ("Biography"), providing alternatives of proofs and generalizing theorems. The Collection is a handbook to all of Greek geometry and is now almost the sole source of history of that science (Thomas 564). The separate books of the Collection were divided by Pappus into numbered sections. In the fourth section, Pappus discusses an extension on the Pythagorean Theorem (Thomas 575) now known as Pappus Area (Williams). Pappus drew parallelograms on two sides of a triangle, extended the external parallels to intersection, connected the included vertex of the triangle and the intersection point, used the direction and length of that segment to construct a parallelogram adjacent to the third side of the triangle, and proved that the sum of the areas of the first two parallelograms is equal to the area of the third parallelogram (Williams, Thomas 578-9). One of Pappus's biggest contributions to geometry is Pappus's Theorem, which states, "If the vertices of a hexagon lie alternately on two lines, then the meets of opposite sides are collinear" ("Pappus"). When put another way, "If A, B and C are three distinct points on one line and if A', B' and C' are three different distinct points on a second line, then the intersections of AC' and CA', AB' and BA', and BC' and CB' are collinear" (Smart 26), Pappus's Theorem spawns the Geometry of Pappus. This is a finite geometry consisting of exactly nine points and nine lines. The pairs of points making up the intersecting lines are interchangeable (Bogomolny 2). Also, Pappus's Theorem is self-dual (Bogomolny 2), meaning that if the words "point" and "line" were interchanged in the theorem, it would still hold true. Thanks to the duality principle, any theorem proved for Pappus's geometry is also true for the dual geometry.
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

Extractions: 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 mathematicians 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:
Geometers
Category Science Math Mathematicians Geometers http//history.math.csusb.edu/Mathematicians/Monge.html.6, pappus of alexandria (c. 320).
http://www.ad.com/Science/Math/Mathematicians/Geometers/
Pappus Of Alexandria - Book 7 Of The Collection Part 1: Introduction Text And Tr
pappus of alexandria Book 7 of the Collection Part 1 Introduction Text andTranslation Part 2 Commentary Index and Figures (Sources in the History of
http://www.easybuchdirekt.de/Jones-Alexander-Pappus-of-Alexandria-Bo-3540962573.
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

Extractions: 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. 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
History Of Math: Author List
100) Claudius Ptolemy (ca. 85165) Diophantus of Alexandria (ca. 200-284)pappus of alexandria (ca. 300-350) Proclus (ca. 410-485) Boethius (ca.
http://www.brown.edu/Facilities/University_Library/exhibits/math/authorfr.html
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

Extractions: 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." 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.
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

Extractions: Bibliography and Acknowledgements (this file) [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.
Eratosthenes
a star catalog. His mathematical work is known principally from thewritings of pappus of alexandria. After study in Alexandria
http://zebu.uoregon.edu/glossary/eratosthenes.html

Extractions: 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.
Euclid
lived during the reign of Ptolemy I (306283 BC). pappus of alexandria(fl. c. 320 AD) in his Collection states that Apollonius of
http://www.crystalinks.com/euclid.html

Extractions: Euclid of Alexandria is the most prominent mathematician of antiquity best known for his treatise on mathematics The Elements . The long lasting nature of The Elements must make Euclid the leading mathematics teacher of all time. For his work in the field, he is known as the father of geometry and is considered one of the great Greek mathematicians. Very little is known about the life of Euclid. Both the dates and places of his birth and death are unknown. It is believed that he was educated at Plato's academy in Athens and stayed there until he was invited by Ptolemy I to teach at his newly founded university in Alexandria. There, Euclid founded the school of mathematics and remained there for the rest of his life. As a teacher, he was probably one of the mentors to Archimedes Little is known of Euclid's life except that he taught at Alexandria in Egypt. According to Proclus (410-485 A.D.) in his Commentary on the First Book of Euclid's Elements , Euclid came after the first pupils of Plato and lived during the reign of Ptolemy I (306-283 B.C.). Pappus of Alexandria (fl. c. 320 A.D.) in his Collection states that Apollonius of Perga (262-190 B.C.) studied for a long while in that city under the pupils of Euclid. Thus it is generally accepted that Euclid flourished at Alexandria in around 300 B.C. and established a mathematical school there. Proclus also says that Euclid "belonged to the persuasion of Plato,'' but there exists some doubt as to whether Euclid could truly be called a Platonist. During the middle ages, Euclid was often identified as Euclid of Megara, due to a confusion with the Socratic philosopher of around 400 B.C.
Pappus Of Alexandria And The Mathematics Of Late Antiquity (in VSCCAT)
pappus of alexandria and the mathematics of late antiquity. Pappusof Alexandria and the mathematics of late antiquity / S. Cuomo.
http://scolar.vsc.edu:8003/VSCCAT/ACU-4219

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