Greek Trigonometry . century. BC) e menelaus of alexandria (III century BC), both authorsof the volumes known under the title of Sphaerica. But the http://www.math.unifi.it/archimede/archimede_inglese/trigonometria/trigonometria
Extractions: of trigonometry The invention of trigonometry can be associated with certainty to the studies of astronomy of the geometric school of Alexandria. The Egyptian city of Alexandria, which bears the name of A LEXANDER T HE G REAT who founded it in the III century B.C. was the capital of the Hellenic kingdom of the P TOLEMY until the Romans conquered it. It had a central position in the Mediterranean world of antiquity and an enlightened cultural policy on the part of the rulers, who equipped it with a library famous for over a millennium, one of the seven beauties of the world. They made of Alexandria the centre of Greek mathematics almost until the Arab conquest, and the "bridge" that allowed classic geometry to reach modern times through the Arab tradition. One of the trends of Alexandrine mathematics, together with the studies of pure mathematics that continued vigorously for various centuries, was constant attention to scientific and technological applications, and consequently to quantitative Mathematics, through which the theoretical results of classic geometry could find their equivalent in the natural sciences. Thus a series of new disciplines developed, together with traditional mathematical ones, that today we would call "applied mathematics", ranging from optics to pneumatics, from mechanics to geodetics. This new point of view found a particularly fertile ground in astronomy, where a prevalently cosmological investigation, aiming at looking into the structure of the universe and the causes of the celestial motion, with its greatest example in the works of Aristotle, and in particular the
Read This: Geometry: Our Cultural Heritage of Miletus, Pythagoras, Plato, Archytas, Euclid, Archimedes, Eratosthenes, Nicomedes,Apollonius, Heron of Alexandria, menelaus of alexandria, Claudius Ptolemy http://www.maa.org/reviews/holmegeom.html
Extractions: by Audun Holme This is a wonderful book based on lectures on geometry given by the author to undergraduate students at the University of Bergen, Norway. The book is intended both for the use of undergraduate students (especially future teachers of mathematics) and for the informed public interested to learn more about geometry viewed as part of our "cultural heritage." To attain this goal, the author divided the text in two distinct parts, very different and at the same time very well connected to each other. Part 1 is called "A Cultural Heritage" and contains material usually not included in a mathematical book; it is not a history of geometry, but it refers to some stories and historical connections with the goal of explaining the beginnings, "the roots of the themes to be treated in Part 2." Although this first part of the book is intended for the general public, it has some rigorous mathematical treatments (many of them not quite complete). Certainly the "walk through geometry" offered by this first part of the book is very interesting and fun to read and provides a very appealing and concise view of the development of geometry, without using many deep mathematical arguments (which might discourage a reader not interested too much in the rigorous mathematical treatment of geometry.) Part 2, "Introduction to Geometry", is a true mathematics textbook that develops geometry beginning with Euclid's postulates and ending with fractal geometry and catastrophe theory. It has 12 chapters: "Axiomatic Geometry", "Axiomatic Projective Geometry", "Models for Non-Euclidean Geometry", "Making Things Precise", "Projective Space", "Geometry in the Affine and the Projective Plane", "Algebraic Curves of Higher Degrees in the Affine Plane ", "Higher Geometry in the Projective Plane", "Sharpening the Sword of Algebra", "Construction with Straightedge and Compass", "Fractal Geometry", "Catastrophe Theory."
Cut The Knot! menelaus of alexandria worked in the 1 st century AD Giovanni Ceva (16481734)was an Italian engineer and geometer who lived some 16 centuries later. http://www.maa.org/editorial/knot/CevaPlus.html
Extractions: by Alex Bogomolny October 1999 I have a recollection. Years ago, a childhood friend of mine, Boris, shared with me with excitement an unusual experience he had on a visit to the Tretj'yakov Art Gallery in Moscow. He was accompanied by a professional painter, a good acquaintance of his older sister. While Boris was making a round in one of the halls, he observed that the painter remained all that time on the same spot studying a certain picture. Curious, my friend asked the painter what was it about the picture that kept him interested in it for so long. According to Boris, the painter did not reply directly, but, instead, stepped over to the picture and covered a spot on the picture with a palm of his hand. "Have a look at the picture and think of what you see," he requested. After a while, he uncovered the spot, stepped back and asked Boris to have another look. Well, almost 4 decades later, with the names of the painter and the picture long forgotten, I still vividly remember Boris' excitement when he told me of how entirely different, deeper and more beautiful, the picture appeared to him then. This recollection is haunting me. In retrospect, I regret to have never arranged with Boris to visit the gallery and learn how to really
Menelaus And Ceva menelaus of alexandria (circa 100 AD) was among the first to clearly recognize geodesicson a curved surface as the natural analogs of straight lines on a flat http://www.mathpages.com/rr/s3-09/3-09.htm
Extractions: 3.9 Menelaus and Ceva Menelaus of Alexandria (circa 100 AD) was among the first to clearly recognize geodesics on a curved surface as the natural analogs of straight lines on a flat plane. Earlier mathematicians had considered figures on a spherical surface, but it was Menelaus who had the insight to construct a complete geometry of the sphere with great circle arcs taking the place of line segments. For example, he defined "spherical triangles" as figures comprised of three great circle arcs, and developed a family of trigonometric relations for such figures. The most famous of these is still known as Menelaus' Theorem, although it's commonly presented only in the planar version (which was probably known to Euclid). In this form the theorem gives the necessary and sufficient condition for three points on the extended edges of a plane triangle to be co-linear. Consider the triangle shown below Letting [xy] denote the distance between points x and y, the Theorem of Menelaus states that the points a,b,c located on the (extended) edges BC, AC, AB of a triangle ABC are colinear if and only if To prove this, consider a rectangular coordinate system xy with respect to which the coordinates of the vertices A,B, and C are (0,0), (
History Of Geometry Mechanics. menelaus of alexandria (70130 AD) developed sphericalgeometry in his only surviving work Sphaerica (3 Books). In http://geometryalgorithms.com/history.htm
Extractions: A Short History of Geometry Ancient This page gives a short outline of geometry's history, exemplified by major geometers responsible for it's evolution. Click on a person's picture or name for an expanded biography at the excellent: History of Mathematics Archive (Univ of St Andrews, Scotland). Also, Click these links for our recommended: Greek Medieval Modern History Books ... History Web Sites The geometry of Babylon (in Mesopotamia) and Egypt was mostly experimentally derived rules used by the engineers of those civilizations. They knew how to compute areas, and even knew the "Pythagorian Theorem" 1000 years before the Greeks (see: Pythagoras's theorem in Babylonian mathematics ). But there is no evidence that they logically deduced geometric facts from basic principles. Nevertheless, they established the framework that inspired Greek geometry. A detailed analysis of Egyptian mathematics is given in the book: Mathematics in the Time of the Pharaohs India (1500 BC - 200 BC)
Mathematicians 100 CE. Balbus (fl. c. 100) *SB. menelaus of alexandria (c. 100 CE) *mt *SB. Nicomachusof Gerasa (c. 100) *SB. Zhang Heng (78139). Theon of Smyrna (c. 125). http://www.chill.org/csss/mathcsss/mathematicians.html
Extractions: List of Mathematicians printed from: http://aleph0.clarku.edu:80/~djoyce/mathhist/mathhist.html 1700 B.C.E. Ahmes (c. 1650 B.C.E.) *mt 700 B.C.E. Baudhayana (c. 700) 600 B.C.E. Thales of Miletus (c. 630-c 550) *MT Apastamba (c. 600) Anaximander of Miletus (c. 610-c. 547) *SB Pythagoras of Samos (c. 570-c. 490) *SB *MT Anaximenes of Miletus (fl. 546) *SB Cleostratus of Tenedos (c. 520) 500 B.C.E. Katyayana (c. 500) Nabu-rimanni (c. 490) Kidinu (c. 480) Anaxagoras of Clazomenae (c. 500-c. 428) *SB *mt Zeno of Elea (c. 490-c. 430) *mt Antiphon of Rhamnos (the Sophist) (c. 480-411) *SB *mt Oenopides of Chios (c. 450?) *SB Leucippus (c. 450) *SB *mt Hippocrates of Chios (fl. c. 440) *SB Meton (c. 430) *SB Hippias of Elis (fl. c. 425) *SB *mt Theodorus of Cyrene (c. 425) Socrates (469-399) Philolaus of Croton (d. c. 390) *SB Democritus of Abdera (c. 460-370) *SB *mt 400 B.C.E. Hippasus of Metapontum (or of Sybaris or Croton) (c. 400?) Archytas of Tarentum (of Taras) (c. 428-c. 347) *SB *mt Plato (427-347) *SB *MT Theaetetus of Athens (c. 415-c. 369) *mt Leodamas of Thasos (fl. c. 380) *SB
Mathematiker Mit Mm Translate this page Maxwell James Clerk (1831 - 1879, Edinburgh). menelaus of alexandria (70- 130, Alexandria). Mersenne Marin (1588 - 1648, Paris). Minkowski http://homepages.compuserve.de/thweidenfeller/mathematiker/m.html
History Of Astronomy: Persons (M) menelaus of alexandria Menelaos von Alexandria (ca. 70 ca. 130)Short biography and references (MacTutor Hist. Math.); Find more http://www.astro.uni-bonn.de/~pbrosche/persons/pers_m.html
The Beginnings Of Trigonometry Both Pappus and Proclus call him menelaus of alexandria (Heath 260), so we may assumethat he spent some of his time in Rome, and much of his time in Alexandria http://www.math.rutgers.edu/courses/436/436-s00/Papers2000/hunt.html
Extractions: 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
Ceva's Theorem: A Matter Of Appreciation menelaus of alexandria worked in the 1 st century AD, Giovanni Ceva (16481734)was an Italian engineer and geometer who lived some 16 centuries later. http://www.cut-the-knot.com/Generalization/CevaPlus.shtml
Extractions: by Alex Bogomolny October 1999 I have a recollection. Years ago, a childhood friend of mine, Boris, shared with me with excitement an unusual experience he had on a visit to the Tretj'yakov Art Gallery in Moscow. He was accompanied by a professional painter, a good acquaintance of his older sister. While Boris was making a round in one of the halls, he observed that the painter remained all that time on the same spot studying a certain picture. Curious, my friend asked the painter what was it about the picture that kept him interested in it for so long. According to Boris, the painter did not reply directly, but, instead, stepped over to the picture and covered a spot on the picture with a palm of his hand. "Have a look at the picture and think of what you see," he requested. After a while, he uncovered the spot, stepped back and asked Boris to have another look. Well, almost 4 decades later, with the names of the painter and the picture long forgotten, I still vividly remember Boris' excitement when he told me of how entirely different, deeper and more beautiful, the picture appeared to him then.
- Great Books - Ptolemy compared his catalogue with those of Aristil, Timocharis, Hipparchus andthe observations of Agrippa and menelaus of alexandria from the early 1st http://www.malaspina.com/site/person_639.asp
Extractions: Hipparchus (Greek: Hipparcos), Greek astronomer, mathematician and geographer, born: 190 B.C., Antigoneia since the year 30 Nicaea (Greek: Nikaia ) when Cisimah gave its name, ancient district Bithynia, (modern-day Iznik) in province Bursa, in modern day Turkey, died: 120 B.C., probably the island of Rhodes. The exact dates of his life are not known for sure, but he is believed to have observed from 162 to 126 B.C. Date of his birth was calculated by J. B. J. Delambre, based on clues in his work. We don't know anything about his youth either. Most of what is known about Hipparchus is from Strabo 's Geographica (Geography), from Pliny the Elder's Naturalis historia (Natural sciences) and from Ptolemy 's Almagest . He probably studied in Alexandria. His main original works are lost. His only preserved work is the Commentary on Aratus , a commentary on a poem by Aratus which describes the constellations and the stars which comprise them. This work contains many measurements of stellar positions. For his accession he holds the place of originator and father of scientific astronomy. He is believed to be the greatest Greek astronomer observer and he is at the same time entitled the greatest astronomer of ancient times, although Cicero still though about Aristarchus of Samos. Some put on this place also
Dr. Matrix' Discussion Of Mathematics methods were developed for solving problems involving plane triangles, and a theoremnamedafter the astronomer menelaus of alexandria was established for http://scientium.com/drmatrix/sciences/mathref.htm
Extractions: Hyperlinked by Dr. Matrix Mathematics , the study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry , or of numbers, as in arithmetic , or of the generalization of these two fields, as in algebra . Toward the middle of the 19th century, however, mathematics came to be regarded increasingly as the science of relations, or as the science that draws necessary conclusions. This latter view encompasses mathematical or symbolic logic, the science of using symbols to provide an exact theory of logical deduction and inference based on definitions, axioms, postulates, and rules for combining and transforming primitive elements into more complex relations and theorems. This brief survey of the history of mathematics traces the evolution of mathematical ideas and concepts, beginning in prehistory. Indeed, mathematics is nearly as old as humanity itself; evidence of a sense of geometry and interest in geometric pattern has been found in the designs of prehistoric pottery and textiles and in cave paintings. Primitive counting systems were almost certainly based on using the fingers of one or both hands, as evidenced by the predominance of the numbers 5 and 10 as the bases for most number systems today.
Webpage which is a work on the geometry of the sphere by Autolycus, Apollonius's Conics,and the later contributions by Heron of Alexandria and menelaus of alexandria. http://www.k12.nf.ca/discovery/curriculum/math/famous/pageone.htm
Innuendo Cornecopria.com - Sagacious Interpretations Of Tool methods were developed for solving problems involving plane triangles, and a theoremnamedafter the astronomer menelaus of alexandriawas established for http://www.innuendocornecopria.com/finger_deep_within_the_borderline/mathematics
Extractions: I INTRODUCTION Mathematics, study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry, or of numbers, as in arithmetic, or of the generalization of these two fields, as in algebra. Toward the middle of the 19th century, however, mathematics came to be regarded increasingly as the science of relations, or as the science that draws necessary conclusions. This latter view encompasses mathematical or symbolic logic, the science of using symbols to provide an exact theory of logical deduction and inference based on definitions, axioms, postulates, and rules for combining and transforming primitive elements into more complex relations and theorems. This brief survey of the history of mathematics traces the evolution of mathematical ideas and concepts, beginning in prehistory. Indeed, mathematics is nearly as old as humanity itself; evidence of a sense of geometry and interest in geometric pattern has been found in the designs of prehistoric pottery and textiles and in cave paintings. Primitive counting systems were almost certainly based on using the fingers of one or both hands, as evidenced by the predominance of the numbers 5 and 10 as the bases for most number systems today.
ONE BOOK, 1393 YEARS - A History Of The Almagest philosophical standpoint. His geometrical methods came from Euclid.His spherical geometry was from menelaus of alexandria. He drew http://www.star-names.freeserve.co.uk/almagest.html
Extractions: ONE BOOK, 1393 YEARS - A history of the Almagest 1.1 Introduction One book dominated astronomy for nearly one-thousand four-hundred years. This was the Almagest of Claudius Ptolemy. Why was just one book so influential and so dominant that it took so long to be surpassed? 1.2 Ptolemy Ptolemy lived in Egypt in the period when it was part of the Roman Empire. We know very little about him personally and the dates of his life (AD.100 to 178) are only approximate. He worked in the city of Alexandria. Alexandria is located on the northern (Mediterranean) coast of Egypt. It was a city renowned for learning and had a famous library and museum. Possibly, Ptolemy himself worked in one or other of these institutions. Ptolemy wrote in Greek, which was the scientific and philosophical language of his day. He is famous for writing many books on scientific subjects. These are: "Mathematical Syntaxis" (The Almagest) Astronomy "On the Apprations of the Fixed Stars and a Collection of Prognostics" Astronomy
The Foundations Of Christianity menelaus of alexandria wrote on mathematics. Ptolemy (Claudius Ptolemaeus) wrotethe astronomical masterpiece the Almagest (the Greatest) in Alexandria. http://members.iinet.net.au/~quentinj/Christianity/No-History.html
Extractions: The first one-and-a-half centuries of Christianity. There is a list found in many places on the Internet, citing authors who lived at the time of Jesus or within a century of him. This list apparently comes from John E. Remsburg's The Christ: A Critical Review and Analysis of the Evidence of His Existence . This page is inspired by that list and my wish to see it expanded, updated and corrected. I present a chronological listing of the writers from the Roman and Greek world of the first century and a half after the alleged crucifixion. The more contemporary and/or important references are given more space, and colour provides a simple classification: Surprising failures of contemporary writers to mention Jesus or the early Christians. Authors who could reasonably be expected to at least mention Jesus or Christianity Non-supporting or suspect or uncertain references sometimes cited as evidence for Jesus. Authors who could not be expected to mention Jesus or Christians. Reliable references to Jesus or Christ Plain coloured text indicates authors who were in a position to mention or describe Jesus and/or the early Christians but did not.
Names Lobachevsky; Lady Lovelace; Colin Maclaurin; menelaus of alexandria; JohnNapier; Isaac Newton; Emmy Noether; Pappus; Henri Poincare; Pythagorous; http://www.jcu.edu/math/faculty/djh/listprov.htm
Extractions: bibliography should include at least three cited references. Niels Abel Maria Agnisi Appolonius Emil Artin George Boole William Burnside Augustin Cauchy Arthur Cayley Richard Dedekind] Giraud DeSargues Rene Descartes George Dodgson Albert Einstein Paul Erdos Euclid Pierre Fermat Fibonacci Jean Baptiste Fourier Evariste Galois Carl Friedrich Gauss William Rowan Hamilton G. H. Hardy Camille Jordan Felix Klein Sonja Kowaleski Leopold Kronecker Johann Lambert Pierre Laplace Gottfried Leibniz Nicholai Lobachevsky Lady Lovelace Colin Maclaurin Menelaus of Alexandria John Napier Isaac Newton Emmy Noether Pappus Henri Poincare Pythagorous George Riemann Julia Robunson Geralamo Saccheri Ludwig Sylow Brooke Taylor Thales of Miletis Karl Weierstrass
APO Contents Table of Papyri. I. Theoretical and Instructional Texts. 4133 menelaus of alexandria(?), Treatise on planetary theory; 4134 Procedure text for planet? http://www.chass.utoronto.ca/~ajones/oxy/papindex.html
Extractions: Return to Astronomical Papyri from Oxyrhynchus Table of Papyri I. Theoretical and Instructional Texts Menelaus of Alexandria (?), Treatise on planetary theory Procedure text for planet? Procedure text for Venus Procedure text for the moon Predictions of lunar eclipses, A.D. 56 and 57 On eclipse prediction Treatise on eclipse prediction Treatise on lunar periods Tabulated lunar phenomena On latitudes of a planet Instructions for Ptolemy's Handy Tables Instructions for Ptolemy's Handy Tables Treatise on kinematic models Procedure text Procedure text Procedure text II. Primary Tables Epochs of the sun, A.D. 161-237 Epochs of the moon, A.D. 96-166 Epochs of the moon, A.D. 187-198, and template Epochs of the moon, A.D. 217-254 Epochs of Mercury Epochs of Mercury, A.D. 206-215 Epochs of Mercury Epochs of Mercury Epochs of Mercury Epochs of Mercury Epochs of Mercury Epochs of Venus Epochs of Venus, A.D. 106-121 Epochs of Mars, A.D. 271-325 Epochs of Mars, A.D. 225-235 Epochs of Mars, A.D. 101-133 Epochs of Jupiter, A.D. 57-80 Epochs of Jupiter, A.D. 6-13
Mathem_abbrev Nicolas, Mandelbrot, Benoit Mansur ibn Ali, Abu Margulis, Gregori Mauchly, JohnMaxwell, James Clerk Menaechmus menelaus of alexandria Menshov, Dmitrii Milnor http://www.pbcc.cc.fl.us/faculty/domnitcj/mgf1107/mathrep1.htm
Extractions: Mathematician Report Index Below is a list of mathematicians. You may choose from this list or report on a mathematician not listed here. In either case, you must discuss with me the mathematician you have chosen prior to starting your report. No two students may write a report on the same mathematician. I would advise you to go to the library before choosing your topic as there might not be much information on the mathematician you have chosen. Also, you should determine the topic early in the term so that you can "lock-in" your report topic!! The report must include: 1. The name of the mathematician. 2. The years the mathematician was alive. 3. A biography. 4. The mathematician's major contribution(s) to mathematics and an explanation of the importance. 5. A historical perspective during the time the mathematician was alive.
OPE-MAT - Historique Translate this page Gabriel Osgood, William Menabrea, Luigi Muir, Thomas Ostrogradski, Mikhail MenaechmusMydorge, Claude Oughtred, William menelaus of alexandria Ozanam, Jacques http://www.gci.ulaval.ca/PIIP/math-app/Historique/mat.htm
Extractions: Abel , Niels Akhiezer , Naum Anthemius of Tralles Abraham bar Hiyya al'Battani , Abu Allah Antiphon the Sophist Abraham, Max al'Biruni , Abu Arrayhan Apollonius of Perga Abu Kamil Shuja al'Haitam , Abu Ali Appell , Paul Abu'l-Wafa al'Buzjani al'Kashi , Ghiyath Arago , Francois Ackermann , Wilhelm al'Khwarizmi , Abu Arbogast , Louis Adams , John Couch Albert of Saxony Arbuthnot , John Adelard of Bath Albert , Abraham Archimedes of Syracuse Adler , August Alberti , Leone Battista Archytas of Tarentum Adrain , Robert Albertus Magnus, Saint Argand , Jean Aepinus , Franz Alcuin of York Aristaeus the Elder Agnesi , Maria Alekandrov , Pavel Aristarchus of Samos Ahmed ibn Yusuf Alexander , James Aristotle Ahmes Arnauld , Antoine Aida Yasuaki Amsler , Jacob Aronhold , Siegfried Aiken , Howard Anaxagoras of Clazomenae Artin , Emil Airy , George Anderson , Oskar Aryabhata the Elder Aitken , Alexander Angeli , Stefano degli Atwood , George Ajima , Chokuyen Anstice , Robert Richard Avicenna , Abu Ali Babbage , Charles Betti , Enrico Bossut , Charles Bachet Beurling , Arne Bouguer , Pierre Bachmann , Paul Boulliau , Ismael Bacon , Roger Bhaskara Bouquet , Jean Backus , John Bianchi , Luigi Bour , Edmond Baer , Reinhold Bieberbach , Ludwig Bourgainville , Louis Baire Billy , Jacques de Boutroux , Pierre Baker , Henry Binet , Jacques Bowditch , Nathaniel Ball , W W Rouse Biot , Jean-Baptiste Bowen , Rufus Balmer , Johann Birkhoff , George Boyle , Robert Banach , Stefan Bjerknes, Carl