Alexandrian Algebra According To Diophantus Diophantus of alexandria had a great impact in the world of mathematics. to Diophantus'dates, based on Diophantus' reference to work by hypsicles who preceded http://www.math.rutgers.edu/courses/436/436-s00/Papers2000/kirschm.html
Extractions: Spring 2000 Alexandrian Algebra can best be viewed through the work of Diophantus of Alexandria. Diophantus of Alexandria had a great impact in the world of mathematics. He is often referred to as the father of Algebra. He produced only a few works, but their influence on mathematics was far reaching. He is known for considering only rational solutions to equations: a negative or irrational solution was considered preposterous. Moreover , he usually obtained only one such rational solution. Numerous scholars have analyzed the methods of Diophantus in detail. It is these styles and methods of solving equations that are most interesting to those who study him, and most difficult to understand, since Diophantus rarely recorded general formulas. The interpretations of his work by Nesselmann and Heath will be examined here, and we will attempt to determine which of these interpretations reflects his work more accurately. The most interesting work of Diophantus is his Arithmetica , which originally contained thirteen books, of which, unfortunately, only six survived, though Diophantus stated in the first book of Arithmetica that it would include thirteen books. Other evidence to support the assumption that additional books had in fact been written is the fact that certain propositions and concepts are left unproved and unexplained in the text as we have it. Gow notes that historians do not think that the propositions of Arithmetica are now found in the order in which they were originally written, and that essential discussions of determinate quadratic equations and indeterminate simple equations are excluded (102). Gow and Heath both refer to another work by Diophantus on Polygonal Numbers that was significantly altered from its original state, so that many proofs are now incomplete. A third work by Diophantus is called
Untitled Document Apollonius. According to another version hypsicles, a pupil of Euclidat alexandria, offered to the king and published Books XIV. and http://www.headmap.com/book/euclid/before/tradition.htm
Extractions: [p. 1] As in the case of the other great mathematicians of Greece, so in Euclid's case, we have only the most meagre particulars of the life and personality of the man. Most of what we have is contained in the passage of Proclus' summary relating to him, which is as follows âNot much younger than these (sc. Hermotimus of Colophon and Philippus of Medma) is Euclid, who put together the Elements, collecting many of Eudoxus' theorems, perfecting many of Theaetetus', and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors. This man lived in the time of the first Ptolemy. For Archimedes, who came immediately after the first (Ptolemy) , makes mention of Euclid: and, further, they say that Ptolemy once asked him if there was in geometry any shorter way than that of the elements, and he answered that there was no royal road to geometry . He is then younger than the pupils of Plato but older than Eratosthenes and Archimedes; for the latter were contemporary with one another, as Eratosthenes somewhere says.â
Re: [HM] An Ancient Greek Library By George L. McDowell, Jr. Eutocius 20.. Euclid 21.. Geminus 22.. Hero(n) of alexandria 23.. Hypatia 24..Hipparchus 25.. Hippocrates of Chios 26.. hypsicles 27.. Iamblichus 28.. http://mathforum.org/epigone/historia_matematica/merpreezan/009501c19c80$c7b37b6
Greek For Euclid: Contents known of the life of Euclid, except that he worked in alexandria, and is 13 Books(two more were added later, apparently the work of hypsicles, and generally http://www.du.edu/~jcalvert/classics/nugreek/contents.htm
Extractions: Sir Winston Churchill Go immediately to Contents Eu)klei/dou Stoixei~a , Euclid's Elements, the classical textbook in geometry, is easy to read in the original ancient Greek, but its grammar and vocabulary are not those familiar from the usual course in elementary Greek, with peculiarities that make it difficult for the beginner. The text of the Elements that we have is written in the literary koinh/ typical of the 1st century AD. This course concentrates on exactly what is necessary to read Euclid, both in vocabulary and grammar. Its sole aim is to teach how to read this work, and similar texts in Greek mathematics, and not to compose Greek sentences, nor to read the Iliad or Plato. All necessary information is included in the course. A great amount of scholarship has been devoted to Euclid, mainly in Latin or German, and this course may expose some of it to a larger audience, to whom it has been largely inaccessible. For authoritative details, reference must be made to these sources, since the present one claims no expertise. There are many websites with information on Euclid and geometry. For example, look at the link to Euclid in the Seven Wonders website that is referenced in the Classics Index page, under the heading Pharos of Alexandria. As is typical of education on the Internet, many sites are poor, repetitive or childish, however.
Untitled 180 hypsicles 360 DEGREE CIRCLE. 150 PERSEUS SPIRES. -140 HIPPARCHUS TRIGONOMETRY.-60 GEMINUS ON THE PARALLEL POSTULATE. +75 HERON OF alexandria. http://www.erols.com/bram/timeline.html
Extractions: CHRONOLOGY OF MATHEMATICIANS -1100 CHOU-PEI -585 THALES OF MILETUS: DEDUCTIVE GEOMETRY PYTHAGORAS : ARITHMETIC AND GEOMETRY -450 PARMENIDES: SPHERICAL EARTH -430 DEMOCRITUS -430 PHILOLAUS: ASTRONOMY -430 HIPPOCRATES OF CHIOS: ELEMENTS -428 ARCHYTAS -420 HIPPIAS: TRISECTRIX -360 EUDOXUS: PROPORTION AND EXHAUSTION -350 MENAECHMUS: CONIC SECTIONS -350 DINOSTRATUS: QUADRATRIX -335 EUDEMUS: HISTORY OF GEOMETRY -330 AUTOLYCUS: ON THE MOVING SPHERE -320 ARISTAEUS: CONICS EUCLID : THE ELEMENTS -260 ARISTARCHUS: HELIOCENTRIC ASTRONOMY -230 ERATOSTHENES: SIEVE -225 APOLLONIUS: CONICS -212 DEATH OF ARCHIMEDES -180 DIOCLES: CISSOID -180 NICOMEDES: CONCHOID -180 HYPSICLES: 360 DEGREE CIRCLE -150 PERSEUS: SPIRES -140 HIPPARCHUS: TRIGONOMETRY -60 GEMINUS: ON THE PARALLEL POSTULATE +75 HERON OF ALEXANDRIA 100 NICOMACHUS: ARITHMETICA 100 MENELAUS: SPHERICS 125 THEON OF SMYRNA: PLATONIC MATHEMATICS PTOLEMY : THE ALMAGEST 250 DIOPHANTUS: ARITHMETICA 320 PAPPUS: MATHEMATICAL COLLECTIONS 390 THEON OF ALEXANDRIA 415 DEATH OF HYPATIA 470 TSU CH'UNG-CHI: VALUE OF PI 476 ARYABHATA 485 DEATH OF PROCLUS 520 ANTHEMIUS OF TRALLES AND ISIDORE OF MILETUS 524 DEATH OF BOETHIUS 560 EUTOCIUS: COMMENTARIES ON ARCHIMEDES 628 BRAHMA-SPHUTA-SIDDHANTA 662 BISHOP SEBOKHT: HINDU NUMERALS 735 DEATH OF BEDE 775 HINDU WORKS TRANSLATED INTO ARABIC 830 AL-KHWARIZMI: ALGEBRA 901 DEATH OF THABIT IBN - QURRA 998 DEATH OF ABU'L - WEFA 1037 DEATH OF AVICENNA 1039 DEATH OF ALHAZEN
Appariement De Unesco 3 Translate this page know that Archimedes was the son of an astronomer, that hypsicles' father was we knowanything much, was the daughter of the mathematician Theon of alexandria. http://www-rali.iro.umontreal.ca/TrialDir/corpus/Unesco3.fr-en.ref.html
Extractions: The very words " mathematics " and " mathematician ", or their equivalents in most European languages, are derived from the Greek word meaning " to know " or " to learn ", Before the classical era, however, when it took on the specialized meaning that it has today, the Greek word mathema meant " that which is taught ", in other words all branches of knowledge.
Diophantus know that he quotes the definition of a polygonal number from the work of hypsicles must have written this later than 150 BC -Theon of alexandria quotes one http://www.saintjoe.edu/~ace2561/Diophantus.html
Diophantus narrowed down to a span of 500 years based on the use of a definition of a polygonalnumber from the work of hypsicles and from Theon of alexandria quoting one http://www.saintjoe.edu/~shf3124/diophantus.html
Extractions: The presentation given by A.J. Claussen and Adam Whitehouse on February 7, 2002 was titled End of the Golden Age of Greek mathematics: Diophantus. During the presentation, information about Diophantus and his discoveries was presented. There was also a hands-on activity to enhance the presentation with also the use of the overhead projector. Diophantus of Alexandria lived around the time of 200 during the "Silver Age." He is known as the 'father of algebra' or the "The Greek Father of Algebra". There is much debate regarding the date at which he lived. It can be narrowed down to a span of 500 years based on the use of a definition of a polygonal number from the work of Hypsicles and from Theon of Alexandria quoting one of Diophantus's definitions. There is a famous riddle of Diophantus that proves that he died at the age of 84 and his son died at age 42, four years after his father. Diophantus wrote three books including On Polygonal Numbers Porisms , and Arithmetica. Arithmetica is considered to be the most outstanding work on algebra in Greek mathematics. It is a collection of 130, 189 or 150 problems based on different sources.
Extractions: Get a Search Engine For Your Web Site Table of Contents I Introduction II Helenism in Asia 1. Hellenization of Syria 2. The Frontier Provinces 3. Foundation of Jundi-Shapur 4. Diocletian and Constantine III The Legacy of Greece 1. Alexandrian Science 2. Philosophy 3. Greek Mathematicians 4. Greek Medicine IV Christianity as a Hellenizing Force 1. Hellenistic Atmosphere of Christianity 2. Expansion of Christianity 3. Ecclesiastical Organization V The Nestorians 1. First School of Nisibis 2. School of Edessa 3. Nestorian Schism 4. Dark Period of the Nestorian Church 5. The Nestorian Reformation VI The Monophysites 1. Beginning of Monophysitism
How Greek Science Passed To The Arabs The complete curriculum of the medical school of alexandria was thus made Luqa alBa'lbakki,a Syrian Christian, who translated hypsicles, Theodosius' Sphaerica http://www.aina.org/aol/peter/greek.htm
Greek Democracy of Pontus Heron, Hipparchus Hippias Hippocrates Hypatia hypsicles Leucippus Marinusof Ptolemy Serenus Simplicius Thales Theodosius Theon of alexandria Theon of http://lilt.ilstu.edu/connections/greek_democracy.htm
Extractions: The Democratic foundation established by the ancient Greeks Abstract: Our integrated project blends the subjects of math and history. Since two of our group members never bothered to show up these are the only two subjects we will be covering, with the two history majors focusing on religion and government respectively. The math portion will focus on famous Greek mathematicians. With the help of a special education major, we will alter the plan to cater to the needs of special needs students. I plan to use the week to explain how the ancient Greeks introduced a democratic form of government. This was a revolutionary form of rule in a world of dictators and tyrants. Throughout the week the class will learn about the origins of Greek democracy and its prominent figures. We will then compare and contrast the Greek form of democracy to the one used in our own government. We will also be discussing the possible reasons why democracy failed in Greece and if it seems possible for the United States to suffer the same fate. Names and Majors of the Team Members: Subjects Integrated: Objectives: Upon completion of this lesson, participating students will be able to note five key similarities between the ancient Greek democracy and the democracy of the United States.
Loq-Man Translations of Mesopotamia, Syria, Palestine and Egypt, until I reached alexandria, but I alBa'lbakki,a Syrian Christian, who translated hypsicles, Theodosius' Sphaerica http://www.loqmantranslations.com/ArabicFacts/ArabTranslators.html
Extractions: Consulting Translators Contact Us Abu Zayd Hunayn ibn Ishaq al-Ibadi (808 - 873) Hunayn ibn Ishaq is most famous as a translator. He was not a mathematician but trained in medicine and made his original contributions to the subject. However, as the leading translator in the House of Wisdom at one of the most remarkable periods of mathematical revival, his influence on the mathematicians of the time is of sufficient importance to merit his inclusion in this archive. His son Ishaq ibn Hunayn, strongly influenced by his father, is famed for his Arabic translation of Euclid's Elements. Hunayn's father was Ishaq, a pharmacist from Hira. The family were from a group who had belonged to the Syrian Nestorian Christian Church before the rise of Islam, and Hunayn was brought up as a Christian. Hunayn became skilled in languages as a young man, in particular learning Arabic at Basra and also learning Syriac. To continue his education Hunayn went to Baghdad to study medicine under the leading teacher of the time. However, after falling out with this teacher, Hunayn left Baghdad and, probably during a period in Alexandria, became an expert in the Greek language. Hunayn returned to Baghdad and established contact with the teacher with whom he had fallen out. The two became firm friends and were close collaborators on medical topics for many years.
Home Introduction Romans Early Christianity Greek Mythology Other of Emesa(871) No year; Hephaeston(874) No year; Hephaeston of alexandria(874) No 2022)year 100 AD; Hyginus(2021) No year; Hyginus(2023) No year; hypsicles(887) No http://education.domaindlx.com/history/Descrpt.asp?Desc=AU
Who Was Who In Roman Times: List By Function, Results Hephaeston of alexandria(874) No year; Heraclides(2008) No year; Heraclides PonticusMinor year; Hyginus(2022) year 100 AD; Hyginus(2021) No year; hypsicles(887) No http://www.romansonline.com/Descrpt.asp?Desc=AU
Extractions: ÅëëçíéêÜ âéâëßá êáé CD! Êáôá÷ùñçóç site Add URL Ôñïðïðïéçóç site ... Bïçèåéá! (ãéÜ üëïõò ôïõò browser) New! Té Íåï Õðáñ÷åé Cool Sites Ôõ÷áéï Link www.argo.ac: Categories Áíáíåùèçêå: 20-Mar-2003- Links: Ancient Greek Science - "Philosophy 6396, Spring 1997; 2:30-5:30 P.M. Wednesdays, 512 Agnes Arnold Hall Dr. Cynthia Freeland, 743-2993, cfreeland@uh.edu, 402 AH. This course..." pop (Added: 21-Oct-1999 Hits: 1004 Rating: 8.00 Votes: 1) Rate It
Euclid (c. 300 BC) Library Of Congress Citations by hypsicles and book XV, the work of a Roman landsurveyor of References gEgyklidEvklid Euclid, of alexandria Uqleidis Euklid Eukleidees nna Euclides Notes http://www.mala.bc.ca/~mcneil/cit/citlceuclid.htm
Extractions: The Little Search Engine that Could Down to Name Citations LC Online Catalog Amazon Search Book Citations [First 20 Records] Author: Byrne, Oliver. Title: The first six books of the elements of Euclid, in which coloured diagrams and symbols are used instead of letters for the greater ease of learners. By Oliver Byrne ... Published: London, W. Pickering, 1847. Description: xxix, 268 p. col. illus. 25 cm. LC Call No.: QA451 .B99 Subjects: Euclid. Elements. Control No.: 03019358 //r84 Author: Euclid. Uniform Title: Elements. French Title: Les belbemens de gbeombetrie d'Euclide, traduits littberalement, et suivis d'un traitbe du cercle, du cylindre, du ccone et de le sphaere, de la mesure des surfaces et des solides, avec des notes. Edition: 2. bed., augm. du cinquiaeme livre, par F. Peyrard ... Ouvrage approvbe par l'Institut, et adoptbe par le gouvernement pour les bibliothaeques des lycbees ... Published: Paris, F. Louis, 1809. Description: xii, 578 p. 270 diagr. on 9 fold. pl. 20 cm. LC Call No.: QA31 .E8755 1809 Other authors: Peyrard, F. (Franpcois), 1760-1822, ed. Control No.: 03020858 //r90 Author: Rabinovitch, Israel Euclid, b. 1861. Title: The foundations of the Euclidian geometry as viewed from the standpoint of kinematics ... by Israel Euclid Rabinovitch ... Published: New York, The author, 1903. Description: xi, 116 p. diagrs. 23 cm. LC Call No.: QA681 .R14 Notes: Thesis (Ph.D.)Johns Hopkins university. "Autobiography." "List of works quoted in the introduction or consulted by the author in preparing the dissertation": p. x-xi. Subjects: Geometry Foundations. Control No.: 04001882 //r882
DIPT:- Alif hypsicles Greek mathematician Founded by Ammonius Saccas (Amuniyus, qv) in the secondcentury CE in alexandria, ending with Proclus (Buruqlus, qv) in the 5 th http://www.muslimphilosophy.com/pd/d-1.htm
Extractions: - Alif ibtihaj Frui or to enjoy God, i.e. to have the bliss and beatitude of the experience of the Divine. abad Eternal a parte post, i.e. eternal without end as opposed to azal (q.v.), eternal a parte ante, i.e. eternal without beginning. Sometimes used synonymous with dahr (q.v.), i.e. time in the absolute sense. According to the philosophers the two terms abad and azal imply each other an the world is both pre-eternal and post-eternal, a view very seriously challenged by the orthodox (notably by Imam Ghazali ) for according to them God alone is abadi and azali Creation from absolute nothingness; to be distinguished from the cognate terms khalq takwin and ihdath , all of which presuppose the temporal priority of cause to effect. In there is no priority of cause to effect; there is only priority in essence so that effect comes to be after not-being with a posteriority in essence. again is of higher order than ihdath or takwin in so far as it signifies granting existence without an intermediary, be it time, or motion, or matter one or other of which is necessarily presupposed in ihdath and takwin . Further is specific to the creation of intelligences
Pedro Nunes, 1502-1578: Fontes: Outras Translate this page autor pouco mais se sabe além de que ensinou em alexandria, onde terá não sãodevidos a Euclides o livro XIV, devido a hypsicles (provavelmente, século http://bnd.bn.pt/ed/pedro-nunes/obras/fontes-p-nunes/pn_fontes_outras_37.asp
Diophantus citeaza definitia numarului poligonal din lucrarea lui hypsicles deci trebuie safi scris dupa 150BC. Pe de alta parte Theon din alexandria tatal Hypetyei http://www.liis.ro/html/pages/MateWeb/13.htm
Extractions: Decedat: probabil 284 Sunt citeva limite care pot fi puse vietii lui Diofand. Pe de o parte Diofand citeaza definitia numarului poligonal din lucrarea lui Hypsicles deci trebuie sa fi scris dupa 150BC. Pe de alta parte Theon din Alexandria tatal Hypetyei citeaza una dintre definitiile lui Diofand, asta insemnand ca acesta nu a scris mai tarziu de 350AD. Oricum asta lasa o diferenta de 500ani deci nu putem limita prea mult datele lui Diofand dupa aceste informatii. Mai exista o informatie care a fost accptata multi ani ca data exacta. Heath [3] citeaza dintr-o scrisoare a lui Michael Psellus care a trait in ultima jumatate a secolului XI. Psellus scrie: Diofand se ocupa cu [aritmetica egipteana] mai multa acuratete, dar invatatul Anatolius aduna cele mai esentiale parti ale doctrinei stabilita de Diofand intr-un mod diferit si in cea mai succinta forma, dedicindu-si munca lui Diofand Psellus mai descrie in scrisoare faptul ca Diphantus da nume puterilor necunescutelor, diferite de cele ale egiptenilor. Aceasta scrisoare a fost mai intii publicata de Paul Tannery[7] si crede ca Psellus citeaza dintr-un comentariu despre Diofand care acum este pierdut si a fost scris probabil de Hypatia. Oricum citatul de mai sus a fost folosit pentru a-l data pe Diofand,folosind teoria ca Anatolius care este mentionat aici este episcopul din Laodicea care a fost un scriitor si profesor de matematica care a trait in secolul III.S-a dedus ca Diofand a scris in jurul anului 250AD si datele sale sunt bazate pe acest argument. Knorr[16] critica aceasta interpretare:
Extractions: Ninth century Euclid's Elements, written about 300 B.C., a comprehensive treatise on geometry, proportions, and the theory of numbers, is the most long-lived of all mathematical works. This manuscript preserves an early version of the text. Shown here is Book I Proposition 47, the Pythagorean Theorem: the square on the hypotenuse of a right triangle is equal to the sum of the squares on the sides. This is a famous and important theorem that receives many notes in the manuscript. Archimedes, Works ca. 1458 In the early 1450s, Pope Nicholas V commissioned Jacobus de Sancto Cassiano Cremonensis to make a new translation of Archimedes with the commentaries of Eutocius. This became the standard version and was finally printed in 1544. This early and very elegant manuscript may have been in the possession of Piero della Francesca before coming to the library of the Duke of Urbino. The pages displayed here show the beginning of Archimedes' On Conoids and Spheroids with highly ornate, and rather curious, illumination.
