Extractions: This article deals with the corpus of diagrams included in Books I-IV of Apollonios of Perga's Conics (ca. 200 B.C.). The original text of these four books has not survived. The Greek as well as the Arabic traditions have handed down to us Eutocius of Ascalon's edition (6th century A.D.), which came with a commentary only preserved by the Greek tradition. After a survey of the usage of construction methods in Greek classical geometry, the author studies diagram practices in the treatise, drawing rules, and the nature of the figures handed down by manuscripts. As far as possible, a distinction between Apollonios's own composition and what must be ascribed to the editor and commentator is drawn. ISSN :
Eutocius Biography of eutocius of ascalon (480540) eutocius of ascalon. Born about 480 in Palestine http://sfabel.tripod.com/mathematik/database/Eutocius.html
Extractions: Previous (Alphabetically) Next Welcome page Eutocius wrote commentaries on 3 works of Archimedes . He also edited and wrote commentaries on the first 4 books of the Conics of Apollonius . The first of his commentaries on Archimedes appears to have been written around 510. Eutocius does not appear to have done any original work. References (4 books/articles) Other Web sites: Library of Congress, USA Previous (Chronologically) Next Biographies Index
History Of Mathematics: Greece of Tralles (dc 534); John Philoponus (c. 520); Isidorus of Miletus(c. 540?); eutocius of ascalon (c. 550?); Isidore of Seville (c. 570 http://aleph0.clarku.edu/~djoyce/mathhist/greece.html
Eutocius eutocius of ascalon. Born about 480 eutocius of ascalon was for along time thought to have been born in 530. It is instructive http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Eutocius.html
Extractions: Eutocius of Ascalon was for a long time thought to have been born in 530. It is instructive to see how this came about for it shows how many pitfalls there are in the study of history. Eutocius wrote commentaries on three works of Archimedes . His commentary on Book II of On the Sphere and Cylinder ends with the statement:- ... the edition was revised by Isidorus of Miletus, the mechanical engineer, our teacher. From this it was thought that Eutocius was a pupil of Isidorus and his dates were deduced from this information. However, further investigation showed that this contradicted other information such the dedications that Eutocius makes in some of his other works. It was then realised that the comment at the end of Eutocius's commentary to Archimedes On the Sphere and Cylinder was inserted by a later editor of the work who was indeed a pupil of Isidorus of Miletus. It is thought that the first of Eutocius's commentaries on Archimedes was written around 510.
Eutocius Biography of Eutocius (480540) eutocius of ascalon. Born about 480 in Ascalon (now Ashqelon), Palestine http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Eutocius.html
Extractions: Eutocius of Ascalon was for a long time thought to have been born in 530. It is instructive to see how this came about for it shows how many pitfalls there are in the study of history. Eutocius wrote commentaries on three works of Archimedes . His commentary on Book II of On the Sphere and Cylinder ends with the statement:- ... the edition was revised by Isidorus of Miletus, the mechanical engineer, our teacher. From this it was thought that Eutocius was a pupil of Isidorus and his dates were deduced from this information. However, further investigation showed that this contradicted other information such the dedications that Eutocius makes in some of his other works. It was then realised that the comment at the end of Eutocius's commentary to Archimedes On the Sphere and Cylinder was inserted by a later editor of the work who was indeed a pupil of Isidorus of Miletus. It is thought that the first of Eutocius's commentaries on Archimedes was written around 510.
Chronology For 500 To 900 About 500 Metrodorus assembles the Greek Anthology consisting of 46 mathematicalproblems. 510 eutocius of ascalon writes commentaries on Archimedes' work. http://www-gap.dcs.st-and.ac.uk/~history/Chronology/500_900.html
E Index Mathematical biographiesE index Euler, Leonhard (4583*). eutocius of ascalon (763). Evans, Griffith (1131*) http://www-groups.dcs.st-and.ac.uk/~history/Indexes/E.html
History Of Mathematics: Chronology Of Mathematicians A list of all of the important mathematicians working in a given century.Category Science Math Mathematicians Directories Zu Chongzhi (Wenyuan) Tsu Ch'ungchih (429-500) *MT; eutocius of ascalon (fl. Eutociusof Ascalon (c. 550?); Liu Zhuo (544-610); Zhen Luan (Shuzun) (fl. http://aleph0.clarku.edu/~djoyce/mathhist/chronology.html
Extractions: Note: there are also a chronological lists of mathematical works and mathematics for China , and chronological lists of mathematicians for the Arabic sphere Europe Greece India , and Japan 1700 B.C.E. 100 B.C.E. 1 C.E. To return to this table of contents from below, just click on the years that appear in the headers. Footnotes (*MT, *MT, *RB, *W, *SB) are explained below Ahmes (c. 1650 B.C.E.) *MT Baudhayana (c. 700) 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) 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
Untitled on Archimedes' proof producing a better appoximation . eutocius of ascalon argued that they both failed to grasp http://dpamuktulum.tripod.com/ArchimedesMethod/ArchiApproPi.pdf
ARCHIMEDES, Opera, Quae Quidem Extant, Omnia... present edition. 'eutocius of ascalon composed his commentaries onthe works of Archimedes early in the sixth century. Although he http://www.polybiblio.com/watbooks/2410.html
Extractions: 'The present edition includes Archimedes' works On the sphere and the cylinder, On the measurement of the circle, On conoids and spheroids, On spirals, On the equilibrium of planes, The sand-reckoner, and On the quadrature of the parabola. The manuscript from which the Greek text was printed, now in Nuremberg, Stadtbibliothek, MS Cent. V app. 12, had been acquired in Rome by the German humanist Willibald Pirckheimer, to whose circle Venatorius belonged. The source of this text was a 9th-century Greek manuscript, now lost but known to scholars as manuscript A, which had been used in the 13th century by William Moerbeke for his Latin translation of the works of both Archimedes and Eutocius. 'The translation printed in the present edition was a new one produced in the 1450s by Jacopo da Cremona, who worked under the auspices of Pope Nicholas V. This was made directly from the text of manuscript A, with consultation of Moerbeke's older Latin version. The Pope sent copies to Nicholas of Cusa, whose work De mathematics complementis was written in response to it, and to Bessarion. Bessarion's manuscript was copied and corrected by Regiomontanus, with reference to a copy of the Greek manuscript A also owned by Bessarion. Regiomontanus, who recognized the mathematical sciences as one of the great creations of the ancient world, praised Archimedes as the pre-eminent mathematician of Antiquity and remarked that the study of his works was and would remain indispensable "even after a thousand centuries". It was Regiomontanus' copy of the corrected Latin version, now Nuremberg, Stadtbibliothek, MS Cent. V 15, that served as the source for the Latin text of the present edition.
Mathematicians Zu Chongzhi (Wenyuan) Tsu Ch'ungchih (429-500) *mt. eutocius of ascalon (fl.c. 480) *SB. Isidorus of Miletus (c. 540?) *SB. eutocius of ascalon (c. 550?). 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
Biography-center - Letter E Eustachi, Bartolomeo www.whonamedit.com/doctor.cfm/1433.html; eutocius of ascalon,wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/Eutocius.html; http://www.biography-center.com/e.html
Extractions: 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 272 biographies Eadred,
History Of Mathematics Text It also contains the critical comments of eutocius of ascalon (early6th Century), In eosdem Archimedis libros commentaria. These http://www.brown.edu/Facilities/University_Library/exhibits/math/textfr.html
Extractions: Brown University Library possess a copy of each sixteenth-century translation of Euclid's Elements of Geometry into a modern language. These vernacular editions, grouped around the first Latin edition of 1482, are displayed in chronological sequence, from 1533 (Greek) to 1594 (Arabic). All copies are opened at Book I, proposition 47, "Pythagoras' Theorem," which asserts: "In right-angled triangles the square of the side opposite the right angle is equal to the sum of the squares of the sides containing the right angle." Most of the translations provide proof of this equation (a + b = c using a geometrical construction known as "the bride's chair." Euclid's Elements of Geometry has been a primary mathematics text for more than two thousand years. It is a compilation of early Greek mathematical knowledge, synthesized and systematically presented by Euclid in ca. 300 BC. Books I-IV are devoted to plane geometry, Book V deals with the theory of proportions, and Book VI with the similarity of plane figures. Books VII-IX are on number theory, Book X on commensurability and incommensurability, Books XI-XII explore three dimensional geometric objects, and Book XIII deals with the construction of the five regular solids. Later non-Euclidian additions include, Book XIV, which is thought to have been contrbuted by Hypsciles (ca. 200 BC), and Book XV, which may have been added by John of Damascus, or by a 6th-century pupil of Isadoros of Miletos.
Greek Mathematics We owe this interpretation to eutocius of ascalon (480540 AD), who wrotethis in his commentary to Archimedes' On the sphere and cylinder. http://members.fortunecity.com/kokhuitan/greek.html
Extractions: The Greeks are responsible for initial explosion of Mathematical ideas. For several centuries, Greek mathematics reign the mathematical world, with great advances in Number Theory, the Theory of Equation, and in particular Geometry. The first great Greek mathematician is Thales of Miletus (624-547 BC). He brought the knowledge of Egyptian Geometry to the Greeks and discovered several theorems in elementary Geometry. He predicted a Solar Eclipse in 585 BC and could calculate the height of a pyramid, as well as how far a ship is from land. One of his pupils, the Greek philosopher, Anaximander of Miletus (610-546 BC), is considered the founder of Astronomy. Perhaps the most prominent Greek mathematicians is Pythagoras of Samos (569-475 BC). His ideas were greatly influenced by Thales and Anaximander. His school of thought practiced great secrecy and he (and his followers, called Pythagoreans) believe everything in the world can be reduced to numbers. This idea stemmed from Pythagoras' observations in Music, Mathematics and Astronomy. E.g. Pythagoras noticed that vibrating strings produce harmonics in which the lengths of the strings are in ratios of whole numbers. In fact, he contributed greatly to the mathematical theory of music. He had the notion of Odd and Even Numbers, Triangular Numbers, Perfect Numbers, etc. In particular, he is well known today for his Pythagoras Theorem. Although this theorem is known to the Babylonians and Chinese long before Pythagoras, he seemed to be the first person to provide a proof of it.
Gadara Home Page pupil, the mathematician Sporus (c. 200 AD), were said to have improved on Archimedes'proof producing a better appoximation, eutocius of ascalon argued that http://research.haifa.ac.il/~mluz/gadara.folder/gadara2.html
Extractions: Ancient Gadara City of Philosophers Index Introduction Cynics of Gadara Other philosophers Rhetoricians of Gadara other Gadarans Roman Inscriptions and papyri the Byzantine baths the Byzantine synagogue Introduction I have often been asked, Why Gadara City of Philosophers? and why a picture (117K) of the late Greco-Roman entrance to its baths on my welcome page? The answer is quite simple: ancient Gadara (Hebrew: Gader) was the birthplace of three famous Cynic philosopher- satirists, one famous Epicurean philosopher-poet, two important rhetoricians and one famous mathematician In addition, a famous neo-Platonic philosopher once taught in its baths of Hammat-Gader. there are also indications of popular poets, charmers and witches from this city mentioned in various ancient inscriptions and papyri. We also know of an active Jewish community in the area from synagogue inscriptions of the Byzantine era. Finally, recent excavations have uncovered some important Christian inscriptions concerning the baths (el-Hameh) at Hammat-Gader, including a short epic poem in praise of its hot springs apparently written by the
History Of Computation - Prehistory Article summarizing and illustrating early methods of counting and representing of numbers.Category Science Math History Other incidences of the use of abaci in late Greek culture are eutocius of ascalon'scomputation of (30133/4)^2; references in the surviving speeches of the http://www.csc.liv.ac.uk/~ped/teachadmin/histsci/htmlform/lect2.html
Extractions: Although the computer and its widespread application in our society, are phenomena that have become predominant in only the last 30 years, many of the concepts underlying these developments have their origins in concerns dating back to the earliest cultures. Computers manipulate data (Latin, plural of datum , neut. p.p. dare , cognate Sanskrit, datta : those things which have been given), i.e. process and transform given representations of information in order to obtain a desired result. Within this basic description of computer behaviour we can discern two fundamental ideas: A symbolic encoding of information provides a vehicle for communication - information can be passed on in a commonly understood form. A record of the process by which the representation is transformed allows the calculation process to be carried out repeatedly on different sets of data, e.g. we have all learned the steps needed to determine the result of multiplying any two large numbers. One might ask, however, why, given a system for encoding information and the sequence of steps needed to manipulate this to a specific end, it should be necessary to seek
Stdin: [HM] The History Of Horn Angles (3/4) This might relate to Eudoxus's solution of the problem of the two mean proportionalsas we hear of it from eutocius of ascalon (c. 530 AD) (Knorr 1986, pp.5261 http://sunsite.utk.edu/math_archives/.http/hypermail/historia/dec99/0227.html
Virtual Encyclopedia Of Mathematics paul eratosthenes of cyrene erdélyi arthur esclangon ernest benjamin euclid of alexandriaeudoxus of cnidus euler leonhard eutocius of ascalon evans griffith http://www.lacim.uqam.ca/~plouffe/Simon/supermath.html
OPE-MAT - Historique Translate this page du Bois-Reymond, Paul Eudoxus of Cnidus Delsarte, Jean du Val, Patrick Euler, LeonhardDemocritus of Abdera Dudeney, Henry eutocius of ascalon Denjoy, Arnaud 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
Mathem_abbrev Elliott, Edwin Eratosthenes of Cyrene Erdös, Paul, Euclid of Alexandria Eudemusof Rhodes Eudoxus of Cnidus Euler, Leonhard eutocius of ascalon Ezra, Abraham. 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.
