21. Biyografiler Abu Sahl Ibn Rustam *Blaise Pascal. *Abu Said Ibn Muhammed *Brahmagupta. *AdrienMarie Legendre *callippus. *Ahmes *CF.Gauss. *Ahmet Cemal Eringen *Chrysippus. http://www.sanalmatematik.com/d/mb1.html

s a n a l m a t e m a t i k c o m kütüphane e -test yazýlar yarýþma ... linkler Matematikçi Biyografileri - 1 1.sayfa 2.sayfa 3.sayfa 4.sayfa ... sonraki sayfa

22. Callippus callippus of Cyzicus. Born about 370 BC in Cyzicus, Asia Minor (now Turkey) Diedabout 310 BC in Not known. We know that callippus was a student of Eudoxus. http://sfabel.tripod.com/mathematik/database/Callippus.html

Callippus of Cyzicus Born: about 370 BC in Cyzicus, Asia Minor (now Turkey) Died: about 310 BC in Not known Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page The dates given for his birth and death are guesses but Callippus of Cyzicus is known to have been working with Aristotle in Athens starting in 330 BC. We know that Callippus was a student of Eudoxus . We also know that he made his astronomical observations on the shores of the Hellespont, which can be deduced from the observations themselves. Callippus made accurate determinations of the lengths of the seasons and constructed a 76 year cycle to harmonise the solar and lunar years which was adopted in 330 BC and used by all later astronomers. The Callippic period is based on the Metonic period devised by Meton (born about 460 BC). Meton's observations were made in Athens in 432 BC but he gave a length for the year which was 1/76 of a day too long. The relation between Callippus's period and that of Meton are explained in [Encyclopaedia Britannica] as follows:- Callippus of Cyzicus (c. 370-300 BC) was perhaps the foremost astronomer of his day. He formed what has been called the Callippic period, essentially a cycle of four Metonic periods. It was more accurate than the original Metonic cycle and made use of the fact that 365.25 days is a more precise value for the tropical year than 365 days. The Callippic period consisted of 4 X 235, or 940 lunar months, but its distribution of hollow and full months was different from Meton's. Instead of having totals of 440 hollow and 500 full months, Callippus adopted 441 hollow and 499 full, thus reducing the length of four Metonic cycles by one day. The total days involved therefore became (441 X 29) + (499 X 30), or 27,759, and 27,759 / (19 X 4) gives 365.25 days exactly. Thus the Callippic cycle fitted 940 lunar months precisely to 76 tropical years of 365.25 days.

23. Untitled Document The Mathematican callippus and the Addition of Spheres. callippusof Cyzius, Asia Minor born 370 BCE ; died 310 BCE. The lineage of http://panther.bsc.edu/~shagen/STUDENT/Cosmo/history/Callippus.htm

The Mathematican Callippus and the Addition of Spheres Callippus of Cyzius, Asia Minor born 370 BCE ; died 310 BCE The lineage of spheres and planetary systems as well the development of medieval cosmology continues with the influence of Callippus. Callippus was taught by Polemarchus in the School of Eudoxus and went to Athens to work with Aristotle circa 330 BCE. Callippus' most major contributions to mathematics included the determination of the lengths of the seasons the development of what was later called Callipic period, a period "that made use of the fact that 365.25 days is a more precise value for the tropical year than 365 days ("MacTutor of History of Mathematics"). Applying these calculations to the study of the motion of heavenly bodies, Callippus took the sphere theories of Eudoxus. His addition of six spheres increased the accuracy of Eudoxus theory while preserving the belief that heavenly bodies moved in circular, and therefore, paths ("MacTutor" ). By Callippus' reckoning, the Sun, Moon, Mercury, Venus and Mars each had five spheres; Jupiter and Saturn each had four; and the stars had one sphere. Callippus theory of concentric spheres remained basically intact until replaced by Ptolemy's epicycle theories and his collaboration and influence on Aristotle is unmistakable.

24. Untitled Document And, of course, Aristotle was familiar with the system of concentric spheresby which Eudoxus and callippus accounted theoretically for the independent http://panther.bsc.edu/~shagen/STUDENT/Cosmo/history/aristotle.htm

"And, of course, Aristotle was familiar with the system of concentric spheres by which Eudoxus and Callippus accounted theoretically for the independent motions of the sun, moon, and planets." Medieval cosmology takes most of its history and scientific heritage from the works of Aristotle, who inherited the framework of his theories from the mathematicians who were his peers and predecessors in the examination of terrestrial and celestial bodies. The works of Aristotle are littered with reflections on issues that would later become so relevant in cosmology the existence and substance of the spheres, as well as the motion of bodies and the causes of that motion. On the Heavens and Physics offer the most material (Grant Physical Science 37), and arguably the most comprehensive, but discussion of cosmological topics also appears throughout Metaphysics. Most simply, Aristotle divided the cosmos into two distinct parts: the terrestrial, or sublunar region, and the celestial, or supralunar region (Grant Physical Science 37). His reckoning suggested that all parts of the sublunar regions were composed of one of the four elements, air, fire, water, and earth, while all celestial bodies were composed of a fifth element, aether (37). Aristotle also hypothesized four types of possible change in the terrestrial universe: change in position (motion), change in substance, change in quality, and change in number, or the increase or decrease of a thing's quantity (36). Celestial bodies appeared impervious to all these types of change, except for change in motion (37). The theories of spheres presented by the mathematicians provided a working model to account for the movement of heavenly bodies and Aristotle's study of motion led him to expand the theories of spheres.

25. Untitled The Homocentric Spheres of Eudoxus, callippus, and Aristotle (NoteThis site is under construction last updated on 30 July 99). http://www.ouc.bc.ca/phys/dkay/eudoxus.htm

The Homocentric Spheres of Eudoxus, Callippus, and Aristotle (Note: This site is under construction last updated on 30 July 99) Ever since the publication of the Principia by Isaac Newton in 1687 one of the principal goals of physics has been the construction of mathematical models to describe how nature works. However, this idea did not originate with Newton. The most famous earlier examples are the laws of planetary motion of Johannes Kepler (1571 - 1630) and the planetary systems of Claudius Ptolemy (2nd century A.D.) and Nicolas Copernicus (1473 - 1543). As Copernicus drew on the methods of Ptolemy, so too did Ptolemy draw on earlier work, particularly that of Apollonius of Perga and Hipparchus of the third and second centuries B.C., respectively. However, the original mathematical model of the cosmos was developed in the fourth-century by the geometer Eudoxus of Cnidus (ca. 400 -347 B.C.). His geometrical model for describing the motions of the planets has come to be known as the Homocentric Spheres. By the beginning of the fourth century B.C. the most widely held view of the universe was that it consisted of a spherical earth at rest in the center of a rotating "celestial sphere" carrying the fixed stars. The planets moved in the region between these two spheres. Outside the sphere of stars was nothing, not even space. The complete celestial catalog was short. There were the fixed stars, and seven "wanderers", the planets Sun, Moon, Mercury (Hermes), Venus (Aphrodite), Mars (Ares), Jupiter (Zeus), and Saturn (Kronos).

26. OUC, Department Of Physics And Astronomy Teaching I teach physics and work at the North Kelowna Campus. My Links.The Homocentric Spheres of Eudoxus, callippus, and Aristotle. http://www.ouc.bc.ca/phys/dkay.html

Home Faculty Select a Page Home Faculty Timetables Daniel Kay Office: Science 260 - North Kelowna Campus Phone: (250) 762-5445 Local 7510 (Kelowna) Address: 3333 College Way Okanagan University College Kelowna, B.C., Canada, V1V 1V7 E-Mail: dkay@ouc.bc.ca Timetable: Fall Timetable Winter Timetable Education: B.Sc., M.Sc., Ph.D. (SFU). Research Interest: Teaching: I teach physics and work at the North Kelowna Campus My Links The Homocentric Spheres of Eudoxus, Callippus, and Aristotle. Faculty of Science Home OUC Home Send feedback about this web-page

27. Perseus Update In Progress Aristotle, like Eudoxus and callippus before him, believed that eachplanet followed the path laid out by a certain number of spheres. http://www.perseus.tufts.edu/GreekScience/Students/Tom/AristotleAstro.html

The Perseus Digital Library is Being Updated Notice The main Perseus web site (at Tufts) is unavailable from 5:00 to 6:00, US Eastern time, in order to rebuild its databases with new or changed meta-data. We apologize for this inconvenience.

28. Summary Theoretical interests in the lengths of the lunar month and solar year beginin 430s (Meton, Euctemon) and continue with callippus (-340), but the http://www.ihns.ac.cn/zhkezh/summaryen.htm

Introduction Geoffrey Lloyd ½ÌÊÚ½éÉÜ Seminar I The Goals of Astronomy In this seminar I shall follow up in greater detail some of the topics raised in my Zhu Kezhen lecture. Astronomy is a field Where we can say that in some sense the phenomena that were there to be investigated (whether by the Chinese or the Greeks) were the same. The questions are: what problems were the Chinese on the one hand, the Greeks on the other, mainly interested in? How did they set about tackling them? In what institutional circumstances did the astronomers work? How were they recruited, how did they earn a living? What were their fundamental aims? I shall concentrate first on three subject-areas, before turning to institutional aspects and aims CALENDARS Regulating the calendar was a key concern of Chinese astronomy from earliest times. The ruler/emperor was responsible for promulgating the calendar, in which changes would be introduced either for political purposes (e. g. at a change of dynasty) or when the calendar got out of step with the seasons. In Greece each city-state had its own luni-solar calendar, with different officials in different states deciding when the new moon was visible, when intercalations were necessary, etc. Theoretical interests in the lengths of the lunar month and solar year begin in -430s (Meton, Euctemon) and continue with Callippus (-340), but the implementation of their results was half-hearted. A uniform calendar was only introduced at the start of the period of Roman domination, as the result of the work of Julius Caesar (-46)

29. Eclipses 441 Monate von 29 Tagen Wenn wir den Durchschnitt der Monatslängen dieser drei Systemeberechnen erhalten wir Meton 29,531915 Sonnentage callippus 29,530851 http://www.specialtyinterests.net/eclipse.html

Main Menu Perpetual Calendar The Medicin Man's Secret and Eclipses in Egypt Any published dates for eclipses in ancient times are only so good as the software is which calculated them! Alle veröffentlichten Daten für Finsternisse sind nur so gut wie die Komputerprogramme, die sie erechneten! In Deutsch He was the most powerful and feared man around. People said the gods spoke to him, - and when they did, watch out, the next victim could be you or someone dear to you. Medicin man or shahmans often had an aura of secrecy about them which was designed to instill this fear among their people that way they could at particular times exercise their mystical powers and prove once more that they held the secret to the very existence to their nation. How did they do it? Because medicin man and shamans, witch doctors, had learned to predict when lunar or solar eclipses would take place, this ability made it appear that they had communications with the gods and acted in their behalf. And there is no doubt that they used this learned wisdom to their own advantage to enrich themselves and cause the people in dramatic ways, often requiring human sacrifices, to acknowledge their superiority. Even kings and queens had to submit to their influence at times like this. Greek Estimates of the Synodic Month by Livio Stecchini The problem that Meton intended to solve was - which is the smallest number of solar years that can be divided exactly into a series of more or less alternating months of 30 and 29 days? He knew that solar years are about 365.25 days and that a lunar month is about 29.5 days. He counted that 19 solar years are:

30. The Parthasarathi Swami Column Surfing the net By Parthasarthi Swami 1 DECEMBER 2000 WHEN callippus OF ATHENS FIXEDAN OLYMPIC MATCH There are lots of sites claiming to give inside dope on http://www.india-syndicate.com/int/ps/1dec00.htm

Surfing the net By Parthasarthi Swami 1 DECEMBER 2000 WHEN CALLIPPUS OF ATHENS FIXED AN OLYMPIC MATCH There are lots of sites claiming to give inside dope on match-fixing. But many of them have run of steam, says Parthasarathi Swami . Anyway, match-fixing is as old as the world's oldest profession It's not cricket to hit a man when he is down. When cricket itself is taking a beating in the wake of the match-fixing scam, it shouldn't really be given the stick. But on the Internet, everything goes. There are hundreds of thousands of articles on match fixing and the message boards have been buzzing with the foul deeds of the flannelled fools. But the many specific sites that threatened to come up on the subject seem to have run out of steam. The domain name matchfix.com was bought up by a London-based organisation early this year, but they have not done anything about it so far. Cricket$cam.com ( http://www.cricketscam.com

31. Internet And Computer World - Updates And Analysis - Content Providers Internati There are still some beauty contests that Indians haven't won, says ParthasarathiSwami When callippus Of Athens Fixed An Olympic Match There are lots of sites http://www.india-syndicate.com/int/ps/ps.htm

Surfing The Net By Parthasarthi Swami The Merry Month of May Though trade unionists may disagree, Parthasarathi Swami discovers that there’s more to May than May Day. Bread Is Not Only For Eating Going by sites on the subject, there's more to bread white, brown or dusty potato than you can imagine discovers Parthasarathi Swami Tic-Tac-Toe My foot ! may be your natural reaction, says Parthasarathi Swami, but don't miss this tour on toes. Recipes for Disaster Some sites provide food for thought, others are simply recipes for disaster, says Parthasarathi Swami. Hate Male and Other 'War' Sites Parthasarathi Swami takes an on-line look at strange gender wars I Spy, You Spy Want to experience a tehelka? Check out these webcams with Parthasarathi Swami Love A Little, Live A Little

32. Ethics Of Philip, Demosthenes, And Alexander By Sanderson Beck A former student of Plato named callippus swore by the great goddesses Demeterand Persephone that he had no evil intentions against Dion, but during the http://www.san.beck.org/EC22-Alexander.html

33. Aristotle's Cosmos callippus (b. ca. Aristotle improves on callippus by including additionalspheres to counteract some of the motions of the planetary spheres. http://ls.poly.edu/~jbain/mms/handouts/mmstotle.htm

Return to HU 341 homepage Return to HU 341 syllabus Aristotle's Cosmos *Aristotle, Metaphysics Book XII, Chap 8

34. Did God Say The Earth The Center Of The Universe? earth. Ptolemy based his system on earlier work from Aristotle, whileAristotle built on theories from Eudoxus and callippus. Later http://home.teleport.com/~salad/4god/geo.htm

Did God Say the Earth is the Center of the Universe? Return Note: The above information was written by John P. Boatwright and is freely given. The information is simply my opinion based on how I perceive the content discussed. Anyone reading such should use their own judgement as to whether or not the information has any value to them. You may copy portions of the above opinions as long as a reference to this page is included and no text within said portion is altered. If copied to another medium other than the internet, include the entire text. The above content may change over time. Best wishes.

35. Energy And Matter Aim 1 Space could not be infinite, because in Aristotle's view, adopted from the workof Eudoxus (c. 460 BC c. 370 BC) and callippus (c. 370 BC-c. 300 BC), the http://www.chemcool.com/biography/aristotle.htm

b iography... home Aristotle (384 BC-322 BC) was a Greek polymath, one of the most imaginative and systematic thinkers in history, whose writings embraced virtually every aspect of contemporary thought, including cosmology. Aristotle was born at Stagirus, a port on the Chalcidic peninsula of Macedonia, in 384 BC. His father, Nichomachus, was court physician to Amyntas III (sometimes called Amyntas II), King of Macedonia, and it seems probable that he introduced Aristotle to the body of medical and biological knowledge at an early age. Nichomachus died in Aristotle' s youth and Aristotle was placed in the care of a ward, who sent him to Athens in 367 BC to study at Plato's Academy. Plato's death in 348/347 BC coincided with a wave of anti-Macedonian fervour in Athens, a combination of events which induced Aristotle to leave the city and go on an extensive tour of Asia Minor, where for the first time he engaged in a serious study of natural history. In 342 BC King Philip II invited Aristotle to the Macedonian court to become tutor to the crown prince, the future Alexander the Great. Shortly after Alexander came to the throne in 336 BC

36. Lunar Cycles Callipic cycle of 76 years, or 940 lunations, or 27,759 days, or in other words4 Metonic cycles, was introduced by the Greek astronomer callippus of Cyzicus http://www.sizes.com/time/lunar_cycles.htm

lunar cycles The amount of time that must pass before the phases of the moon fall again on the same days that they do in the present year. Neither the tropical year nor the synodic month are a whole number of days. Not only that, but they have no common factor. If there were a whole number X such that dividing the number of days in X tropical years by the number of days in a synodic month left no remainder, then the phases of the moon would fall on the same days of the year as they had X years before. Actually, there is always a remainder, but historically several approximations have proven useful in making calendars that predict the phases of the Moon. Metonic cycle The Metonic cycle of 19 years, or 235 lunations, or 6,940 days. Although known earlier in Babylon and China, the cycle is named for the Greek astronomer Meton ( 5th century bce ), who wrote a book titled Enneadecaterides on the cycle. (Meton is also remembered for pretending insanity to avoid "the draft," having foreseen that the Athenian attack on Syracuse would end in disaster.) Taking the length of the tropical year and synodic month in Meton’s time

37. Addenda & Corrigenda To TLG Canon, 3rd Edition Cod Hymn. callippus Comic. (0427 In 002, change breakdown to read Dup. 227,vv.57). callippus Hist. (2270) In 001, add cross-reference to read Cf. http://www.tlg.uci.edu/A&C.html

The TLG Canon Addenda and Corrigenda to the TLG Canon, 3 rd edition NOTE: The following addenda and corrigenda are provided for quick reference. The format of this document does not allow for the Greek fonts used in the Thesaurus Linguae Graecae Canon of Greek Authors and Works , third edition, by Luci Berkowitz and Karl A. Squitier (New York and Oxford: Oxford University Press, 1990). Those who wish to obtain a copy of these addenda and corrigenda, formatted to concur with TLG Canon, 3rd edition, should contact the Thesaurus Linguae Graecae Changes in Index of Citation Systems ABARIS Hist. (1883): Add square brackets to read [ABARIS] Hist. ADAMANTIUS Scr. Eccl. (2950): Change author epithet to Theol. Also, in 001, change work title to read De recta in deum fide (olim sub auctore Origene Adamantio). AESCHINES SOCRATICUS Phil. (0673): Delete works 002 and 003; substitute new entry for 002 as follows: Fragmenta , ed. L. Rossetti, Corpus dei papiri filosofici greci e latini , vol. 1.1: Autori noti . Florence: Olschki, 1989: 123-128, 135-136, 140-142. fr. 1: Alcibiades (

38. TLGE 2218, Calliphon et Democedes Med. et Phil. 0427, callippus Comic. 2270,callippus Hist. 0534, Callisthenes Hist. 1239, Domitius Callistratus Hist. http://www.tlg.uci.edu/CDROME.html

CD-ROM E Authors Abydenus Hist. Acacius Theol. Acesander Hist. Achaeus Trag. Achilles Tatius Astron. Achilles Tatius Scr. Erot. Gaius Acilius Hist. et Phil. Georgius Acropolites Hist. Acta Alexandrinorum Acta Barnabae Acta Et Martyrium Apollonii Acta Eupli Acta Joannis Acta Justini Et Septem Sodalium Acta Pauli Acta Petri Acta Phileae Acta Philippi Acta Scillitanorum Martyrum Acta Thomae Acta Xanthippae Et Polyxenae Acusilaus Hist. Adamantius Judaeus Med. Adamantius Theol. Adespota Papyracea (SH) Adrianus Rhet. et Soph. Aegimius Claudius Aelianus Soph. Aelianus Tact. Aelius Dius Hist. Aeneas Phil. et Rhet. Aeneas Tact. Aeschines Orat. Aeschines Socraticus Phil. Aeschrion Lyr. Aeschylus Trag. Aeschylus Trag. Aesopus Scr. Fab. et Aesopica Aethiopis Aethlius Hist. Ae+tius Doxogr. Ae+tius Med. Agaclytus Hist. Agamestor Eleg. Agatharchides Geogr. [Agatharchides] Hist. Agathemerus Geogr. Agathias Scholasticus Epigr. et Hist. Agathocles Hist. [Agathodaemon] Alchem. Pseudo- Agathon Epigr. [Agathon] Hist. Agathon Trag. Agathyllus Eleg. Agesilaus Hist. Aglai+s Poet. Med. Agl(a)osthenes Hist. Agroetas Hist.

39. A Smaller History Of Greece By William Smith-Chapter 18 His unpopularity continued to increase, till at length one of his bosom friendstheAthenian callippusseized the opportunity to mount to power by his murder http://www.nalanda.nitc.ac.in/resources/english/etext-project/history/greece/cha

A SMALLER HISTORY OF GREECE By William Smith Project Gutenberg File Converted into HTML pages by Nalanda Digital Library CHAPTER XVIII. HISTORY OF THE SICILIAN GREEKS FROM THE DESTRUCTION OF THE ATHENIAN ARMAMENT TO THE DEATH OF TIMOLEON. The affairs of the Sicilian Greeks, an important branch of the Hellenic race, deserve a passing notice. A few years after the destruction of the Athenian armament, Dionysius made himself master of Syracuse, and openly seized upon the supreme power (B.C. 405). His reign as tyrant or despot was long and prosperous. After conquering the Carthaginians, who more than once invaded Sicily, he extended his dominion over a great part of the island, and over a considerable portion of Magna Graecia. He raised Syracuse to be one of the chief Grecian states, second in influence, if indeed second, to Sparta alone. Under his sway Syracuse was strengthened and embellished with new fortifications, docks, arsenals, and other public buildings, and became superior even to Athens in extent and population. Dionysius was a warm patron of literature, and was anxious to gain distinction by his literary compositions. In the midst of his political and military cares he devoted himself assiduously to poetry, and not only caused his poems to be publicly recited at the Olympic games, but repeatedly contended for the prize of tragedy at Athens. In accordance with the same spirit we find him seeking the society of men distinguished in literature and philosophy. Plato, who visited Sicily about the year 389 from a curiosity to see Mount AEtna, was introduced to Dionysius by Dion. The high moral tone of Plato's conversation did not however prove so attractive to Dionysius as it had done to Dion; and the philosopher was not only dismissed with aversion and dislike, but even, it seems through the machinations of Dionysius, seized, bound, and sold for a slave in the island of AEgina. He was, however, repurchased by Anniceris of Cyrene, and sent back to Athens.

40. Phil./Hist.Chem.380.html Henry Mendell, Handouts on Babylonian mathematics and astronomy, Egyptian mathematics,Eudoxus and callippus Selections from Simplicius, Commentary on http://www.calstatela.edu/faculty/hmendel/Classwork/Phil380/Phil.380.html

Phil./Hist./Chem. 380 Ancient and Modern Science Instructor: Henry Mendell Classroom SH 172 Time MW. 10:50-12:30 Office Telephone email hmendel@calstatela.edu Office Hours (check web site for cancellations) MW 9:30-10:30, 3:10-4:10 (by appointment) Reading Requirements Overview of the course Schedule ... Syllabus in PDF Required Reading: Books Philip Kitcher, Abusing Science (Cambridge: MIT, 1982) G.E.R. Lloyd, Early Greek Science: Thales to Aristotle (New York: W.W. Norton, 1970) G.E.R. Lloyd, Greek Science after Aristotle (New York: W.W. Norton, 1973) Michael Matthews, Scientific Background to Modern Philosophy (Indianapolis: Hackett, 1989) Xeroxes (presently in the packet) Henry Mendell, Handout on Babylonian and Egyptian Mathematics From Hippocrates of Cos. Hippocratic Writings . Trans. E. Chadwick, W.N. Mann et al. Ed. with intro. G.E.R. Lloyd. Harmondsworth: Penguin, 1978. "The Nature of Man," 260-271. "The Sacred Disease," 237-251. From Plato. Republic . Trans. G.M.A. Grube. Revised Reeve. . In Plato, Complete Works (ed. John Cooper; Indianapolis: Hackett, 1997). Republic VI 507B-VII 541B From Plato.

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