1. TMTh:: XENOCRATES OF CHALCEDON Notes on his life and mathematical achievements. http://www.tmth.edu.gr/en/aet/1/98.html

Home Ancient Greek Scientists AGRICULTURALISTS ARCHITECTS ... PHYSICISTS MATHEMATICIAN, ASTRONOMER XENOCRATES OF CHALCEDON (fl. 397 - 314 BC) Life Work Xenocrates' writings are lost except for fragments. He is cited by Stobaeus; and Diogenes Laertius, in his biography, provides the following list of his works: "On logic": 9 books. "On mathematics": 6 books. "On the theory of numbers" "On intervals" "On astrology": 6 books. "On geometry": 5 books. History of geometry. "On the teachings of Pythagoras" "On learning" "On physics": 6 books. Contact the Technology Museum

2. Xenocrates xenocrates of chalcedon. Born xenocrates of chalcedon was a studentof Plato who entered the Academy in Athens in about 376 BC. In http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Xenocrates.html

Xenocrates of Chalcedon Born: Died: 314 BC in Athens, Greece Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Xenocrates of Chalcedon was a student of Plato who entered the Academy in Athens in about 376 BC. In about 367 BC Xenocrates accompanied Plato on his journey to Syracuse following the death of Dionysius I . Xenocrates left Athens with Aristotle after Plato 's death in 347 BC when they were both invited to Assos. Xenocrates remained for around five years in Assos. Plato 's nephew Speusippus had become head of the Academy on Plato 's death, but in 340 BC he sent for Xenocrates to return to Athens to prepare to become his successor. Despite Xenocrates having been chosen to head the Academy by Speusippus, an election took place to find a successor to Speusippus after his death. It was a close battle between Xenocrates, Menedemus of Pyrrha and Heraclides Ponticus but Xenocrates triumphed by just a few votes. Although Xenocrates had been many years in Athens he had refused to become a citizen of that state since he did not approve of its close relations with Macedonia. In this respect he contrasted strongly with his predecessor Speusippus who had strongly supported the political ties between Athens and Macedonia. It is clear that the Academy at this time was far from what many picture it as, namely an institution where scholars sat thinking, isolated from the world around them. On the contrary, the

3. Aristotle in Plato s absence. Speusippus, Plato s nephew, was also teaching atthe Academy as was xenocrates of chalcedon. After being a student http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Aristotle.html

Aristotle Born: 384 BC in Stagirus, Macedonia, Greece Died: 322 BC in Chalcis, Euboea, Greece Click the picture above to see six larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Aristotle was not primarily a mathematician but made important contributions by systematising deductive logic. He wrote on physical subjects: some parts of his Analytica posteriora show an unusual grasp of the mathematical method. Primarily, however, he is important in the development of all knowledge for, as the authors of [2] write:- Aristotle, more than any other thinker, determined the orientation and the content of Western intellectual history. He was the author of a philosophical and scientific system that through the centuries became the support and vehicle for both medieval Christian and Islamic scholastic thought: until the end of the 17 th century, Western culture was Aristotelian. And, even after the intellectual revolutions of centuries to follow, Aristotelian concepts and ideas remained embedded in Western thinking. Aristotle was born in Stagirus, or Stagira, or Stageirus, on the Chalcidic peninsula of northern Greece. His father was Nicomachus, a medical doctor, while his mother was named Phaestis. Nicomachus was certainly living in Chalcidice when Aristotle was born and he had probably been born in that region. Aristotle's mother, Phaestis, came from Chalcis in Euboea and her family owned property there.

4. Xenocrates Biography of Xenocrates (396BC314BC) xenocrates of chalcedon. Born 396 BC in Chalcedon (now Kadiköy, near Istanbul), Bithynia (now Turkey) xenocrates of chalcedon was a student of Plato who http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Xenocrates.html

Xenocrates of Chalcedon Born: Died: 314 BC in Athens, Greece Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Xenocrates of Chalcedon was a student of Plato who entered the Academy in Athens in about 376 BC. In about 367 BC Xenocrates accompanied Plato on his journey to Syracuse following the death of Dionysius I . Xenocrates left Athens with Aristotle after Plato 's death in 347 BC when they were both invited to Assos. Xenocrates remained for around five years in Assos. Plato 's nephew Speusippus had become head of the Academy on Plato 's death, but in 340 BC he sent for Xenocrates to return to Athens to prepare to become his successor. Despite Xenocrates having been chosen to head the Academy by Speusippus, an election took place to find a successor to Speusippus after his death. It was a close battle between Xenocrates, Menedemus of Pyrrha and Heraclides Ponticus but Xenocrates triumphed by just a few votes. Although Xenocrates had been many years in Athens he had refused to become a citizen of that state since he did not approve of its close relations with Macedonia. In this respect he contrasted strongly with his predecessor Speusippus who had strongly supported the political ties between Athens and Macedonia. It is clear that the Academy at this time was far from what many picture it as, namely an institution where scholars sat thinking, isolated from the world around them. On the contrary, the

5. TPCN - Great Quotations (Quotes) By Xenocrates Of Chalcedon To Inspire And Motiv xenocrates of chalcedon. Q U O T E S T O I N S P I R E Y O U. Greatquotes to inspire, empower and motivate you to live the life of http://www.cyber-nation.com/victory/quotations/authors/quotes_xenocratesofchalce

Xenocrates of Chalcedon Q U O T E S T O I N S P I R E Y O U Great quotes to inspire, empower and motivate you to live the life of your dreams and become the person you've always wanted to be! Silence I have often repented speaking, but never of holding my tongue. List By Author : A B C D ... Z Display By Subject : A B C D ... Press here or the BACK BUTTON on your browser to return to the previous page... or choose from the following options: Are You Looking For More Great Quotes? Check Out The Ultimate Success Quotations Library Over 43,000 Quotes. Download Your FREE Evaluation Program... And Learn How You Can Make Your Writing And Speeches More Powerful! Go Here To Download Your FREE Ultimate Quotations Screen Saver! You Can Use Tony Robbins' Personal Power Program To Achieve Your Dreams! How To Double Your Internet Business Within The Next 97 Days... Guaranteed! ... Return To Victory City Directory And Check Out Other Fabulous Places! If you have any technical questions about this site, please send your email to webmaster@cybernation.com

6. TPCN - Great Quotations (Quotes) To Inspire And Motivate You! - Silence silent. ~ Ludwig Wittgenstein ~. I have often repented speaking, butnever of holding my tongue. ~ xenocrates of chalcedon ~. Silence http://www.cyber-nation.com/victory/quotations/subjects/quotes_silence.html

Silence Q U O T E S T O I N S P I R E Y O U Great quotes to inspire, empower and motivate you to live the life of your dreams and become the person you've always wanted to be! S ilence is the virtue of fools. Francis Bacon S ilence is one of the hardest arguments to refute. Josh Billings T here are times when silence has the loudest voice. Leroy Brownlow W hen the oak is felled the whole forest echoes with it fall, but a hundred acorns are sown in silence by an unnoticed breeze. Thomas Carlyle S ilence is the great teacher, and to learn its lessons you must pay attention to it. There is no substitute for the creative inspiration, knowledge, and stability that come from knowing how to contact your core of inner silence. The great Sufi poet Rumi wrote, "Only let the moving waters calm down, and the sun and moon will be reflected on the surface of your being. Deepak Chopra S ilence is foolish if we are wise, but wise if we are foolish. Charles Caleb Colton T hese be three silent things: The Falling snow... the hour before the dawn... the mouth of one just dead. Adelaide Crapsey A n now the silences come in a single lifetime, in a single year... when species die, leaving a silent space in the world song that can never be filled.

7. EntWagon.com : Famous Quotations From Xenocrates Of Chalcedon, Famous Sayings, Q Cards Tell A Friend Suggest A Site Contact Us. Quotations From Xenocratesof Chalcedon. xenocrates of chalcedon. Prev Next . http://www.entwagon.com/cgi-bin/quotes/author.pl?auth=Xenocrates_of_Chalcedon

8. Search Results For Sophist Sophism Trachymachus Chalcedon - Encyclopædia Brita The Fourth Ecumenical Council The Council of Chalcedon, A.D. 451 of a play written by the Greek philosopher Plato, in 360 B.C. xenocrates of chalcedon. University of St http://www.britannica.com/search?query=sophist sophism trachymachus chalcedon&am

9. Xenocrates xenocrates of chalcedon. Born Greece. xenocrates of chalcedon was a studentof Plato who entered the Academy in Athens in about 376 BC. http://homepages.compuserve.de/thweidenfeller/mathematiker/Xenocrates.htm

Xenocrates of Chalcedon Born: 396 BC in Chalcedon (now Kadiköy, near Istanbul), Bithynia (now Turkey) Died: 314 BC in Athens, Greece Xenocrates of Chalcedon was a student of Plato who entered the Academy in Athens in about 376 BC. In about 367 BC Xenocrates accompanied Plato on his journey to Syracuse following the death of Dionysius I . Xenocrates left Athens with Aristotle after Plato 's death in 347 BC when they were both invited to Assos. Xenocrates remained for around five years in Assos. Plato 's nephew Speusippus had become head of the Academy on Plato 's death, but in 340 BC he sent for Xenocrates to return to Athens to prepare to become his successor. Despite Xenocrates having been chosen to head the Academy by Speusippus, an election took place to find a successor to Speusippus after his death. It was a close battle between Xenocrates, Menedemus of Pyrrha and Heraclides Ponticus but Xenocrates triumphed by just a few votes. Although Xenocrates had been many years in Athens he had refused to become a citizen of that state since he did not approve of its close relations with Macedonia. In this respect he contrasted strongly with his predecessor Speusippus who had strongly supported the political ties between Athens and Macedonia. It is clear that the Academy at this time was far from what many picture it as, namely an institution where scholars sat thinking, isolated from the world around them. On the contrary, the Academy was highly involved in the politics of the day and different political views strove for supremacy.

10. The Heirs Of Plato: A Study Of The Old Academy (347-274 BC) of the Academy, namely his nephew Speusippus of Athens (head 347339 BC Chapter Two), xenocrates of chalcedon (339 from those of Xenocrates and of other Academics http://ndpr.icaap.org/content/archives/2004/3/tsouna-dillon.html

Notre Dame Philosophical Reviews 2004.03.13 John Dillon, The Heirs of Plato: A Study of the Old Academy (347-274 BC) , Oxford, 2003, 264pp, $65.00 (hbk), ISBN 0198237669. Reviewed by: Voula Tsouna University of California, Santa Barbara tetraktys Although it remains uncertain just how many the Forms are, it is reasonably clear that Plato envisages some hierarchical arrangement according to which the primal numbers occupy a privileged position. In any event, the four numbers that comprise the tetractys Timaeus Timaeus Timaeus Timaeus On Pythagorean Numbers De communi mathematica scientia plethos on Timaeus Parmenides (56-59), and his theory of mathematics emerging from OPN. tetraktys If one accepts that this account is a plausible interpretation of the Timaeus tetraktys One important upshot of this thesis is that it posits indivisible minima in both the intelligible and the sensible realms. Regarding the latter, Dillon plausibly suggests that, by postulating Forms of species as well as elementary material particles, Xenocrates develops the atomistic implications of the theory of basic triangles in the Timaeus aei aei So far, there has been mention of two levels of reality, intelligible and sensible, to which Xenocrates (following Plato) attaches respectively two forms of cognition

11. Spirit And Sky Philosophy: Philosophers: X: Xenocrates Ancient Greek Scientists xenocrates of chalcedon Ancient Greek Scientists Xenocratesof Chalcedon. MacTutor History of Mathematics xenocrates of chalcedon http://www.spiritandsky.com/philosophy/philosophers/x/xenocrates/

Home philosophy philosophers x : xenocrates the entire directory only this category More search options Home Search Suggest a Site ... x : xenocrates Links: Ancient Greek Scientists: Xenocrates of Chalcedon Ancient Greek Scientists: Xenocrates of Chalcedon Notes on his life and mathematical achievements. (Added: Thu Jan 01 2004) ID 115858 Biography.com: Xenocrates Biography.com: Xenocrates Concise paragraph on his teachings. (Added: Thu Jan 01 2004) ID 115855 Columbia Encyclopedia: Xenocrates Columbia Encyclopedia: Xenocrates Concise paragraph on this early scholarch. (Added: Thu Jan 01 2004) ID 115854 FOLDOC: Xenocrates FOLDOC: Xenocrates Entry from the philosophical database, with links to related entries. (Added: Thu Jan 01 2004) ID 115856 Life of Xenocrates Life of Xenocrates Section from the Lives of the Philosophers, as compiled by Diogenes Laertius and translated by C.D. Yonge. (Added: Thu Jan 01 2004) ID 115860 MacTutor History of Mathematics: Xenocrates of Chalcedon MacTutor History of Mathematics: Xenocrates of Chalcedon Biography, bibliography and list of related topics.

12. Xenocrates Google Directory Society Philosophy Philosophers X MacTutor History of Mathematics xenocrates of chalcedon - http//www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Xenocrates.htmlBiography, bibliography and http://history.math.csusb.edu/Mathematicians/Xenocrates.html

Xenocrates of Chalcedon Born: Died: 314 BC in Athens, Greece Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Xenocrates of Chalcedon was a student of Plato who entered the Academy in Athens in about 376 BC. In about 367 BC Xenocrates accompanied Plato on his journey to Syracuse following the death of Dionysius I . Xenocrates left Athens with Aristotle after Plato 's death in 347 BC when they were both invited to Assos. Xenocrates remained for around five years in Assos. Plato 's nephew Speusippus had become head of the Academy on Plato 's death, but in 340 BC he sent for Xenocrates to return to Athens to prepare to become his successor. Despite Xenocrates having been chosen to head the Academy by Speusippus, an election took place to find a successor to Speusippus after his death. It was a close battle between Xenocrates, Menedemus of Pyrrha and Heraclides Ponticus but Xenocrates triumphed by just a few votes. Although Xenocrates had been many years in Athens he had refused to become a citizen of that state since he did not approve of its close relations with Macedonia. In this respect he contrasted strongly with his predecessor Speusippus who had strongly supported the political ties between Athens and Macedonia. It is clear that the Academy at this time was far from what many picture it as, namely an institution where scholars sat thinking, isolated from the world around them. On the contrary, the

13. Xenocrates xenocrates of chalcedon. Born 396 BC in Chalcedon (now Kadikoy, near Istanbul),Bithynia (now Turkey) Died 314 BC in Athens, Greece. Show birthplace location http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/Xncrts.htm

Xenocrates of Chalcedon Born: 396 BC in Chalcedon (now Kadikoy, near Istanbul), Bithynia (now Turkey) Died: 314 BC in Athens, Greece Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page Xenocrates was a student of Plato who left Athens with Aristotle after Plato 's death in 347 BC, returning in 339 BC when he was elected as head of the Academy. He remained at the Academy in Athens for the rest of his life. Xenocrates wrote on philosophy and mathematics. All his books are lost and it would appear that there only ever existed a single copy of each in his own hand. Xenocrates believed that matter is composed of indivisible units, so he may be regarded as an early believer in the atomic theory. He agreed with Pythagoras regarding the importance of numbers in philosophy and attributed to Pythagoras an atomic view of acoustics where sound, perceived as a single entity, consists of discrete sounds. Xenocrates believed in human beings having threefold existence, mind, body and soul. It is not clear whether he was the instigator of this belief. He also believed that people die twice, once on Earth, then for a second time on the Moon when the mind separates from the soul and travels to the Sun. References (3 books/articles) Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page History Topics Index Famous curves index ... Search Suggestions JOC/EFR December 1996 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Xenocrates.html

14. References For Xenocrates References for xenocrates of chalcedon. Biography in Dictionary of ScientificBiography (New York 19701990). Biography in Encyclopaedia Britannica. http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/~DZ97DB.htm

References for Xenocrates of Chalcedon Biography in Dictionary of Scientific Biography (New York 1970-1990). Biography in Encyclopaedia Britannica. Articles: R D Hicks, Lives of the Eminent Philosophers I (Cambridge, Mass.-London, 1966), 380-393. Close this window or click this link to go back to Xenocrates Welcome page Biographies Index History Topics Index Famous curves index ... Search Suggestions JOC/EFR December 1996 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/References/Xenocrates.html

15. Cool Quotes Collection I have often repented speaking, but never of holding my tongue. xenocrates of chalcedon(the original). Correction. They sicken of the calm who know the storm. http://www.coolquotescollection.com/cat/wisdom/02/

Cool Quotes Collection Wisdom Home Laughs Wisdom Computer ... Forum Current visitors Page 2 of 116 (2318 quotes in this category) "War is progress, peace is stagnation." Hegel Correction A cynic is a person searching for an honest man, with a stolen lantern. Edgar A. Shoaff Correction A fanatic is one who can't change his mind and won't change the subject. Winston Churchill Correction An expert is one who knows more and more about less and less until he knows absolutely everything about nothing. Correction Beware of altruism. It is based on self-deception, the root of all evil. Ayn Rand Correction Man will occasionally stumble over the truth, but most of the time he will pick himself up and continue on. Churchill Correction Conserve energy make love more slowly. Correction Enjoy every minute. There's plenty of time to be dead. Correction He who has the courage to laugh is almost as much a master of the world as he who is ready to die. Giacomo Leopardi Correction If people are good only because they fear punishment, and hope for reward, then we are a sorry lot indeed. Einstein Correction Imagination is the one weapon in the war against reality.

16. Search Results For Sophist Sophism Trachymachus Chalcedon - Encyclopædia Brita 1997. Council of Chalcedon, 451 Documents from the Fourth Ecumenical Council.xenocrates of chalcedon University of St. Andrews, Scotland http://www.britannica.com/search?query=sophist sophism trachymachus chalcedon&ct

17. Chalcedon --  Encyclopædia Britannica of relevance. , xenocrates of chalcedon University of St. Andrews andphilosopher. , xenocrates of chalcedon University of St. Andrews http://www.britannica.com/eb/article?eu=22604&tocid=0&query=sophist sophism trac

18. Xenocrates (c. 396 B.C. - 314 B.C.) XENOCRATES. xenocrates of chalcedon attached himself to Plato, whomhe accompanied in his journey to Dionysus, in Sicily. The greater http://www.usefultrivia.com/biographies/xenocrates_001.html

XENOCRATES XENOCRATES of Chalcedon attached himself to Plato, whom he accompanied in his journey to Dionysus, in Sicily. The greater part of his life was spent in the Academy, over which he presided after the death of Plato's pupil, Speusippus, for twenty-five yearsB.C. 339-314. He was noted for gravity of demeanour, for temperance, veracity, and integrity, and is frequently praised and cited by Cicero . When sent as a member of the Athenian embassy to Philip of Macedon, he stood alone in inflexible refusal to receive bribe or favour; and he maintained the same character in his embassy to Antipator. He was a voluminous writer, but nothing except the catalogue of his works has come down to us. He died at the age of 82. His position in philosophy is that of an immediate successor to Plato, who developed the Platonic system, especially in its tendency to Monotheism as the basis of a purer and stronger moral life. Find more articles on Xenocrates Purchase books on Greek philosophy This biography is reprinted from The New Calendar of Great Men . Ed. Frederic Harrison. London: Macmillan and Co., 1920.

19. Philosophy - Plato: Overview in the first of these were Speusippus (son of Plato s sister), who succeeded himas the head of the school (till 339), and xenocrates of chalcedon (till 314). http://www.archaeonia.com/philosophy/plato/main.htm

PLATO (428-348 B.C.) P lato of Athens (428-348), also combined the genius of Socrates with all the principles established by earlier philosophers, in so far as they had been legitimate, and developed the whole of this material into the unity of a comprehensive system. The groundwork of Plato's scheme, though nowhere expressly stated by him, is the threefold division of philosophy into dialectic ethics , and physics ; its central point is the theory of forms or ideas . This theory is a combination of the Eleatic doctrine of the One with Heraclitus's theory of a perpetual flux and with the Socratic method of concepts . The multitude of objects of sense, being involved in perpetual change, are thereby deprived of all genuine existence. The only true being in them is founded upon the ideas, the eternal unchangeable (independent of all that is accidental, and therefore perfect) types, of which the particular objects of sense are imperfect copies . The quantity of the forms is defined by the number of universal concepts which can be derived from the particular objects of sense. The highest idea is that of the Good , which is the ultimate basis of the rest, and the first cause of being and knowledge. Apprehensions derived from the impression of sense can never give us the knowledge of true being i.e. of the forms. It can only be obtained by the

20. Combinatorics And Hipparchus xenocrates of chalcedon, who succeeded Speusippus as head of Plato s Academy(339 BC 314 BC) solved a combinatorial analysis problem finding that http://www.mlahanas.de/Greeks/Combinatorics.htm

Hipparchus on Compound Statements Xenocrates of Chalcedon, who succeeded Speusippus as head of Plato's Academy (339 BC- 314 BC) solved a combinatorial analysis problem finding that 1002000000000 syllables can be written with the letters of the Greek alphabet. ( Technology Museum of Thessaloniki Archimedes considered a combinatorial problem of the stomachion n, n ), contain no points above the line y = x , and are composed only of steps (0, 1), (1, 0), and (1, 1). The corresponding s(n) are obtained using: (s(1),s(2),s(3), s(4),...,s(10),...) = (1,1,3,11,...,103049,...) The numbers can be obtained by the following relation: (n+2)s(n+2)-3(2n+1)s(n+1)+(n-1)s(n) = 0, n greater or equal 1., s(1)=s(2)=1. "In pure mathematics [Hipparchus] is said to have considered a problem in permutations and combinations, the problem of finding the number of different possible combinations of 10 axioms or assumptions, which he made to be 103049 (v.l. 101049) or 310952 according as the axioms were affirmed or denied. It seems impossible to make anything of these figures." Heath , History of Greek Mathematics According to [ST97] Plutarch (50-120 AD) said "Chrysippus says that the number of compound propositions that can be made from only ten simple propositions exceeds a million. (Hipparchus, to be sure, refuted this by showing that on the affirmative side there are 103049 compound statements, and on the negative side 310952.)"

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