1. TMTh:: ARCHYTAS OF TARENTUM Brief biography from the Thessaloniki Museum of Technology. http://www.tmth.edu.gr/en/aet/1/14.html

Home Ancient Greek Scientists AGRICULTURALISTS ARCHITECTS ... PHYSICISTS MATHEMATICIAN ARCHYTAS OF TARENTUM (fl. 428-347 BC) Life Pythagorean philosopher, mathematician and astronomer, Archytas is sometimes called the father of mathematical mechanics. Aristotle wrote a special treatise on his work, entitled "The Philosophy of Archytas". His theories on the exact sciences are based on two principles: a) that there is no absolute difference between the organic and the inorganic world, and b) that the law of causality cannot interpret phenomena. In mathematics, Archytas was the first to distinguish between arithmetic and geometric progressions; he also found a solution to the problem of doubling the cube. He is thought to be the inventor of the screw and the pulley, and a forefather of mechanical flight. He was a friend of Plato and a teacher of Eudoxus of Cnidus. A valley at the North Pole of the moon has been named "Archytas" in his honour. Work The idea of flight had a perennial and passionate fascination for many ancient peoples; this is especially true of Greece, where not only the gods but also an assortment of demigods and mythical creatures were endowed with this gift. From myth to reality, however, is a long step, even though it was partially spanned by Daedalus with his famous airborne escape from Crete. While the flight of Daedalus and Icarus was probably mythical (opinion is divided), the feat of Archytas by contrast was truly revolutionary: in 425 BC he constructed the first flying machine in history. His "pigeon" (as he called it) was powered by a system of jet propulsion, and in one experiment it flew a distance of 200 metres. Once it fell to the ground, however, this machine could not take off again. Evanghelos Stamatis thinks it must have been some sort of jet-propelled craft driven by a compressed air system.

2. Archytas Of Tarentum --  Encyclopædia Britannica MLA style " archytas of tarentum." Encyclopædia Britannica. 2004 APA style archytas of tarentum. Encyclopædia Britannica. Retrieved April 30, 2004, from Encyclopædia Britannica http://www.britannica.com/eb/article?eu=9411

3. Archytas Archytas. archytas of tarentum was a Greek mathematician, political leader and philosopher, active in the first great number of works were forged in Archytas' name starting in the http://plato.stanford.edu/entries/archytas

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z This document uses XHTML-1/Unicode to format the display. Older browsers and/or operating systems may not display the formatting correctly. last substantive content change JUN Archytas Archytas of Tarentum was a Greek mathematician, political leader and philosopher, active in the first half of the fourth century BC (i.e., during Plato's lifetime). He was the last prominent figure in the early Pythagorean tradition and the dominant political figure in Tarentum, being elected general seven consecutive times. He sent a ship to rescue Plato from the clutches of the tyrant of Syracuse, Dionysius II, in 361, but his personal and philosophical connections to Plato are complex, and there are many signs of disagreement between the two philosophers. A great number of works were forged in Archytas' name starting in the first century BC, and only four fragments of his genuine work survive, although these are supplemented by a number of important testimonia. Archytas was the first to solve one of the most celebrated mathematical problems in antiquity, the duplication of the cube. We also have his proof showing that ratios of the form ( n n , which are important in music theory, cannot be divided by a mean proportional. He was the most sophisticated of the Pythagorean harmonic theorists and provided mathematical accounts of musical scales used by the practicing musicians of his day. He was the first to identify the group of four canonical sciences (logistic [arithmetic], geometry, astronomy and music), which would become known as the

4. Archytas of Tarentum. Diogenes Laertes Life of Archytas archytas of tarentum, son of Mnesagoras, or of Hestius, according to Aristoxenus, also was a Pythagorean. It was he who, by a letter, saved Plato from http://www.csun.edu/~hcfll004/archytas.html

ARCHYTAS of Tarentum Diogenes Laertes Life of Archytas: Archytas of Tarentum, son of Mnesagoras, or of Hestius, according to Aristoxenus, also was a Pythagorean. It was he who, by a letter, saved Plato from the death threatened by Dionysus. He possessed all the virtues, so that, being the admiration of the crowd, he was seven times named general, in spite of the law which prohibited reelection after one year. Plato wrote him two letters, in response to this one of Archytas: Greetings: It is fortunate for you that you have recovered from your illness, for I have heard of it not only from you, but also from Lamiscus. I have busied myself about those notes, and took a trip into Lucania, where I met descendants of Ocellus. I have in my possession the treatises On Law and On Kingship On Sanctity , and On the Origin of All Things , and I am sending them to you. The others could not be discovered. Should they be found, they will be sent to you. Plato answered: Greetings: I am delighted to have received the works which you have sent me, and I acknowledge a great admiration for him who wrote them. He seems to be worthy of his ancient and glorious ancestors, who are said to be from Myra, and among the number of those Trojans who emigrated under the leadership of Laomedon, all worthy people, as the legend proves. Those works of mine about which you wrote me are not in a sufficient state of perfection, but I send them such as they are. Both of us are in perfect agreement on the subject of protecting them. No use to renew the request. May your health improve.

5. Dupcubfin.html The ancient Greeks originated numerous mathematical questions, most of which they learned to solve using simple mathematical tools, such as the straight edge and the collapsable compass. unit2 unit3 ruler mark1 mark2 line1 line2 line3 scaling=constrained); archytas of tarentum's Solution is the solution developed by archytas of tarentum. His solution, however, lies http://www.ms.uky.edu/~carl/ma330/projects/dupcubfin1.html

Duplication of the Cube : Darrell Mattingly, Cateryn Kiernan The ancient Greeks originated numerous mathematical questions, most of which they learned to solve using simple mathematical tools, such as the straight edge and the collapsable compass. Three of these problems persist today, challenging students in contemporary classrooms. This triology of problems, the trisection of a given angle, the squaring of a circle, and the duplication of the cube, have since been proved impossible using exclusively the straight edge and the compass. In the quest to solve these problems using those specific tools, however, mathematicians developed numerous alternate solutions using other mathematical tools. The last problem of the trilogy is the focus of this discussion, and it challenged mathematicians for centuries, due to the restriction of using only the aforementioned tools. Origin of the Problem Proof that NO Platoic Solution Exists for the "Delian" Problem After centuries of mathematicians had worked on this problem, a proof developed that it could not be done using exclusively the straight edge and compass. This proof is based on theorems about the powers of degrees of subfields generated by the x and y coordinates of the side of the cube to be duplicated. Although the desired point can be approximated, it cannot in fact be found based on these theorems.

6. Archytas archytas of tarentum. Born about 428 BC in Tarentum (now Taranto),Magna Graecia (now Italy) Died about 350 BC. Click the picture http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Archytas.html

Archytas of Tarentum Born: about 428 BC in Tarentum (now Taranto), Magna Graecia (now Italy) Died: about 350 BC Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Archytas of Tarentum was a mathematician, statesman and philosopher who lived in Tarentum in Magna Graecia, an area of southern Italy which was under Greek control in the fifth century BC. The Pythagoreans, who had at one stage been strong throughout Magna Graecia, were attacked and expelled until only the town of Tarentum remained a stronghold for them. Archytas led the Pythagoreans in Tarentum and tried to unite the Greek towns in the area to form an alliance against their non-Greek neighbours. He was commander in chief of the forces in Tarentum for seven years despite there being a law that nobody could hold the post for more than a year. Plato , who became a close friend, made his acquaintance while saying in Magna Graecia. Heath writes in [4]:- ... he is said, by means of a letter, to have saved

7. A Index Appell, Paul (1377*) Arago, François (345*) Arbogast, Louis (1029) Arbuthnot,John (251*) Archimedes of Syracuse (3190*) archytas of tarentum (1366*) Arf http://www-gap.dcs.st-and.ac.uk/~history/Indexes/A.html

Names beginning with A The number of words in the biography is given in brackets. A * indicates that there is a portrait. Abbe , Ernst (602*) Abel , Niels Henrik (2899*) Abraham bar Hiyya (641) Abraham, Max Abu Kamil Shuja (1012) Abu Jafar Abu'l-Wafa al-Buzjani (1115) Ackermann , Wilhelm (205*) Adams, John Couch Adams, J Frank Adelard of Bath (1008) Adler , August (114) Adrain , Robert (1317*) Adrianus , Romanus (419) Aepinus , Franz (822) Agnesi , Maria (2018*) Ahlfors , Lars (725*) Ahmed ibn Yusuf (660) Ahmes Aida Yasuaki (696) Aiken , Howard (665*) Airy , George (2362*) Aitken , Alec (1220*) Ajima , Naonobu (144) Akhiezer , Naum Il'ich (248*) al-Baghdadi , Abu (947) al-Banna , al-Marrakushi (861) al-Battani , Abu Allah (1333*) al-Biruni , Abu Arrayhan (3002*) al-Farisi , Kamal (1102) al-Haitam , Abu Ali (2490*) al-Hasib Abu Kamil (1012) al-Haytham , Abu Ali (2490*) al-Jawhari , al-Abbas (627) al-Jayyani , Abu (892) al-Karaji , Abu (1789) al-Karkhi al-Kashi , Ghiyath (1725*) al-Khazin , Abu (1148) al-Khalili , Shams (677) al-Khayyami , Omar (2140*) al-Khwarizmi , Abu (2847*) al-Khujandi , Abu (713) al-Kindi , Abu (1151) al-Kuhi , Abu (1146) al-Maghribi , Muhyi (602) al-Mahani , Abu (507) al-Marrakushi , ibn al-Banna (861) al-Nasawi , Abu (681) al-Nayrizi , Abu'l (621) al-Qalasadi , Abu'l (1247) al-Quhi , Abu (1146) al-Samarqandi , Shams (202) al-Samawal , Ibn (1569) al-Sijzi , Abu (708) al-Tusi , Nasir (1912*) al-Tusi , Sharaf (1138) al-Umawi , Abu (1014) al-Uqlidisi , Abu'l (1028) Albanese , Giacomo (282) Albategnius (al-Battani) (1333*) Albert, A Adrian

8. Archytas Biography of archytas of tarentum (BCBC) archytas of tarentum. Born about 428 BC in Tarentum (now Taranto), Magna Graecia (now Italy) Welcome page. Archytas was a mathematician, statesman http://sfabel.tripod.com/mathematik/database/Archytas.html

var cm_role = "live" var cm_host = "tripod.lycos.com" var cm_taxid = "/memberembedded" Archytas of Tarentum Born: about 428 BC in Tarentum (now Taranto), Magna Graecia (now Italy) Died: about 350 BC Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page Archytas was a mathematician, statesman and philosopher. He worked on the harmonic mean and gave it that name. The reason he worked on this was his interest in the problem of duplicating the cube, finding the side of a cube with volume twice that of a given cube. Hippocrates reduced the problem to finding mean proportionals. Archytas solved the problem with a remarkable geometric solution (not of course a ruler and compass construction). He is sometimes called the founder of mechanics and Plato , a close friend, made use of his mathematics. Euclid also borrowed his work for Book 8 of the Elements References (6 books/articles) References elsewhere in this archive: There is a Crater Archytas on the moon. There is also a

9. Archytas Biography of Archytas (428BC350BC) archytas of tarentum. Born about 428 BC in Tarentum (now Taranto), Magna Graecia archytas of tarentum was a mathematician, statesman and philosopher who http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Archytas.html

Archytas of Tarentum Born: about 428 BC in Tarentum (now Taranto), Magna Graecia (now Italy) Died: about 350 BC Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Archytas of Tarentum was a mathematician, statesman and philosopher who lived in Tarentum in Magna Graecia, an area of southern Italy which was under Greek control in the fifth century BC. The Pythagoreans, who had at one stage been strong throughout Magna Graecia, were attacked and expelled until only the town of Tarentum remained a stronghold for them. Archytas led the Pythagoreans in Tarentum and tried to unite the Greek towns in the area to form an alliance against their non-Greek neighbours. He was commander in chief of the forces in Tarentum for seven years despite there being a law that nobody could hold the post for more than a year. Plato , who became a close friend, made his acquaintance while saying in Magna Graecia. Heath writes in [4]:- ... he is said, by means of a letter, to have saved

10. Lysis Of Tarentum --  Encyclopædia Britannica probably through the , archytas of tarentum Greek scientist,philosopher, and major Pythagorean mathematician. Plato, a close http://www.britannica.com/eb/article?eu=50750

11. Archytas Of Tarentum Plato and his dialogues Home Biography - Works - History of interpretation - New hypotheses - Map of dialogues table version or non tabular version. Tools Index of persons and locations - http://www.plato-dialogues.org/tools/char/archytas.htm

Bernard SUZANNE Last updated December 5, 1998 Plato and his dialogues : Home Biography Works History of interpretation ... New hypotheses - Map of dialogues : table version or non tabular version . Tools : Index of persons and locations Detailed and synoptic chronologies - Maps of Ancient Greek World . Site information : About the author This page is part of the "tools" section of a site, Plato and his dialogues , dedicated to developing a new interpretation of Plato's dialogues. The "tools" section provides historical and geographical context (chronology, maps, entries on characters and locations) for Socrates, Plato and their time. For more information on the structure of entries and links available from them, read the notice at the beginning of the index of persons and locations . . . . WORK IN PROGRESS - PLEASE BE PATIENT . . . To Perseus general lookup encyclopedia mentions in ancient authors Plato and his dialogues : Home Biography Works History of interpretation ... New hypotheses - Map of dialogues : table version or non tabular version . Tools : Index of persons and locations Detailed and synoptic chronologies - Maps of Ancient Greek World . Site information : About the author First published January 4, 1998 - Last updated December 5, 1998

12. Archytas archytas of tarentum was a Greek mathematician, political leader and philosopher,active in the first half of the fourth century BC (ie, during Plato s lifetime http://www.mlahanas.de/Greeks/Archytas.htm

Archytas Archytas son of Hestiaeus, politician, mathematician and philosopher was born around 500 BC in Tarent (or Tarentum). He was probably Pythagorean and student of Philolaus. tour de force Aristotle thought that the stars were spheres at a range of distances from the Earth. In medieval times stars were considered as holes in the surface of a sphere that let through light from behind. Archytas believed that the universe is infinite, has no limits. Assume he said that the universe is finite and I am at one border of the universe. What hinders me to stretch my hand beyond this limit? (Simplicius 467,26) What is behind these limits (see Image above)? It is not clear why Plato and Aristotle have not accepted this argument but probably because they had some problems accepting the existence of a body without boundaries and the infinite in general A similar idea had Euclid in his proof of the infinite number of primes. The idea of Euclid is to add 1 to the product of all assumed limited number of primes showing then that this number is either itself prime or a prime number exists that is larger than the largest prime used in the product. Other adopted also supported the idea of a infinite Universe such as Democritus and Epicurus with similar arguments.

13. Title Details - Cambridge University Press Home Catalogue archytas of tarentum. Related Areas archytas of tarentum.Pythagorean, Philosopher and Mathematician King. Carl Huffman. c. £85.00. http://titles.cambridge.org/catalogue.asp?isbn=0521837464

14. Emai A Friend About This Title: Archytas Of Tarentum - Cambridge University Pres Would you like to email your friend about archytas of tarentum. To From Reply toSubject Title archytas of tarentum at Cambridge University Press website. http://titles.cambridge.org/emailfriend.asp?ISBN=0521837464

15. Archytas Of Tarentum © 1998 Bernard SUZANNE, Last updated December 5, 1998. Plato and hisdialogues Home Biography - Works - History of interpretation http://plato-dialogues.org/tools/char/archytas.htm

Bernard SUZANNE Last updated December 5, 1998 Plato and his dialogues : Home Biography Works History of interpretation ... New hypotheses - Map of dialogues : table version or non tabular version . Tools : Index of persons and locations Detailed and synoptic chronologies - Maps of Ancient Greek World . Site information : About the author This page is part of the "tools" section of a site, Plato and his dialogues , dedicated to developing a new interpretation of Plato's dialogues. The "tools" section provides historical and geographical context (chronology, maps, entries on characters and locations) for Socrates, Plato and their time. For more information on the structure of entries and links available from them, read the notice at the beginning of the index of persons and locations . . . . WORK IN PROGRESS - PLEASE BE PATIENT . . . To Perseus general lookup encyclopedia mentions in ancient authors Plato and his dialogues : Home Biography Works History of interpretation ... New hypotheses - Map of dialogues : table version or non tabular version . Tools : Index of persons and locations Detailed and synoptic chronologies - Maps of Ancient Greek World . Site information : About the author First published January 4, 1998 - Last updated December 5, 1998

16. Comparative Chronology Of Greek And Contemporay Thinkers And Writers and thinkers shown (on rose background) are Æschylus, Anaxagoras, Anaximenes,Anaximander, Antisthenes the Cynic, archytas of tarentum, Aristippus of Cyrene http://plato-dialogues.org/tools/compare.htm

Bernard SUZANNE Last updated January 7, 1999 Plato and his dialogues : Home Biography Works and links to them History of interpretation New hypotheses - Map of dialogues : table version or non tabular version . Tools : Index of persons and locations Detailed and synoptic chronologies - Maps of Ancient Greek World . Site information : About the author Comparative chronology of Greek and Contemporay Thinkers and Writers This synopsis is a modified version of the synoptic chronology of Greek thinkers and writers presented on another page of this site, which compares it to modern chronology in order to give the reader a concrete feel for temporal distances in Plato's world. In order to do this, two temporal scales have been put in parallel : the Greek chronology down to Plato's old days and modern chronology down to "today" (1999), taking the year of the assassination of Dion (354), which is also the probable year of writing of the VIIth Letter if it is from Plato (which I believe), as "today", that is, 1999. In 354, Plato was about 74 and 7 years away from his death (which, in the parallel modern scale, would be in 2006). In my hypotheses about the dialogues, in which it is very possible that most of them were written late in Plato's life, this might be the time he was writing them (it was, even in the usually accepted chronology, the time he was probably writing what is called the "late" dialogues, such as the Philebus or Laws

17. Spirit And Sky Philosophy: Philosophers: A: Archytas-of-tarentum (Added Thu Jan 01 2004) ID 112606. archytas of tarentum Archytas ofTarentum. Brief biography from the Thessaloniki Museum of Technology. http://www.spiritandsky.com/philosophy/philosophers/a/archytas-of-tarentum/

Home philosophy philosophers a : archytas-of-tarentum the entire directory only this category More search options Home Search Suggest a Site ... a : archytas-of-tarentum Links: Archytas Archytas Life and work of fourth century BC Greek mathematician, political leader and philosopher; from the Stanford Encyclopedia by Carl Huffman. (Added: Thu Jan 01 2004) ID 112604 Archytas Archytas Biography of Archytas (428BC-350BC) from the MacTutor History of Mathematics Archive. (Added: Thu Jan 01 2004) ID 112606 Archytas of Tarentum Archytas of Tarentum Brief biography from the Thessaloniki Museum of Technology. (Added: Thu Jan 01 2004) ID 112605 Home philosophy philosophers a : archytas-of-tarentum Home Search Suggest a Site Submission Guidelines ... About The Artist permission from spiritandsky.com is strictly prohibited.

18. ªüº¸§Æ¶ð´µ¡£Archytas Of Tarentum¡¤ The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set. http://www.edp.ust.hk/math/history/3/3_78.htm

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19. Archytas Of Tarentum From Linkspider UK Society Directory archytas of tarentum by Linkspider UK, archytas of tarentum links andarchytas of tarentum topics from our Society directory. Helping http://linkspider.co.uk/Society/Philosophy/Philosophers/A/ArchytasofTarentum/

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20. Archytas archytas of tarentum. Born about 428 BC in Tarentum (now Taranto), MagnaGraecia (now Italy) Died about 350 BC. Show birthplace location http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/rchyts.htm

Archytas of Tarentum Born: about 428 BC in Tarentum (now Taranto), Magna Graecia (now Italy) Died: about 350 BC Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page Archytas was a mathematician, statesman and philosopher. He worked on the harmonic mean and gave it that name. The reason he worked on this was his interest in the problem of duplicating the cube, finding the side of a cube with volume twice that of a given cube. Hippocrates reduced the problem to finding mean proportionals. Archytas solved the problem with a remarkable geometric solution (not of course a ruler and compass construction). He is sometimes called the founder of mechanics and Plato , a close friend, made use of his mathematics. Euclid also borrowed his work for Book 8 of the Elements References (6 books/articles) References elsewhere in this archive: There is a Crater Archytas on the moon. There is also a Rima Archytas . You can see a list of lunar features named after mathematicians. 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/Archytas.html

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