1. Dionysodorus Biography of dionysodorus (250BC190BC) There is certainly more than onemathematician called dionysodorus and this does make it a little difficult in http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Dionysodorus.html

Dionysodorus Born: about 250 BC in Caunus, Caria, Asia Minor (now in Turkey) Died: about 190 BC Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing There is certainly more than one mathematician called Dionysodorus and this does make it a little difficult in deciding exactly what was studied by each. Strabo , the Greek geographer and historian (about 64 BC - about 24 AD), describes a mathematician named Dionysodorus who was born in Amisene, Pontus in northeastern Anatolia on the Black Sea. The Dionysodorus we are interested in here is the mathematician Dionysodorus who Eutocius states solved the problem of the cubic equation using the intersection of a parabola and a hyperbola . This was related to a problem of Archimedes given in On the Sphere and Cylinder. It was thought until early this century that the Dionysodorus who Eutocius refers to was Dionysodorus of Amisene described by Strabo. There is a second Dionysodorus who appears in the writings of Pliny . In Natural history Pliny mentions a certain Dionysodorus who measured the earth's radius and gave the value 42000 stades. Strabo distinguishes this Dionysodorus from Dionysodorus of Amisene and it is now thought that the Dionysodorus referred to by Pliny is not the mathematician who solved the problem of the cubic equation. Interestingly Pliny died as a result of the eruption of Vesuvius in 79 AD and it is as a consequence of this eruption that new information regarding a mathematician Dionysodorus was published in 1900.

2. Dionysodorus Biography of dionysodorus (250BC190BC) http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

3. References For Dionysodorus References for the biography of dionysodorus. W Schmidt, Über den griechischenMathematiker dionysodorus, Bibliotheca mathematica 4 (1904), 321325. http://www-groups.dcs.st-and.ac.uk/~history/References/Dionysodorus.html

References for Dionysodorus Version for printing Biography in Dictionary of Scientific Biography (New York 1970-1990). Books: F D Cousins, Sundials (London, 1969). T L Heath, A History of Greek Mathematics II (Oxford, 1921). I Thomas, Selections illustrating the history of Greek mathematics II (London, 1941). Articles: Bibliotheca mathematica Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR April 1999 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/References/Dionysodorus.html

4. "Philip Of Macedon United The Greek City-states" "dionysodorus, the representative of King Attalus of Pergamum, was the first to rise. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

5. The Internet Classics Archive | Against Dionysodorus By Demosthenes Against dionysodorus By Demosthenes Translated by Vince/DeWitt/Murray. This workis only provided via the Perseus Project at Tufts University. http://classics.mit.edu/Demosthenes/dem.56.html

Home Browse and Comment Search ... Help Against Dionysodorus By Demosthenes Translated by Vince/DeWitt/Murray This work is only provided via the Perseus Project at Tufts University. You may begin reading the English translation as well as the Greek version and a Greek version with morphological links If you have any questions about the Perseus Project texts in the Internet Classics Archive, including the Perseus Project , please consult the help pages . Please direct any inquiries about the texts themselves to the Perseus Project Webmaster at webmaster@perseus.tufts.edu. Commentary: No comments have been posted about Against Dionysodorus Add your own comment to start discussion. Reader Recommendations: Recommend a Web site you feel is appropriate to this work, list recommended Web sites , or visit a random recommended Web site

6. Scholia - Browse By Volume, Department Of Classics, University Of Who is the Demosthenes at the End of Demosthenes 56, Against dionysodorus? http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. Law And Economy In Classical Athens [Demosthenes], “Against Tradition has passed the speech against dionysodorus down to the present day asone of the many speeches written by Demosthenes, but scholars have come to http://www.stoa.org/projects/demos/article_law_economy?page=1&greekEncoding=Unic

8. Dionysodorus There is certainly more than one mathematician called dionysodorus and this does make it a little difficult in deciding exactly what was studied by http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. Law And Economy In Classical Athens [Demosthenes], “Against About a year before, in the month of Metageitnion, dionysodorus and Parmeniscus dionysodorus could easily have invented this part of the narrative to http://www.stoa.org/projects/demos/article_law_economy?page=9&greekEncoding=Unic

10. BookFinder.com Aspects Of Athenian Society In The Fourth Century B.C. A Historical Introduction to and Commentary on the ParagrapheSpeeches and the Speech Against dionysodorus in the Corpus Demosthenicum http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. Dionysodorus There is certainly more than one mathematician called dionysodorus and this doesmake it The dionysodorus we are interested in here is the mathematician http://www.palmers.ac.uk/internet/Previous Events/Eric Excellence day/webs2003/J

Dionysodorus There is certainly more than one mathematician called Dionysodorus and this does make it a little difficult in deciding exactly what was studied by each. Strabo , the Greek geographer and historian (about 64 BC - about 24 AD), describes a mathematician named Dionysodorus who was born in Amisene, Pontus in northeastern Anatolia on the Black Sea. The Dionysodorus we are interested in here is the mathematician Dionysodorus who Eutocius states solved the problem of the cubic equation using the intersection of a parabola and a hyperbola . This was related to a problem of Archimedes given in On the Sphere and Cylinder. It was thought until early this century that the Dionysodorus who Eutocius refers to was Dionysodorus of Amisene described by Strabo. There is a second Dionysodorus who appears in the writings of Pliny . In Natural history Pliny mentions a certain Dionysodorus who measured the earth's radius and gave the value 42000 stades. Strabo distinguishes this Dionysodorus from Dionysodorus of Amisene and it is now thought that the Dionysodorus referred to by Pliny is not the mathematician who solved the problem of the cubic equation. Interestingly Pliny died as a result of the eruption of Vesuvius in 79 AD and it is as a consequence of this eruption that new information regarding a mathematician Dionysodorus was published in 1900 Back

12. References For Dionysodorus References for the biography of dionysodorus http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

13. Cubes In Greece A Story Tells Us About King Minos Being must almost certainly be written by the dionysodorus we are describing here.In this work dionysodorus calculates the volume of a torus and shows that http://hem.passagen.se/ceem/greece.htm

Cubes in Greece A story tells us about King Minos being disappointed with his son, Glaukos´ cubic tombstone, he wanted the tombstone to be replaced by one having twice the volume. But his mathematicans failed to construct the new one. One example of where a value of a cubic root is approximated is in Heron's *metrica* in which he simply gives a numerical recipe, without either its general form or any justification or explanation. He writes: [to find the cube of 100] "Take the nearest cube numbers to 100 that are greater and lesser, these are 125 and 64. Then compute the differences with the number sought: 125-100=25 and 100-64=36. Multiply 5 by 36; this is 180. Add 100, getting 280. Divide 180 by 280, this gives 9/14. Add this to the side of the smaller cube, this gives 4 9/14. This is as near as is possible to the cubic parts [cubic side] of 100." There has been some discussion and conjecture on what 'formula' Heron might have had, or what the origin of this recipe might have been. Hippocrates of Chios was the first known to 'reduce' a problem, when he showed that to solve the doubling-the-cube problem (by ruler-and-compass construction only), one can do it if one can construct two mean proportionals. Solving the two mean proportion problem then became the issue at stake. Archytas, perhaps a generation or so later, showed another reduction although not a ruler-and-compass construction, so not a complete or proof-satisfactory solution.

14. History Of Mathematics Greece Amisus dionysodorus Antinopolis Serenus Apameia Posidonius dionysodorus of Amisus (c. 200?) Diocles of Carystus (c. 180) http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

15. Demosthenes, Speeches 51-61 I am inclined to think, however, dionysodorus and Euthydemus, http://www.perseus.tufts.edu/cgi-bin/ptext?lookup=Dem. 56 1

16. TMTh PHILONIDES OF LAODICEA Student of Eudemus, Apollonius of Perga (who called him the 'great geometer) and dionysodorus the Younger. Cited by Polybius and Stobaeus. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

17. Plato EUTHYDEMUS 380 BC Part Three Translated By Benjamin Jowett You are ruining the argument, said Euthydemus to dionysodorus; he will be proved What, replied dionysodorus in a moment; am I the brother of Euthydemus? http://evans-experientialism.freewebspace.com/plato_euthydemus03.htm

Evans Experientialism - Evans Experientialism - Evans Experientialism Greek Academy Reading Room Plato EUTHYDEMUS 380 BC Part Three Translated by Benjamin Jowett Crito: And do you mean, Socrates, that the youngster said all this? Socrates: Are you incredulous, Crito? Crito: Indeed, I am; for if he did say so, then in my opinion he needs neither Euthydemus nor any one else to be his instructor. Socrates: Perhaps I may have forgotten, and Ctesippus was the real answerer. Crito: Ctesippus! nonsense. Socrates: All I know is that I heard these words, and that they were not spoken either by Euthydemus or Dionysodorus. I dare say, my good Crito, that they may have been spoken by some superior person: that I heard them I am certain. Crito: Yes, indeed, Socrates, by some one a good deal superior, as I should be disposed to think. But did you carry the search any further, and did you find the art which you were seeking? Socrates: Find! my dear sir, no indeed. And we cut a poor figure; we were like children after larks, always on the point of catching the art, which was always getting away from us. But why should I repeat the whole story? At last we came to the kingly art, and enquired whether that gave and caused happiness, and then we got into a labyrinth, and when we thought we were at the end, came out again at the beginning, having still to seek as much as ever. Crito: How did that happen, Socrates?

18. Euthydemus - Part I P b ERSONS OF THE DIALOGUE /b Socrates, who is the narrator of the Dialogue. Crito, Cleinias, Euthydemus, dionysodorus, Ctesippus. b SCENE /b http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

19. 20th WCP: Two Kinds Of Paideia In Plato's Euthydemus At the hands of Euthydemus and dionysodorus, the boy is simply bewildered and Furthermore, the whispered comments of dionysodorus in the ear of Socrates http://www.bu.edu/wcp/Papers/Anci/AnciSpra.htm

Ancient Philosophy Two Kinds of Paideia in Plato's Euthydemus Rosamond Kent Sprague University of South Carolina ABSTRACT: The structure of the Euthydemus Euthydemus is 'pedimental' in construction, although disagreeing with him as to where the central peripateia occurs. To place the turning point, as I would do, at 286E, is to show that the theme of the dialogue is paideia I Plato could hardly have made it more clear to the reader of the Euthydemus that his purpose in that dialogue is to contrast two kinds of education, to the praise of one and the detraction of the other. The very structure of the dialogue leads to this conclusion. Within an outer frame, in which Socrates' old friend Crito expresses anxiety about the education of his two young sons, are set five dramatic scenes. Of these the first, third, and fifth consist of displays of eristic technique on the part of two visiting sophists, the brothers Euthydemus and Dionysodorus. The remaining two scenes, the second and fourth, show Socrates in the exercise of dialctic. Not content with this overt juxtaposition of the two educational methods, Plato contrasts the two in subtler ways. Socrates and the young man Cleinias, for whose educational future he and his friends are concerned, are surrounded, not only by the alternating eristic scenes, but physically, in the actual seating arrangements indicated by Plato; Dionysodorus sits down on the left of Socrates, Euthydemus on the right of Cleinias. We appear to have an attempt on the part of eristic to encircle and imprison dialectic.

20. The Memorabilia - BOOK III "Laches." 2 dionysodorus of Chios, presumably. See Plat. "Euthyd." 271 C foll. 3 A professor of the science and art of strategy. 4 Lit. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

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