1. References For Zeno_of_Sidon References for zeno of sidon. Biography in Dictionary of ScientificBiography (New York 19701990). Books TL Heath, A history of http://www-gap.dcs.st-and.ac.uk/~history/References/Zeno_of_Sidon.html

References for Zeno of Sidon Biography in Dictionary of Scientific Biography (New York 1970-1990). Books: T L Heath, A history of Greek mathematics I, II (Oxford, 1931). L Adam, Das Wahrheits- und Hypothesenproblem bei Demokrit, Epikur und Zeno, dem Epikureer Articles: G Vlastos, Zeno of Sidon as a Critic of Euclid, in The Clasical Tradition : Literary and Historical Studies in Honor of Harry Caplan (New York, 1966), 148-159. 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/history/References/Zeno_of_Sidon.html

2. ZENO OF SIDON @desc http://65.1911encyclopedia.org/Z/ZE/ZENO_OF_SIDON.htm

document.write(""); ZENO OF SIDON ZENO OF SIDON, Epicurean philosopher of the first century B.C., and contemporary of Cicero. In the De Natura Deorum (i. 34), Cicero states that he was contemptuous of other philosophers and even called Socrates " the Attic Buffoon." Diogenes Laertius and Cicero both speak of him with respect and describe him as an accurate and polished thinker. He held that happiness' includes not merely present enjoyment and prosperity, but also a reasonable expectation of their continuance. His views were made the subject of a special treatise by Posidonius.

3. Zeno_of_Sidon zeno of sidon. Born about zeno of sidon was born in the city of Sidonon the Mediterranean coast of what today is Lebanon. Sidon was http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Zeno_of_Sidon.html

Zeno of Sidon Born: about 150 BC in Sidon (now Saida in Lebanon) Died: about 70 BC in Athens, Greece Click the picture above to see a larger version Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Zeno of Sidon was born in the city of Sidon on the Mediterranean coast of what today is Lebanon. Sidon was one of the oldest Phoenician cities and, from its founding in the 3rd millennium BC, was ruled by many different peoples: Assyria, Babylonia, Persia, Alexander the Great , the Seleucids of Syria, the Ptolemys of Egypt, and the Romans. To understand the philosophy of Zeno we need to make some comments about the philosopher Epicurus who founded the Epicurean School to which Zeno later belonged. Epicurus, who lived from 341BC to 270 BC, founded his own School of philosophy based on his teachings. These teachings were designed to indicate a means of living ones life, and they aimed both to guarantee happiness and to provide a means to find it. Epicurus had no interest in science for its own sake and he was a severe critic of mathematics. On science he wrote:- If we were not troubled by our suspicions of the phenomena of the sky and about death, and also by our failure to grasp the limits of pain and desires, we should have no need of natural science.

4. Zeno_of_Sidon Biography of zeno of sidon (150BC70BC) zeno of sidon. Born about 150 BC in Sidon (now Saida in Lebanon) http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Zeno_of_Sidon.html

Zeno of Sidon Born: about 150 BC in Sidon (now Saida in Lebanon) Died: about 70 BC in Athens, Greece Click the picture above to see a larger version Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Zeno of Sidon was born in the city of Sidon on the Mediterranean coast of what today is Lebanon. Sidon was one of the oldest Phoenician cities and, from its founding in the 3rd millennium BC, was ruled by many different peoples: Assyria, Babylonia, Persia, Alexander the Great , the Seleucids of Syria, the Ptolemys of Egypt, and the Romans. To understand the philosophy of Zeno we need to make some comments about the philosopher Epicurus who founded the Epicurean School to which Zeno later belonged. Epicurus, who lived from 341BC to 270 BC, founded his own School of philosophy based on his teachings. These teachings were designed to indicate a means of living ones life, and they aimed both to guarantee happiness and to provide a means to find it. Epicurus had no interest in science for its own sake and he was a severe critic of mathematics. On science he wrote:- If we were not troubled by our suspicions of the phenomena of the sky and about death, and also by our failure to grasp the limits of pain and desires, we should have no need of natural science.

5. Zeno Of Sidon Name Zeno. Occupation From Sidon. Son of Occupation Dates fl.15070 BC. Brief biography An Epicurean. Raised some fundamental http://www.swan.ac.uk/classics/staff/ter/grst/People/ZenoSidon.htm

Name Zeno Occupation: From Sidon Son of: Occupation: Dates fl . 150-70 BC Brief biography An Epicurean. Raised some fundamental criticisms of Euclid’s Elements , but it is exaggeration to say that he was the first to contemplate the possibility of non-Euclidean geometry. If the full implications of his criticisms had been grasped by those trying to refute him, then the history of maths may have been different. Context Works References K von Fritz DSB T E Rihll Last modified: 18 June 2001

6. The Big Picture Karneades, Kritolaos, Diogenes at Rome as envoys (155) and lecture on philosophy.150, Third Punic War begins (149), Nikander fl.; Seleucus fl.; b. zeno of sidon, http://www.swan.ac.uk/classics/staff/ter/grst/big.htm

The Big Picture The value of a table like this is to be able to see what is going on in many areas simultaneously, so to keep the table to reasonable proportions all events are tabulated in the nearest 5 year cell; actual date (if known) is given in brackets. Innovations and developments in technology are very difficult to date accurately. Unless there is a date in brackets after such an entry, its position in the table should be regarded as approximate, indicating our earliest evidence of such a technology, rather than the date of its invention (which would be earlier). This page is continuously under development. It is large, and will take a minute to download. 1-250 AD is now included. X(X) indicates battle(s). b . indicates birth. d . indicates death. c circa ) means approximately. fl floruit ) means active around this time. MSS means manuscripts. Aqua is an aqueduct of Rome, Fossa a canal. Date BC Military Technology Political Science Other Eupalinos' tunnel , 1km long; Eretria jetty 700m long, 20m deep. Ionian Revolt (499-94 BC) Herakleitos fl Skulax fl b Anaxagoras d Pythagoras Anchor with flukes b Sophokles Persians invade Greece;

7. Phoenicia, Phoenicians: Zeno Of Sidon Biography of zeno of sidon (150BC70BC) http://www.phoenicia.org/zeno.html

A Bequest Unearthed Phoenicia Zeno of Sidon Comprehesive Website on the Phoenicians SEARCH Phoenicia Get a Search Engine For Your Web Site Born c. 150 BC in Sidon, Phoenicia and died in Athens, Greece c. 70 BC. To understand the philosophy of Zeno one needs to make some comments about the philosopher Epicurus who founded the Epicurean School to which Zeno later belonged. Epicurus, who lived from 341 BC to 270 BC, founded his own School of philosophy based on his teachings. These teachings were designed to indicate a means of living ones life, and they aimed both to guarantee happiness and to provide a means to find it. Epicurus had no interest in science for its own sake and he was a severe critic of mathematics. On science he wrote: If we were not troubled by our suspicions of the phenomena of the sky and about death, and also by our failure to grasp the limits of pain and desires, we should have no need of natural science. His criticisms of mathematics were very superficial of little importance since he clearly had very little understanding of the subject. In 306 BC he founded his School in Athens in the garden of his house. Reasonably enough the School became known as The Garden.

8. Phoenicia, Phoenicians: Zeno Of Sidon zeno of sidon, the Genius at Work Born c. 150 BC in Sidon, Phoeniciaand died in Athens, Greece c. 70 BC. To understand the philosophy http://phoenicia.org/zeno.html

A Bequest Unearthed Phoenicia Zeno of Sidon Comprehesive Website on the Phoenicians SEARCH Phoenicia Get a Search Engine For Your Web Site Born c. 150 BC in Sidon, Phoenicia and died in Athens, Greece c. 70 BC. To understand the philosophy of Zeno one needs to make some comments about the philosopher Epicurus who founded the Epicurean School to which Zeno later belonged. Epicurus, who lived from 341 BC to 270 BC, founded his own School of philosophy based on his teachings. These teachings were designed to indicate a means of living ones life, and they aimed both to guarantee happiness and to provide a means to find it. Epicurus had no interest in science for its own sake and he was a severe critic of mathematics. On science he wrote: If we were not troubled by our suspicions of the phenomena of the sky and about death, and also by our failure to grasp the limits of pain and desires, we should have no need of natural science. His criticisms of mathematics were very superficial of little importance since he clearly had very little understanding of the subject. In 306 BC he founded his School in Athens in the garden of his house. Reasonably enough the School became known as The Garden.

9. Zeno_of_Sidon Portraits zeno of sidon. This is a detail from the fresco The School of Athens by Raphael http://www-history.mcs.st-and.ac.uk/PictDisplay/Zeno_of_Sidon.html

Zeno of Sidon This is a detail from the fresco The School of Athens by Raphael You can see the whole fresco JOC/EFR August 2001 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/PictDisplay/Zeno_of_Sidon.html

10. Phoenicia, Phoenicians: A Bequest Unearthed, Summary And Introduction Theodosia of Tyre, Christian martyr (died 293 AD) Ulpian, Jurist Zadok the PriestZeno of Citium, Philosopher zeno of sidon, Philosopher Others (more to come). http://phoenicia.org/noframe.html

A Bequest Unearthed Phoenicia Summary: Introduction Comprehesive Website on the Phoenicians SEARCH Phoenicia Get a Search Engine For Your Web Site HOME Alphabet America ... (Guestbook) Missionaries of Civilization Phoenician, what's in a name? It is not certain what the Phoenicians called themselves in their own language; it appears to have been Kena'ani (Akkadian: Kinahna), "Canaanites." In Hebrew the word kena'ani has the secondary meaning of "merchant," a term that well characterizes the Phoenicians. The Greeks gave the new appellation Phoenicians to those Canaanites who lived on the seacoast and traded with them. Phoenicia is the Greek work for "purple". The most probable reason for giving this name is the famous Tyrian purple cloth which the Phoenicians manufactured and sold to the rich of the ancient world. Ethnic Origin and Language The Phoenicians probably arrived in the Eastern Mediterranean about 3000 B.C., however, nothing is known of their original homeland. What may be the most common ethnic origin they are considered to be is Semitic; however, some studies suggest that their original homeland may have been in the Indian sub-continent long before 3000 B.C. while other studies trace their origin, according to Irish records, to suggest that they descend from a Scythian King named Phoeniusa Farsa...according to the

11. History 150-70 BC zeno of sidon could be well described as a nonconformist or a very critical mathematician. Born in approximately 150 B.C, in Sidon or presently Saida in Lebanon, Zeno was particularly critical of Euclid's work with Geometry. http://employees.oxy.edu/jquinn/home/Math490/Timeline/100BC.html

150-70 BC Zeno of Sidon could be well described as a non-conformist or a very critical mathematician. Born in approximately 150 B.C, in Sidon or presently Saida in Lebanon, Zeno was particularly critical of Euclid's work with Geometry. Specifically, Zeno criticized Euclid's 1st proposition on the grounds that it was necessary for Euclid to include an axiom stating that two straight lines can intersect in at most one point. Furthermore, Zeno was also reluctant to accept the existence of a right angle. He challenged Euclid's proof on the equality of right triangles. For this reason, Zeno could be considered the pioneer of non-Euclidean geometry. Author: Filiberto Barajas References: Biography in Dictionary of Scientific Biography (New York, 1970-1990) G Vlastos, Zeno of Sidon as a Critic of Euclid. The Classical Tradition: Literary and Historical Studies in Honor of Harry Caplan (New York, 1966), 148-159. As listed in URL Math 490 Home Class Tasks Class Mailing List History Links ... Timeline Last updated September 1998

12. PHILTAR - Compendium Of Philosophers/Z Zenos paradox of the arrow. zeno of sidon (c150c70) http://www.philtar.ucsm.ac.uk/compendium_of_philosophers/z

Compendium of Philosophers Z Links to materials by and/or about over a thousand philosophers from thousands of years from all over the world from A to Z This compendium contains entries large and small, single or multiple, on hundreds of philosophers. Links vary in size from a few lines of biography to the whole of the Summa Theologica. Sometimes you are directed to a site which has further links. In that case there is no guarantee that all the further links will work, but enough work to make a visit worthwhile. This compendium does not provide links to philosophers’ own home pages. A list of them can be found here A B C ... Z Zallinger zum Thurn, Jacob Anton (1735-1813) A brief introduction from TCE Zarathustra [Zoroaster] (7th century BC) This page provides an outline of his life, with links to more detailed materials This site provides links to a number of essays introducing his teachings Zeno of Citium (342-270 BC) Zeno of Citium A useful essay on the founder of Stoicism. Zeno of Elea (5th century BC) An introduction to his life and thought from the on-line edition of Burnet’s Early Greek Philosophy An introduction to his life and work from the IEP More on Zeno’s race course The paradox of the race course. ... Zeno’s paradox of the arrow Zeno of Sidon (c150-c70) An introduction to his life and work Zermelo, Ernst Friedrich Ferdinand (1871-1953)

13. ZENODOTUS OF EPHESUS 972 P P zeno of sidon—ZENODOTUS P P Russell, Principles of Mathematics(Cambridge, 1903), pp. ZENODOTUS OF EPHESUS. 972. zeno of sidon—ZENODOTUS. http://69.1911encyclopedia.org/Z/ZE/ZENODOTUS_OF_EPHESUS.htm

document.write(""); ZENODOTUS OF EPHESUS ZENO OF SIDON—ZENODOTUS Russell, Principles of Mathematics (Cambridge, 1903), pp. 346-354. For histories of philosophy and other works upon Eleaticism see PARMENIDES. (H. JA.) ZENO OF SIDON, Epicurean philosopher of the first century B.C., and contemporary of Cicero. In the De Natura Deorum (i. 34), Cicero states that he was contemptuous of other philosophers and even called Socrates " the Attic Buffoon." Diogenes Laertius and Cicero both speak of him with respect and describe him as an accurate and polished thinker. He held that happiness' includes not merely present enjoyment and prosperity, but also a reasonable expectation of their continuance. His views were made the subject of a special treatise by Posidonius. ZENO OF TARSUS, Stoic philosopher and pupil of Chry-sippus, belonged to the period of the Middle Stoa. He appears to have accepted all the Stoic doctrines except that he denied the final conflagration of the universe (see STOICS). 1 See the Palmyrene inscriptions given in Vogiie', Syrie centrale, Nos. 28, 29 = Cooke, North-Semitic Inscriptions, Nos. 130, 131. Zabbai, an abbreviation of some such form as Za.bd-ila, = dowry of Cod, was a common Palmyrene name; it occurs in the Old Testament, Ezr. x. 28; Neh. iii. 20. help from the Persian king;2 they were captured on the bank of the Euphrates, and the Palmyrenes, losing heart

14. Ze ZEALAND (ISL.) ZEBRA ZEBULUN ZECHARIAH ZEDEKIAH ZEEBARIAH ZEEHAN ZEELAND ZEERUST ZEISSBERG, HEINRICH, RITTER VON ZEITUN ZEITZ ZELLER, EDUARD ZEMARCHUS ZENAGA ZENANA ZENATA ZENDAVESTA ZENGG ZENITH ZENJAN ZENO ZENO OF ELEA zeno of sidon http://www.1911ency.org/Z/ZE

Z/ZE ZEALAND (ISL.) ZEBRA ZEBULUN ZECHARIAH ... ZEUXIS

15. ZENTA 972 P P zeno of sidon—ZENODOTUS P P Russell, Principles of Mathematics(Cambridge, 1903), pp. ZENTA. 972. zeno of sidon—ZENODOTUS. http://70.1911encyclopedia.org/Z/ZE/ZENTA.htm

document.write(""); ZENTA ZENO OF SIDON—ZENODOTUS Russell, Principles of Mathematics (Cambridge, 1903), pp. 346-354. For histories of philosophy and other works upon Eleaticism see PARMENIDES. (H. JA.) ZENO OF SIDON, Epicurean philosopher of the first century B.C., and contemporary of Cicero. In the De Natura Deorum (i. 34), Cicero states that he was contemptuous of other philosophers and even called Socrates " the Attic Buffoon." Diogenes Laertius and Cicero both speak of him with respect and describe him as an accurate and polished thinker. He held that happiness' includes not merely present enjoyment and prosperity, but also a reasonable expectation of their continuance. His views were made the subject of a special treatise by Posidonius. ZENO OF TARSUS, Stoic philosopher and pupil of Chry-sippus, belonged to the period of the Middle Stoa. He appears to have accepted all the Stoic doctrines except that he denied the final conflagration of the universe (see STOICS). 1 See the Palmyrene inscriptions given in Vogiie', Syrie centrale, Nos. 28, 29 = Cooke, North-Semitic Inscriptions, Nos. 130, 131. Zabbai, an abbreviation of some such form as Za.bd-ila, = dowry of Cod, was a common Palmyrene name; it occurs in the Old Testament, Ezr. x. 28; Neh. iii. 20. help from the Persian king;2 they were captured on the bank of the Euphrates, and the Palmyrenes, losing heart

16. Greek Index Zeno of Elea. zeno of sidon. Zenodorus. Greek Mathematicans/Philosophers http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Greek_index.html

Index of Greek mathematicians Below are various lists of Greek mathematicians. Full list Mathematicans/Philosophers Mathematicians/Astronomers Mathematicians/Astronomers/Philosophers ... Later circle squarers Some History Topics about Greek mathematics. Squaring the circle Doubling the cube Trisecting an angle Greek Astronomy Click on a name below to go to that biography. Full List of Greek Mathematicians in our archive Anaxagoras Anthemius Antiphon Apollonius ... Zenodorus Greek Mathematicans/Philosophers Anaxagoras Antiphon Archytas Aristotle ... Zeno of Elea Greek Mathematicians/Astronomers Apollonius Archimedes Aristarchus Aristotle ... Theon of Smyrna Greek Mathematicians/Astronomers/Philosophers Aristotle Cleomedes Democritus Eudoxus ... Thales Greek Circle squarers Anaxagoras Antiphon Apollonius Archimedes ... Bryson Carpus Dinostratus Hippias Hippocrates Nicomedes ... Sporus Later Circle squarers al-Haytham Johann Bernoulli Cusa James Gregory ... Societies, honours, etc JOC/EFR January 2000 The URL of this page is: School of Mathematics and Statistics University of St Andrews, Scotland http://www-history.mcs.st-andrews.ac.uk/history/Indexes/Greek_index.html

17. Biography-center - Letter Z Mathematicians/Zeno_of_Elea.html; zeno of sidon, wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/Zeno_of_Sidon.html;Zeppelin, Ferdinand http://www.biography-center.com/z.html

Visit a 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 Z 69 biographies Zada, al-Rumi Qadi www-history.mcs.st-and.ac.uk/~history/Mathematicians/Qadi_Zada.html Zakharchenko, M V- www-history.mcs.st-and.ac.uk/~history/Mathematicians/Vashchenko.html Zanardi, Alessandro www.grandprix.com/gpe/drv-zanale.html Zanotti, Giampietro www.getty.edu/art/collections/bio/a3532-1.html Zapata, flag.blackened.net/revolt/ws/zapata41.html Zarankiewicz, Kazimierz www-history.mcs.st-and.ac.uk/~history/Mathematicians/Zarankiewicz.html Zaremba, Stanislaw www-history.mcs.st-and.ac.uk/~history/Mathematicians/Zaremba.html Zariski, Oscar www-history.mcs.st-and.ac.uk/~history/Mathematicians/Zariski.html Zassenhaus, Hans www-history.mcs.st-and.ac.uk/~history/Mathematicians/Zassenhaus.html Zatopek, Emil

18. History 150-70 BC 15070 BC zeno of sidon could be well described as a non-conformist or a verycritical mathematician. G Vlastos, zeno of sidon as a Critic of Euclid. http://faculty.oxy.edu/jquinn/home/Math490/Timeline/100BC.html

150-70 BC Zeno of Sidon could be well described as a non-conformist or a very critical mathematician. Born in approximately 150 B.C, in Sidon or presently Saida in Lebanon, Zeno was particularly critical of Euclid's work with Geometry. Specifically, Zeno criticized Euclid's 1st proposition on the grounds that it was necessary for Euclid to include an axiom stating that two straight lines can intersect in at most one point. Furthermore, Zeno was also reluctant to accept the existence of a right angle. He challenged Euclid's proof on the equality of right triangles. For this reason, Zeno could be considered the pioneer of non-Euclidean geometry. Author: Filiberto Barajas References: Biography in Dictionary of Scientific Biography (New York, 1970-1990) G Vlastos, Zeno of Sidon as a Critic of Euclid. The Classical Tradition: Literary and Historical Studies in Honor of Harry Caplan (New York, 1966), 148-159. As listed in URL Math 490 Home Class Tasks Class Mailing List History Links ... Timeline Last updated September 1998

19. Zeno_of_Sidon zeno of sidon. Born about Athens, Greece. zeno of sidon was born in thecity of Sidon on the Mediterranean coast of what today is Lebanon. http://homepages.compuserve.de/thweidenfeller/mathematiker/Zeno_of_Sidon.htm

Zeno of Sidon Born: about 150 BC in Sidon (now Saida in Lebanon) Died: about 70 BC in Athens, Greece Zeno of Sidon was born in the city of Sidon on the Mediterranean coast of what today is Lebanon. Sidon was one of the oldest Phoenician cities and, from its founding in the 3rd millennium BC, was ruled by many different peoples: Assyria, Babylonia, Persia, Alexander the Great , the Seleucids of Syria, the Ptolemys of Egypt, and the Romans. To understand the philosophy of Zeno we need to make some comments about the philosopher Epicurus who founded the Epicurean School to which Zeno later belonged. Epicurus, who lived from 341BC to 270 BC, founded his own School of philosophy based on his teachings. These teachings were designed to indicate a means of living ones life, and they aimed both to guarantee happiness and to provide a means to find it. Epicurus had no interest in science for its own sake and he was a severe critic of mathematics. On science he wrote:- If we were not troubled by our suspicions of the phenomena of the sky and about death, and also by our failure to grasp the limits of pain and desires, we should have no need of natural science. His criticisms of mathematics were very superficial of little importance since he clearly had very little understanding of the subject. In 306 BC he founded his School in Athens in the garden of his house. Reasonably enough the School became known as The Garden.

20. Euclid's Elements, Book I, Proposition 1 Proclus relates that early on there were critiques of the proof and describes thatof zeno of sidon, an Epicurean philosopher of the early first century BCE http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI1.html

Proposition 1 To construct an equilateral triangle on a given finite straight line. Let AB be the given finite straight line. It is required to construct an equilateral triangle on the straight line AB. Describe the circle BCD with center A and radius AB. Again describe the circle ACE with center B and radius BA. Join the straight lines CA and CB from the point C at which the circles cut one another to the points A and B. Post.3 Post.1 Now, since the point A is the center of the circle CDB, therefore AC equals AB. Again, since the point B is the center of the circle CAE, therefore BC equals BA. I.Def.15 But AC was proved equal to AB, therefore each of the straight lines AC and BC equals AB. And things which equal the same thing also equal one another, therefore AC also equals BC. C.N.1 Therefore the three straight lines AC, AB, and BC equal one another. Therefore the triangle ABC is equilateral, and it has been constructed on the given finite straight line AB. I.Def.20 Q.E.F. This proposition is a very pleasant choice for the first proposition in the Elements.

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