1. Euclid's Elements, Book I, Proposition 1 were critiques of the proof and describes that of zeno of sidon, an Epicurean philosopher of the early zeno of sidon criticized the proof because it was not shown that 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.

2. 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 72 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 Zapatero, Jose Luis Rodriguez www.spainview.com/biog21.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

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 3 rd 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 Comprehensive studies on of everything Canaanite Phoenicians in Lebanon, Israel, Syria, world zeno of sidon. 900 pages onPhoenicians follower of Epicurus who lived in the 2nd century BC. Zeno http://www.phoenicia.org/zeno.html

A Bequest Unearthed Phoenicia Encyclopedia Phoeniciana Zeno of Sidon 900 pages on Phoenicians Search Phoenicia Get a Search Eine For Your Site TRANSLATE this page 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.

5. 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 Classical 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/References/Zeno_of_Sidon.html

6. 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 the subject of a special treatise by Posidonius. «. ZENO OF ELEA. ZENO OF TARSUS http://www.1911encyclopedia.org/Z/ZE/ZENO_OF_SIDON.htm

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. ZENO OF ELEA ZENO OF TARSUS

7. ZENO OF SIDON zeno of sidon, Epicurean philosopher of the first century BC, and contemporaryof Cicero. In the De Natura states that he was. zeno of sidon. http://65.1911encyclopedia.org/Z/ZE/ZENO_OF_SIDON.htm

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. ZENO OF ELEA ZENO OF TARSUS

8. Zeno_of_Sidon Biography of zeno of sidon (150BC70BC) zeno of sidon. Born about 150 BC in Sidon (now Saida in Lebanon) zeno of sidon was born in the city of Sidon on the Mediterranean coast of 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 3 rd 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.

9. Zeno Of Sidon, The Genius At Work 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://www.cartage.org.lb/en/themes/GeogHist/histories/Oldcivilization/phoenicia

Themes History Old Civilizations Phoenicia Zeno of Sidon Zeno of Sidon, the Genius at Work 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.

10. ZENO OF TARSUS ZENO OF TARSUS. ZENO OF TARSUS, Stoic philosopher and pupil of Chrysippus, belonged to the period final conflagration of the universe (see STOICS). «. zeno of sidon. ZENTA http://www.1911encyclopedia.org/Z/ZE/ZENO_OF_TARSUS.htm

ZENO OF TARSUS 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). ZENO OF SIDON ZENTA

11. Index: Phoenicia their earliest home in India. Treasures zeno of sidon, the Geniusat Work Zeno of Citium, Founder of Stoic School of Philosophy. http://www.cartage.org.lb/en/themes/GeogHist/histories/Oldcivilization/phoenicia

Themes History Old Civilizations Phoenicia Information supplied by: "http://phoenicia.org Alphabet Architecture Art Australia ... Philosophy

12. Spoken Lebanese Gibran Khalil GIBRAN. zeno of sidon. Places In Lebanon Gibran Khalil GIBRAN. zeno of sidon. Notice Microsoft has no responsibility for the content featured in this group http://groups.msn.com/spokenlebanese/lebaneseauthors.msnw

var nEditorialCatId = 258; MSN Home My MSN Hotmail Shopping ... Money Web Search: Groups Groups Home My Groups Language ... Help Spoken Lebanese spokenlebanese@groups.msn.com What's New Join Now The Lebanese Constitution National Anthem ... Zeno of Sidon Notice: Microsoft has no responsibility for the content featured in this group. Click here for more info. Try MSN Internet Software for FREE! MSN Home My MSN ... GetNetWise

13. Zeno Of Sidon zeno of sidon. zeno of sidon was a student of Apollodorus and he studied, and latertaught, in the Garden in Athens. Cicero heard him teaching there in 79 BC. http://phoenicia.org/zeno.html

A Bequest Unearthed Phoenicia Encyclopedia Phoeniciana Zeno of Sidon 900 pages on Phoenicians Search Phoenicia Get a Search Eine For Your Site TRANSLATE this page 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.

14. Spoken Lebanese Gibran Khalil GIBRAN. zeno of sidon. Places In Lebanon Gibran Khalil GIBRAN. zeno of sidon. Notice Microsoft has no responsibility for the content featured in this group http://groups.msn.com/SpokenLebanese/lebaneseauthors.msnw

var nEditorialCatId = 258; MSN Home My MSN Hotmail Shopping ... Money Web Search: Groups Groups Home My Groups Language ... Help Spoken Lebanese SpokenLebanese@groups.msn.com What's New Join Now The Lebanese Constitution National Anthem ... Zeno of Sidon Notice: Microsoft has no responsibility for the content featured in this group. Click here for more info. Try MSN Internet Software for FREE! MSN Home My MSN ... GetNetWise

15. 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 Encyclopedia Phoeniciana Summary: Introduction 900 pages on Phoenicians Search Phoenicia Get a Search Eine For Your Site TRANSLATE this page HOME Adonis ... (Guestbook) take my poll at: Phoenicians Today: htmlGEAR.com 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

16. A Bequest Unearthed, Summary And Introduction Jezebel Princess of Sidon and Queen of Israel (wife of King Ahab of Israel) Zadok the Priest. Zeno of Citium, Philosopher. zeno of sidon, Philosopher. Others (more to come http://www.phoenicia.org/noframe.html

A Bequest Unearthed Phoenicia Encyclopedia Phoeniciana Summary: Introduction 900 pages on Phoenicians Search Phoenicia Get a Search Eine For Your Site TRANSLATE this page HOME Adonis ... (Guestbook) take my poll at: Phoenicians Today: htmlGEAR.com 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

17. Zeno_of_Sidon zeno of sidon. Born about 150 BC in Sidon (now Saida in Lebanon) Died about70 BC in Athens, Greece. zeno of sidon made deep criticisms of Euclid. http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/ZnfSdn.htm

Zeno of Sidon Born: about 150 BC in Sidon (now Saida in Lebanon) Died: about 70 BC in Athens, Greece Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page Zeno of Sidon made deep criticisms of Euclid . For example he claimed that Euclid 's first proposition assumes that two straight lines can intersect in at most one point but Euclid does not have this as an axiom. He attacked Euclid 's proof of the equality of right angles on the grounds that it presupposes the existence of a right angle. Some have suggested that these claims give Zeno of Sidon some justification to be considered as having first considered the possibility of non-Euclidean geometry. Zeno also discussed the principle of induction. References (2 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/Zeno_of_Sidon.html

18. Greek Index Theodosius. Theon of Alexandria. Theon of Smyrna. Thymaridas. Xenocrates. Zeno of Elea. zeno of sidon. Zenodorus Proclus. Ptolemy. Pythagoras. Simplicius. Thales. Xenocrates. Zeno of Elea http://stm21645-01.k12.fsu.edu/Greek_Index.htm

Index of Greek mathematicians Below are various lists of Greek mathematicians. Full list Mathematicans/Philosophers Mathematicians/Astronomers Mathematicians/Astronomers/Philosophers ... Later circle squarers Click on a name to go to that biography. Some History Topics about Greek mathematics. Squaring the circle Doubling the cube Trisecting an angle Greek Astronomy 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'Haitam Johann Bernoulli Cusa Franco of Liège James Gregory Lambert Leonardo Lindemann ... Search Suggestions JOC/EFR April 1999 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/Indexes/Greek_index.html

19. References For Zeno_of_Sidon References for zeno of sidon. Biography in Dictionary of ScientificBiography (New York 19701990). Articles G Vlastos, Zeno of http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/~DZ9377.htm

References for Zeno of Sidon Biography in Dictionary of Scientific Biography (New York 1970-1990). Articles: G Vlastos, Zeno of Sidon as a Critic of Euclid, The Clasical Tradition : Literary and Historical Studies in Honor of Harry Caplan (New York, 1966), 148-159. Close this window or click this link to go back to Zeno of Sidon 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/Zeno_of_Sidon.html

20. 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

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