81. Classics-L: RE: Never Mind Loneliest: Is 1 A Number At All? I am afraid I don't have the time to give an exact reference either, at the moment,but a good place to start is either nicomachus' of gerasa (who defined http://omega.cohums.ohio-state.edu:8080/hyper-lists/classics-l/99-12-01/0525.htm

RE: Never mind loneliest: is 1 a number at all? Date view Thread view Subject view Author view Subject: RE: Never mind loneliest: is 1 a number at all? From: Rainer Thiel ( thielr@Mailer.Uni-Marburg.DE Date: Fri Nov 26 1999 - 04:48:01 EST Next message: J.F. Gannon: "Re: Never mind loneliest: is 1 a number at all?" Previous message: Herrelko@aol.com: "Re: Mary and servants" In reply to: Jacob Knee: "RE: Ownership of the Elgin Marbles" Reply: J.F. Gannon: "Re: Never mind loneliest: is 1 a number at all?" I am afraid I don't have the time to give an exact reference either, at the moment, but a good place to start is either Nicomachus' of Gerasa (who defined himself as Pythagorean, hence Prof. Gannon is right) Introductio arithmetica (or Boethius close paraphrase thereof) or Proclus' commentary on the first book of Euclid's Elements. The Short Answer is: In an abstract way, one could also say that as number is defined as unity composed of a plurality of units, 1 cannot be considered as a number, because it is not composed, and doesn't consist of a plurality of numbers. Priv.-Doz. Dr. Rainer Thiel

82. NICOMACHUS nicomachus. nicomachus, a Neopythagorean philosopher and mathematician,born at gerasa in Arabia Petraea, flourished about AD 100. http://67.1911encyclopedia.org/N/NI/NICOMACHUS.htm

document.write(""); NICOMACHUS 1 Matthias may have been a cousin of Richard Nicolls; his family were of Islip, Oxford; he was secretary of the province, held various judicial positions, and was mayor of New York City in 1672. Matthias's son William (1657—1723), a lawyer, was a member of the New York Assembly from 1702 until his death and was speaker in 1702-1718; he received a royal patent for what is now the town of Islip on Long Island. Descendants of Richard and of Matthias Nicolls spell the name " Nicoll." (The Theology of Arithmetic), written in a spirit of Pythagorean mysticism and Oriental superstition, and setting forth the application of arithmetic, or rather of the first ten numbers, to the origin and attributes of the gods. But the extracts in Photius are now generally attributed to lamblichus. Other works of Nicomachus were: a Life of Pythagorcts and a 'ollection of Pythagorean Doctrines, the chief source of the life of Pythagoras and the account of his philosophy by lamblichus. NICOMACHUS, of Thebes, Greek painter, of the early part of the 4th century, was a contemporary of the greatest painters of Greece; Vitruvius observes that if his fame was less than theirs, it was the fault of fortune rather than of demerit. Pliny (xxxv. 108) gives a list of his works; among them a " Rape of Persephone," " Victory in a Quadriga," a group of Apollo and Artemis, and the " Mother of the Gods seated on a Lion." Pliny tells us that he was a very rapid worker and used but four colours (the last seems impossible). Plutarch mentions his paintings as possessing the Homeric merit of ease and absence of effort.

83. M598/M700 - MATHIESEN - SPRING 2000 Music Library Reserve Books And Scores nicomachus, of gerasa. Encheiridion harmonikes. English The manual of harmonicsof nicomachus the Pythagorean / translation and commentary by Flora R. Levin. http://www.dlib.indiana.edu/variations/reserves/old/spring00/m598m700mlo.html

William and Gayle Cook Music Library M598/M700 - MATHIESEN - SPRING 2000 Reserve Books and Scores Aristides Quintilianus. On music, in three books / Aristides Quintilianus ; translation with introduction, commentary, and annotations by Thomas J. Mathiesen. New Haven : Yale University Press, c1983. (Music theory translation series) Aristoxenus. Aristoxenou Harmonika stoicheia = The harmonics of Aristoxenus / edited with translation notes, introduction, and index of words by Henry S. Macran. Oxford : Clarendon Press, 1902. Augustine, Saint, Bishop of Hippo. cn (The Fathers of the Church) BR60.F2 A92 vol. 2 Barbera, Charles Andre. The persistence of Pythagorean mathematics in ancient musical thought / Charles Andre Barbera. 1980. Bernard Silvestris, fl. 1136. The Cosmographia of Bernardus Silvestris. A translation with introd. and notes by Winthrop Wetherbee. New York, Columbia University Press, 1973. Boethius, his life, thought, and influence / edited by Margaret Gibson. Oxford : Blackwell, 1981. Boethius, d. 524. Fundamentals of music / Anicius Manlius Severinus Boethius ; translated, with

84. Sieb Des Eratosthenes Translate this page Etwa 300 Jahre später überlieferte nicomachus von gerasa das Verfahren in seinemBuch ?Introductio Arithmeticae“ und gab ihm den Namen ?Sieb des http://www.primzahlen.de/files/referent/kw/sieb.htm

Walisch Kim: Sieb des Eratosthenes (EcprimeV1.12) Eratosthenes Programm Algorithmus Benchmark ... Download Eratosthenes von Kyrene: Sieb des Eratosthenes: Das Sieb des Eratosthenes und das davon abgeleitete Sieb von Atkin sind bis heute die schnellsten Methoden um alle Primzahlen bis circa 10^10 zu finden. Programm Beschreibung: Algorithmus: Das Programm ist in effizientem C/C++ geschrieben. 31, 37, 41, 43, 47, 49, 53, 59 //Byte Benchmarks: Getestet auf einem Pentium III 550MHZ, Sieve size 15015 bytes. x Prims(x) Twins(x) Time 0.010 sek 0.010 sek 0.010 sek 0.010 sek 0.010 sek 0.010 sek 0.030 sek 0.200 sek 2.533 sek 38.515 sek Intel C++ 6.0 Download: ecprime.exe.zip 46 kb Windows ecprime.source.zip 10 kb Windows Forschung: pix.html (noch nicht komplett) Feedback: kim_walisch@gmx.net Links: http://wwwhomes.uni-bielefeld.de/achim/prime_sieve.html (The Art of Prime Sieving) http://cr.yp.to/primegen.html (D. J Bernstein, primegen) http://www.trnicely.net/pi/tabpi.html (table of prime counts)

85. Biography-center - Letter N Nicollier, Claude www.jsc.nasa.gov/Bios/htmlbios/nicollie.html; nicomachus ofGerasa, wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/nicomachus.html; http://www.biography-center.com/n.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 N 187 biographies Nabokov, Vladimir www.libraries.psu.edu/iasweb/nabokov/bio.htm Nabokov, Vladimir www.randomhouse.com/features/nabokov/biography.html Nadar, www.getty.edu/art/collections/bio/a1622-1.html Nadar, Paul www.getty.edu/art/collections/bio/a1621-1.html Nadi, Nedo www.olympic.org/uk/athletes/heroes/bio_uk.asp?PAR_I_ID=54806 Naegeli, Oskar www.whonamedit.com/doctor.cfm/984.html Naffziger, Howard Christian www.whonamedit.com/doctor.cfm/752.html Nagel, Steven R. www.jsc.nasa.gov/Bios/htmlbios/nagel.html Nageotte, Jean www.whonamedit.com/doctor.cfm/756.html Nagyrapolt, Albert Szent-Györgyi www.whonamedit.com/doctor.cfm/1542.html Naher, Walter www.grandprix.com/gpe/cref-nahwal.html Naipaul, Sir Vidiadhar Surajprasad www.nobel.se/literature/laureates/2001/naipaul-bibl.html Naish, Robby

86. Visualisation Des Réponses Translate this page Visualisation des réponses Criddle (AH), The chronology of Nicomachusof gerasa CQ (Classical Quarterly - Oxford), 48, 1998, pp. http://misha1.u-strasbg.fr/cgi-bin/aurweb/BAHR/VoirBAHR?CRITK=NEOPYTHAGORISME&au

87. Ancient History From Primary Sources: A Literary Timeline Marcus Aurelius; Martial; Menander; Nepos; Nicolaus of Damascus; Nicomachusof gerasa; Origen; Ovid; Pacuvius; Pausanias; Pericles; Philo; Pindar; http://www.triviumpursuit.com/catalog/ancient_history_from_primary_sources.htm

Ancient History from Primary Sources: A Literary Timeline Table of Contents Full Texts which are Included on the Two CDs Four Sections of this Book Examples from the Book by Harvey and Laurie Bluedorn This is a reference book which guides the student on a selective timeline tour through ancient history, outlining the major events and personalities, and noting the primary literary sources from which these things are known. Time-wise, this book covers the period from the creation of the world to the fall of Rome in A.D. 476. Space-wise, this book covers the civilizations of the near east and west. Each event or person in history is accompanied by suggested readings from various ancient sources. Included with the book are two CDs which contain the full text English translations of most of the classical literature which we reference in the book. This book will lead you by the hand through the maze of ancient literature and help you find what is appropriate for you and your children to read as you pursue your study of ancient history. And with the CDs, you have the full texts of the works of literature right at your fingertips. Generally speaking, the classical literature we cite is suitable for students ages twelve and up. Some of the literature is suitable for younger students (Aesop, some of Xenophon, Plutarch, Quintus Curtius, Gellius, Josephus and several others).

88. The Classical Quarterly, Volume 48, Issue 1: 1998. pp. 320324 Details. Shorter note. The chronology of nicomachus ofGerasa AH Criddle pp. 324-327 Details. Shorter note. Philoponus http://www3.oup.co.uk/clquaj/hdb/Volume_48/Issue_01/

Home Online Resources The Classical Quarterly Table of Contents Volume 48, Issue 1: 1998. The Homeric poems as oral dictated texts R Janko pp. 1-13 Details and in Homer M Finkelberg pp. 14-28 Details The text of Iliad 18.603-6 and the presence of an [agr][igr][dgr][ogr][zgr] on the shield of Achilles M Revermann pp. 29-38 Details The social function of Attic tragedy J Griffin pp. 39-61 Details Studies in the later manuscript tradition of Aristophanes' Peace SD Olson pp. 62-74 Details Telestes and the 'five-rodded joining of strings' A Barker pp. 75-81 Details Notes on pseudo-Plutarch's Life of Antiphon MJ Edwards pp. 82-92 Details The shape of Athenian laws C Carey pp. 93-109 Details Was Kerkyra a member of the second Athenian league? CM Fauber pp. 110-116 Details Socrates' last words: another look at an ancient riddle J Crooks pp. 117-125 Details The historical reader of Plato's Protagoras D Wolfsdorf pp. 126-133 Details The Hippocratic treatise On Anatomy EM Craik pp. 135-167 Details Eros in government: Zeno and the virtuous city G Boys-Stones pp. 168-174

89. NICOMACHUS (OF THEBES) nicomachus, a Neopythagorean philosopher and mathematician, born atGerasa in Arabia Petraea, flourished about AD 100. In his musical http://68.1911encyclopedia.org/N/NI/NICOMACHUS_OF_THEBES_.htm

document.write(""); NICOMACHUS (OF THEBES) NICOLSON—NICOMEDIA See ]. R. Brodhead, History of the State of New York (2 vols., rev. ed., 1872). For the " Duke's Laws " see Laws of Colonial New York, i. 6-100. NICOLSON, WILLIAM (1655-1727), English divine and antiquary, was educated at Queen's College, Oxford (M.A., 1679; fellow, 1679-1682). After visiting Leipzig to learn German he was made prebendary of Carlisle in 1681, archdeacon in 1682. Twenty years later he was appointed bishop of the same diocese, where he remained until his translation to Derry in 1718. In 1727 he was nominated archbishop of Cashel and Emly, but died before he could assume charge. Nicolson is remembered by the impulsiveness of his temperament, which led him into a good deal of strife as a bishop, and more happily by his zeal in collecting and guarding manuscripts and other official documents. For this purpose he had special rooms built at Derry. His chief works were the Historical Library (English, 1696-97-99; Scottish, 1702; Irish, 1724; complete later editions, 1732 and 1776), and Leges Marchiarum or Border Laws (1705, new ed., 1747). 1 Matthias may have been a cousin of Richard Nicolls; his family were of Islip, Oxford; he was secretary of the province, held various judicial positions, and was mayor of New York City in 1672. Matthias's son William (1657—1723), a lawyer, was a member of the New York Assembly from 1702 until his death and was speaker in 1702-1718; he received a royal patent for what is now the town of Islip on Long Island. Descendants of Richard and of Matthias Nicolls spell the name " Nicoll."

90. The Great Books The Spirit of Laws N. NEWTON, GBWW I 34vii Principles Optics NICOMACHUSOF gerasa, GBWW I 11811 Arithmetic O. P. PASCAL, GBWW I http://www.thegreatideas.org/gb.html

The Great Ideas from The Great Books Index of Authors AUTHOR, location in GBWW [I] volume:page A B C D ... Z Title or collection For electronic texts on-line, consult Great Books Index A AESCHYLUS, GBWW [I] 5:1 Tragedies APOLLONIUS OF PERGA, GBWW [I] 11:603 Conics AQUINAS, GBWW [I] 19-20 Summa Theologica ARCHIMEDES, GBWW [I] 11:403 Elements ARISTOPHANES, GBWW [I] 5:449 Comedies ARISTOTLE, GBWW [I] 8-9 Complete Works Articles of Confederation GBWW [I] 43:5 AUGUSTINE, GBWW [I] 18 Confessions GBWW [I] 18:ix City of God GBWW [I] 18:127 Christian Doctrine GBWW [I] 18:619 AURELIUS, GBWW [I] 12:253 Meditations B BACON, GBWW [I] 30 Advancement of Learning GBWW [I] 30:ix Novum Organum GBWW [I] 30:103 New Atlantis GBWW [I] 30:197 BERKELEY, GBWW [I] 35:397 Human Knowledge Bible GBWW Bible , OLD TESTAMENT: K. J. V. (D) [Douay] Bible , NEW TESTAMENT: K. J. V. (D) [Douay] BOSWELL, GBWW [I] 44 Johnson C CERVANTES, GBWW [I] 29 Don Quixote CHAUCER, GBWW [I] 22 Troilus and Cressida GBWW [I] 22:ix Canterbury Tales GBWW [I] 22:157 Constitution GBWW [I] 43:11 COPERNICUS, GBWW [I] 16:481, 505 Revolutions of the Heavenly Spheres D DANTE

91. Recommended Reading List 23. Tacitus (c.55117). Histories Annals Agricola Germania. 24. nicomachus ofGerasa (fl.c. 100 AD). Introduction to Arithmetic. 25. Epictetus (c.60-120). http://www.sheboyganfalls.k12.wi.us/staff/dehogue/AP/recommended_reading_list.ht

A Recommended Reading List Home Books currently in our curriculum are in color. from Appendix A of How to Read a Book , by Mortimer Adler and Charles Van Doren 1. Homer (9th Century B.C.?) Iliad Odyssey 2. The Old Testament 3. Aeschylus (c.525-456 B.C.) Tragedies 4. Sophocles (c.495-406 B.C.) Tragedies ( Oedipus Rex 5. Herodotus (c.484-425 B.C.) History 6. Euripides (c.485-406 B.C.) Tragedies 7. Thucydides (c.460-400 B.C.) History of the Peloponnesian War 8. Hippocrates (c.460-377? B.C.) Medical Writings 9. Aristophanes (c.448-380 B.C.) Comedies 10. Plato (c.427-347 B.C.) Dialogues 11. Aristotle (384-322 B.C.) Works 12. Epicurus (c.341-270 B.C.) ``Letter to Herodotus'' ``Letter to Menoecus'' 13. Euclid (fl.c. 300 B.C.) Elements 14. Archimedes (c.287-212 B.C.) Works 15. Apollonius of Perga (fl.c.240 B.C.) Conic Sections 16. Cicero (106-43 B.C.) Works 17. Lucretius (c.95-55 B.C.) On the Nature of Things 18. Virgil (70-19 B.C.) Works 19. Horace (65-8 B.C.) Works 20. Livy (59 B.C.A.D. 17) History of Rome 21. Ovid (43 B.C.A.D. 17) Works 22. Plutarch (c.45-120) Parallel Lives Moralia 23. Tacitus (c.55-117)

92. The Harmony Of The Spheres Preface and Acknowledgments I. Classical 1. Plato 2. Pliny The Elder 3. Nicomachusof gerasa 4. Theon of Smyrna 5. Ptolemy 6. Censorinus 7. The Hymns of http://www.parkstpress.com/titles/harsph.htm

The Harmony of the Spheres: The Pythagorean Tradition In Music by Joscelyn Godwin ISBN 0-89281-265-6 Inner Traditions International 512 pages, 6 x 9 Hardcover, $29.95 (CAN $48.00) About the Book About the Author Table of Contents Reviews Excerpt Ordering Return to Inner Traditions' homepage About the Book Professor of Music at Colgate University and a widely respected musicologist, Godwin here traces the idea, held since ancient times, that the whole cosmos is in some way a musical or harmonious entity. Table of Contents The Harmony of the Spheres The Pythagorean Tradition In Music Preface and Acknowledgments I. Classical 1. Plato 2. Pliny The Elder 3. Nicomachus of Gerasa 4. Theon of Smyrna 5. Ptolemy 6. Censorinus 7. The Hymns of Orpheus 8. Saint Athanasius 9. Aristeides Quintilianus 10. Calcidius 11. Macrobius 12. Proclus 13. Boethius II. Medieval 14. Hunayn 15. Aurelian of Reome 16. John Scotus Eriugena 17. Regino of Prum 18. The Ikhwan Al-Safa" (Brethren of Purity) 19. Al-Hasan Al-Katib 20. Anonymous of the Twelfth Century 21. Isaac Ben Abraham Ibn Latif

93. Access The Great Books [226-300, Page 4 Of 4] . Access Foundation. From the ancient classics to the masterpieces ofthe twentieth century, the Great Books are all the introduction http://www.anova.org/gb.html

Access Foundation Section: Hammurabi (18th c. BCE) to John Milton La Rochefoucauld to Emily Brontë Karl Marx to Arthur Miller Saul Bellow to Annie Dillard Access the Great Books is a compilation of over 240 great authors and their works. The Access Foundation List is liberal in scope, robust in its cataloging, and voluminously linked to other sites related to the study of literature. This list devotes notable attention to works of philosophy and science, and is unrivaled in its organizational structure, background, and biographical content on the authors listed. ACCESS FOUNDATION holds that time spent reading the Great Books is time well spent. Great books lists are not meant to be exclusive of any tradition or culture, but rather form a foundation of knowledge on which to stand. Reading the great books allays the "busyness" of modern life; encourages self-examination, increases reflection, and provokes intellectual curiosity. What follows is a list compiled by ACCESS FOUNDATION from a variety of sources, and based most notably from the one developed for the Great Books collection of the

94. Human Indexes Of My Books On Mathematics; Na Ni Nu Ne No In The summary for this Japanese page contains characters that cannot be correctly displayed in this language/character set. http://www.com.mie-u.ac.jp/~kanie/tosm/humanind/jinmei_n.htm

TOSMŽOd‚̃z[ƒ€ w‰ðÍ‹³’öx w”—‰ðÍ‚̃pƒCƒIƒjƒA‚½‚¿x w”Šw–¼ŠˆÄ“àx ... w“V‘‚̏ؖ¾x @l–¼õˆø@‚ȁ[‚Ì l–¼õˆø‘–ÚŽŸ ƒiƒQƒ‹ ƒj[ƒEƒFƒ“ƒeƒBƒCƒg ƒj[ƒ”ƒ“ ... ƒgƒbƒv ƒiƒQƒ‹ (Trygve Nagell, 1895.7.13-1988.) @ƒmƒ‹ƒEƒF[CƒIƒXƒ‚ɐ¶‚Ü‚êCƒXƒEƒF[ƒfƒ“‚̃EƒvƒTƒ‰‚ÉŽ€‚·DƒIƒXƒ‘åŠw‘²‹ÆŒã(1920)CƒIƒXƒ‘åŠw‚Ì‹³ˆõ‚Æ‚È‚èC•‹³Žö(1930-31)DƒXƒEƒF[ƒfƒ“‚̃EƒvƒTƒ‰‘åŠw‹³Žö(1931-1962)D @®”˜_C’ŠÛ‘㐔D“Á‚ɁC•s’è•û’öŽ®C‘㐔“I”CŠÂ˜_‚ɋƐсD w”˜_“ü–åx( Introduction to Number Theory , ‘æ2”ŁCChelsea, New York, 1964) ƒgƒbƒv (Napoleon I, Bonaparte, 1769.8.15-1821.5.5.) @ƒRƒ‹ƒVƒJ“‡‚ɐ¶‚Ü‚êCƒZƒ“ƒgEƒwƒŒƒi“‡‚ÉŽ€‚·D @ƒtƒ‰ƒ“ƒXc’éD ƒ‰ƒCƒvƒjƒbƒc ‚É’ñˆÄ‚µ‚½ƒtƒ‰ƒ“ƒX‚̃GƒWƒuƒgª•ž‚ðŽÀsD@ [‰ðl], [ƒp11, l] ƒgƒbƒv ƒgƒbƒv ƒj[ƒEƒFƒ“ƒeƒBƒCƒg Aƒxƒ‹ƒiƒ‹ƒg (Bernard Nieuwentijt, 1654-1718). @ƒIƒ‰ƒ“ƒ_‚̈ãŽÒEŠô‰½ŠwŽÒB”÷Ï•ª–@‚ɑ΂·‚é”á”»ŽÒD@ [‰ðII.1] ƒgƒbƒv ƒj[ƒ”ƒ“ (Ivan Morton Niven, 1915.10.25-.) @ƒJƒiƒ_Cƒoƒ“ƒN[ƒo[‚̐¶‚Ü‚êD @ƒIƒŒƒSƒ“B—§‘åŠw‹³ŽöD‰Á–@“I®”˜_( ƒEƒFƒAƒŠƒ“ƒO ‚Ì–â‘è‚È‚Ç)Dƒj[ƒ”ƒ“”(ŠeŒ ‚̐”‚̘a‚ÅŠ„‚èØ‚ê‚鐔)DwƒAƒƒŠƒJ”ŠwŒŽ•ñx‚̕ҏWD @ ‚Æ‚Ì‹¤’˜w”˜_“ü–åC‘æ3”Łx( An Introduction to the Theory of Numbers , 1972F1991”N”Å‚Í H.ƒ‚ƒ“ƒSƒƒŠ

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