61. DDM Antiquity nicomachus of gerasa Manual of Harmonics Translation and Commentary. Ph.D., GeneralLanguage and Lit., Columbia University, 1967. xi, 275 p. http://www.music.indiana.edu/ddm/Antiquityold.html

DOCTORAL DISSERTATIONS IN MUSICOLOGY-ONLINE School of Music Indiana University Bloomington, IN 47405 ANTIQUITY from Doctoral Dissertations in Musicology , 2d International Edition (1984) and Doctoral Dissertations in Musicology , 2d Series, 2d Cumulative Edition (1996) with updates and corrections (An asterisk following the DDM code indicates a dissertation in progress) Historical Musicology Drama and Music Frangoulis, A. C. A Study of the Dramatic Role of the Sophoclean Chorus. Ph.D., Music, Liverpool, 1977. DDM Code: 11drFraA; DA no.: RILM no.: UM no.: Haldane, J. A. The Greek Hymn, with Special Reference to the Athenian Drama of the Fifth Century. Ph.D., Musicology, King's, London, 1963. DDM Code: 11drHalJ; DA no.: RILM no.: UM no.: Iconography Crowhurst, R. Representations of Performance of Choral Lyric on the Greek Monuments, 800-350 BC. Ph.D., External, London, 1963. DDM Code: 11icCroR; DA no.: RILM no.: UM no.: Literature and Music Sowers, Cynthia Ann. Studies in Homeric Narrative: The Shared Structure of Craft and Song. Ph.D., Music, University of Michigan, 1978. 366 p.

62. History Of Philosophy 20 Apollonius of Tyana and Moderatus of Gades, both of whom lived in Nero s time;and nicomachus of gerasa, who lived in the time of the Antonines. http://www.nd.edu/Departments/Maritain/etext/hop20.htm

Jacques Maritain Center History of Philosophy / by William Turner CHAPTER XX NEO-PYTHAGOREANISM AND NEO-PLATONISM During the Greco-Oriental period of its history philosophy seemed to turn to the supernatural for light and assistance. While, however, Philo sought to supply this supernatural element by bringing to bear on philosophical problems the whole wealth of Jewish religious ideas, Neo-Platonism looked for supernatural light, not in any system of religion, but in such communication with the Divine as each man may, by his own individual effort, attain. Neo-Platonism was, therefore, the last effort which pagan philosophy made to save itself from dissolution. In the Neo-Platonic movement we may distinguish (1) the transition schools; (2) Neo-Platonism in its earlier form; (3) the Syrian school, (4) the school of Constantinople; (5) the Athenian school; (6) the Alexandrian school Transition Schools . The way was prepared for the Neo-Platonic movement by Neo-Pythagoreans and Pythagorizing Platonists who, before the time of Plotinus, agreed in admitting that philosophical knowledge is to be supplemented and perfected by communication with a more or less vaguely defined transcendent, divine something. The chief Neo-Pythagoreans were Figulus (45 B.C.), of whom Cicero speaks;

63. Henry Mendell Articles on Theodorus of Cyrene and Theaetetus of Athens, Aristarchus ofSamos , nicomachus of gerasa in The Encyclopedia of Classical Philosophy (ed. http://www.ceu.hu/sun/sun_2003/CV/henry_mendell_2003.htm

Central European University A Program for University Teachers, Advanced Ph.D. Students, Researchers and Professionals in the Social Sciences and Humanities Summer University Henry Mendell Philosophy Department, California State University, Los Angeles5151 State U. Dr. Education 1977-85: Stanford University (Ph.D. Jan., 1986) 1972-74: St. John's College, Cambridge, England (B.A. 1974, M.A. 1980in Philosophy) 1968-72: Cornell University (A.B. 1971 in Classics (Magna cum laude) and Philosophy) Dissertation Topic: Aristotle and the Mathematicians: Some Cross-Currents in the Fourth Century Principal Thesis Adviser: Julius Moravcsik AOS: Ancient Philosophy, Early Greek Mathematics and Astronomy AOC: Philosophy of Science, Metaphysics Publications Book with Pat Suppesand Julius Moravcsik (eds.). Ancient and Medieval Traditions in the Exact Sciences: Essays in Memory of Wilbur Knorr. Stanford: CSLI (distr. University of Chicago Press), 2001. Articles "The Trouble withEudoxus". In Pat Suppes, Julius Moravcsik, and Henry Mendell (eds.), Ancient and Medieval Traditions in the Exact Sciences: Essays in Memory of Wilbur Knorr (Stanford: CSLI (distr. University of Chicago Press), 2001), 59-138 "Making Sense of Aristotelian Demonstration". Oxford Studies in Ancient Philosophy, 16 (1998), 160-225.

64. Book Review A number of obscure characters such as Moderatus of Gades and nicomachus of gerasaalso flit across the pages from time to time, receiving a rare but http://www.practical-philosophy.org.uk/Volume5Reviews/Pythagoras.htm

PRACTICAL PHILOSOPHY THE JOURNAL OF THE SOCIETY FOR PHILOSOPHY IN PRACTICE www.practical-philosophy.org.uk www.society-for-philosophy-in-practice.org Pythagoras and the Pythagoreans: a brief history Charles H. Kahn 2001 Indianapolis: Hackett. pp. xi + 195 ISBN 0-87220-575-4 (pb). £10.95 Practical Philosophy (Book Reviews) Spring 2002Volume 4.2 Reviewed by: Trevor Curnow Although not usually regarded as the first western philosopher (that accolade being traditionally reserved for Thales), Pythagoras is nevertheless a seminal figure. In one sense perhaps he was the first ‘philosopher’, as he is widely credited with the invention of that term. More importantly, however, he seems to have been the first to see philosophy as involving a particular way of life, and it was in the hope of learning more about what that way of life entailed that I approached this book. Unfortunately, it did not have very much to say on the subject. However, that is not the author’s fault. Kahn is to be commended for sticking close to what is actually known, and resisting the temptation to indulge in groundless speculation so as to fill in the many gaps. What emerges is a sketchy but engaging narrative, with several interesting twists and turns. One of the difficulties in getting to the bottom of the Pythagorean philosophy is the fact that its founder wrote nothing and its earliest adherents were bound by a vow of silence. It is not always easy to disentangle the original teaching from its later accretions and adaptations. Vegetarianism, for example, while often associated with Pythagorean living, seems not to have been practised from the outset, although dietary regulations of some kind (including the famous injunction not to eat beans) were obviously always important. More generally, since so little was known about Pythagoras, he became a convenient figure for later generations to attribute all kinds of ideas and activities to, presumably because such attributions were so difficult to disprove.

65. Kairouz.com We observe, too, the Pythagorean diatonism clearly described in the second centuryby nicomachus of gerasa and Theon of Smyrna. http://www.kairouz.com/melchitteeng.html

ALBUMS SACRED MELKITE CHANT CD audio -1994 Harmonia Mundi 901577 Ensemble de la Paix SONG TITLES AUDIO VIDEO PRESS Axion Esti Ya walidata l ilah 'Adhimi ya nafsi Inna l baraya Inna l lazouna Ihfadhi uma l ilah Istabchiri ayuha l ard Allahu r rabou Inna l malak Ifrahi ayatuha malika Ayatuha ssayidatu Liyataazam Jamiou l ajyal Anti ya walidata lah NOTES The chant of the melkite Church - the arabic name for the imperial Byzantine Church, derived from the syriac malka , king - belongs to the liturgies of the Near East : it is, therefore, practiced in a region constituting a veritable mosaic of civilizations. We should remember that this Phonician Greek Church came into existence in a place of intense religious, philosophical, poetic, judicial, grammatic, rhetorical and philological activity where Hebrew, Aramaic, Greek, Latin and Arabic rubbed shoulders even in the streets, and in which the civilisations of Antiquity, both Eastern and western, were still trying to survive, in spite of time, and unknown to men. These poetic texts, taken from the Canons of the Church Fathers (9th Ode) and dedicated to the Mother of God, are attached in various ways to extremely ancient traditions. Whether the text is in Greek or in Arabic, we find the micro-intervals characteristic of antique musical theories, which would have been translated into Syriac, then from Syriac into Arabic, or directly from Greek into Arabic. We observe, too, the Pythagorean diatonism clearly described in the second century by Nicomachus of Gerasa and Theon of Smyrna.

66. Greek Music. Plato. Pythagoras. Apollo. Borghese Plaques At Hammerwood. Partheno this tradition of musical thought flourished throughout antiquity in suchtheorists as nicomachus of gerasa (2d century AD) and PTOLEMY (2d century AD) http://www.hammerwood.mistral.co.uk/gmusic.htm

Greek music and the Greek Gods The musical culture of ancient Greece is known more through literary references than through preserved musical documents. About 20 fragments of music are extant written in a relatively late Greek notational system, but references to music performed at various rites and social occasions abound in the works of ancient Greek authors. Consequently, most modern discussions of Greek music either speculate about the sound of the music itself, or deal with the role and nature of music in that society. Dance, poetry, rite, and music seem inseparably associated in the early history of music in ancient Greece. Homer's Iliad and Odyssey report vintners' songs, dirges, and hymns of praise to Apollo (paeans). Music was described as an art exerting great power (ethos) over human beings, and certain musical styles came to be associated with particular peoples and deities. The KITHARA, a plucked string instrument, came to be linked with Apollo , the god of the Sun and reason, while the aulos, a loud double-reed instrument, came to be identified with

67. Strawberry Hill Farm Studio Home Page nicomachus of gerasa recorded the process and it was picked up by Iamblichusbefore 350 AD. We inherit the work of Leonardo of Pisa, also known as Fibonacci http://members.aol.com/bhero/HomePage.html

Welcome! Since August 28, 1996 you are visitor number: I hope you enjoy your visit and will return often! Introduction By Donald Beaman, Professor (retired) Boston University Barbara Hero is a current witness to a phenomenon investigated by Pythagoras (c. 582-500 B.C.) and known to him as the Lambdoma Matrix. Nicomachus of Gerasa recorded the process and it was picked up by Iamblichus before 350 A.D. We inherit the work of Leonardo of Pisa, also known as Fibonacci, who lived in he early thirteenth century. In time, Renaissance Europe both discovered and lost the Lambdoma pursuing mathematics and musical intervals. A whole language of relationship followed. ...Ratios ...Frequencies ...Wave Lengths ...Undertones and Overtones. Barbara acts as our guide in this world of rarified discernment, giving us sounds, drawings, charts and even laser projections, synthesized into a vast tapestry that is art and science ...music, sound and light. She counsels us from THE LAMBDOMA HARMONIC KEYBOARD, giving us a personal reading based on our favorite color, and a musical interval appropriate to our blended presence, designed to enhance our wellbeing. The call is to harmony of spirit, mind, emotion and physicality within one dynamic presence. We may ask, "why is the Lambdoma Matrix important to us?" ... "Is it anything more than a complicated opinion?" ...

68. Summary Of Pythagorean Theology I: Introduction nicomachus of gerasa (fl. 130) is especially known for his development ofPythagorean numerology. Numenius of Apamea (fl. 160) compared his very dualistic http://www.cs.utk.edu/~mclennan/BA/ETP/I.html

A Summary of Pythagorean Theology Part I: Introduction May Hermes, the God of Eloquence, stand by my side to aid me, and the Muses also and Apollo, the Leader of the Muses..., and may They grant that I utter only what the Gods approve that people should say and believe about Them. Julian ( Oration IV Contents History Theogony Triadic Structure History This document presents a summary and synthesis of the theology of Pythagoreanism, a spiritual tradition that has been practiced continuously, in one form or another, for at least twenty-six centuries. But first, a little history. (Note: I will refer to all of the following philosophers and theologians as Pythagoreans or Platonists, which is what they usually called themselves, for the terms "Neo-Pythagorean" and "Neo-Platonist" are modern inventions. This history is of necessity incomplete and superficial.) According to ancient Greek tradition, Pythagoras (572-497 BCE) studied with the Egyptians, Phoenicians, Chaldeans, Brahmans, and Zoroastrians, and was initiated into all their mysteries. He is supposed to have met with Zoroaster (Zarathustra), but, since scholars now believe that Zoroaster probably lived in the second millennium BCE, it is likely that the Greek tradition reflects a meeting between Pythagoras and Zoroastrian Magi. In any case, there are many traces of Zoroastrianism in Pythagorean doctrine. In particular, there are similarities between the central Duality of Pythagoreanism and the dual Gods of Zoroaster (Ahura-Mazda and Ahriman). However, there are also connections to

69. The Institute Of Ismaili Studies: The Classification Of The Sciences According T these four mathematical sciences as a prerequisite to any other studies hadbeen endorsed in the West by such great authorities as nicomachus of gerasa, http://www.iis.ac.uk/learning/life_long_learning/rasail_ikhwan/rasail_ikhwan.htm

Learning Curriculum Materials PTE Programme Teaching ... Reading Lists Lifelong Learning: Articles Godefroid de Callataÿ This article is based on a paper delivered at The Institute of Ismaili Studies on May 22, 2003 as part of its Department of Academic Research and Publications Lecture Series Download PDF version of article (154 KB) Abstract The Epistles of the Brethren of Purity ) is a unique work in Islamic history consisting of approximately fifty-two epistles ( Key Words Table of contents Introduction Two Types of Classification of Sciences in The Science of Language Religious and Conventional Sciences ... Appendix Introduction The work most commonly known as the Epistles of the Brethren of Purity ) is a Gnostic and philosophical encyclopaedia which was written in Arabic during the classical age of Islam and whose nature, contents and purposes have no equivalent of any kind both inside and outside the Muslim world. Scholarship specifically devoted to this work has only started to develop in recent times, so that large parts of the encyclopaedia remain unexplored. To this day only one section out of the four that form the whole corpus has been edited on a scientific basis and a vast majority of epistles have never been properly translated into English or into any other European language. It is now generally agreed that the authors of the Epistles ) at the end of the corpus. The

70. Baylor University || University Scholars || Ancient Texts nicomachus of gerasa. Introduction to Arithmetic. Epicetetus. Handbook. Ptolemy.Almagest (3). Marcus Aurelius. Meditations. Galen. On the Natural Faculties http://www.baylor.edu/univ_sch/index.php?id=17448

71. PGListNF0802 nicomachus of gerasa, Introduction to Arithmetic, N. Nizami, Ganjavi, Haft PaykarA Medieval Persian Romance, O. Novalis, Aphorisms, B http://www.steveharris.net/PGListNF0604.htm

This is a list of the 287 items from the consolidated list which have not been found in any etext source: Sources B- Bloom E- Everyman F- Franklin 100 M- Modern Library O- Oxford N - Nominated ( by others) P- Penguin S- PW Best Sellers Intro Page Consolidated List Author (last) Author (first) Title Source Anon. Romance of Tristan O Anon. Saga of King Hrolf Kraki P Anon. Tale of Sinuhe O Anon. Till Eulenspiegel: His Adventures O Abaelardus Petrus The Letters of Abelard and Heloise P Addams Jane A New Conscience and an Ancient Evil S Aksakov Sergey A Family Chronicle B Aksakov Sergey A Russian Gentleman O Alcott Louisa May The Inheritance P Alfieri Vittorio Saul B Alkman Various B Allen James Lane The Mettle of the Pasture S Appian The Civil Wars P Appleton Edward J. With the Colors S Appolilonius of Perga Conics N Archilochus Various B Archimedes Book of Lemmas N Archimedes The Method of Treating of Mechanical Problems N Aristotle Meteorology N Aristotle On Interpretation N Aristotle On Longevity and Shortness of Life N Aristotle On Memory and Reminiscence N Aristotle On Prophesying by Dreams N Aristotle On Sleep and Sleeplessness N Aristotle On Sophistical Refutations N Aristotle On the Gait of Animals N Aristotle On the Motion of Animals N Arrian The Campaigns of Alexander P Atherton Gertrude Black Oxen S Aubrey John Brief Lives B Bailey Temple The Dim Lantern S Bailey Temple The Tin Soldier S Basho Matsuo The Narrow Road to the Deep North and Other Travel Sketches P Bataille Georges

72. Springnews Introduction to Arithmetic (AD 150) by nicomachus of gerasa was one the fewsources of knowledge of formal Greek arithmetic in the Middle Ages. http://math.cudenver.edu/~maa-rm/rmnewslett/newss00.html

Program Highlights This year's meeting will open with an address by our 1999 Burton W. Jones Distinguished Teaching Award Recipient, Professor Bill Briggs of CU-Denver. Respected as one of the best teachers within the University of Colorado system, Professor Briggs is widely recognized for excellence in both teaching and exposition. In addition to his DTA Invited Lecture entitled "An Ideal Problem: The Mathematics of Population Genetics ", Professor Briggs has agreed to deliver a workshop entitled Quantitative Reasoning for Liberal Arts Students on Friday morning. See the abstracts on page 4 for more workshop information. Another special feature of this year's meeting will be Professor Joseph Gallian's Polya Lecture "Breaking Drivers' License Codes" on Friday afternoon. Supported by the National MAA to promote excellence in Mathematics Exposition, the Polya Lecturer Program has selected Professor Gallian as one of its two current lecturers. Hailing from the University of Minnesota, Professor Gallian holds many teaching and exposition awards, including the MAA Trevor Evans Award for Exposition, the MAA Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching, and the MAA Allendoerfer Award for Exposition. He has authored several textbooks and numerous papers, and served as supervisor for over 70 student papers which have been accepted for publication in mainstream journals. Professor Gallian's highly entertaining talk will be especially interesting to students.

73. The Helenistic Period Of Greek Mathematics nicomachus of gerasa (fl 100 AD). tex2html_wrap_inline841 Nicomachus was probablya neoPythagorean as he wrote on numbers and music. http://www.math.tamu.edu/~don.allen/history/helnistc/helnistc.html

Next: About this document Aristarchus of Samos (ca. 310-230 BC) He was very knowledgeable in all sciences, especially astronomy and mathematics. He discovered an improved sundial, with a concave hemispherical circle. He was the first to formulate the Copernican hypotheses and is sometimes called the Ancient Copernican He countered the nonparallax objection by asserting that the stars to be so far distant that parallax was not measurable. Wrote On the Sizes and Distances of the Sun and Moon . In it he observed that when the moon is half full, the angle between the lines of sight to the sun and the moon is less than a right angle by 1/30 of a quadrant. From this he concluded that the distance from the earth to the sun is more than 18 but less than 20 times the distance from the earth to the moon. (Actual ). Without trigonometry he was aware of and used the fact that He also made other trigonometic estimates without trigonometry. ARCHIMEDES Apollonius of Perga (ca 262 BC - 190 BC) Apollonius was born in Perga in Pamphilia (now Turkey), but was possibly educated in Alexandria where he spent some time teaching. Very little is known of his life. He seems to have felt himself a rival of Archimedes. In any event he worked on similar problems. He was known as the ``great geometer" because of his work on conics.

74. Corecompetencies (nicomachus of gerasa, 100 AD). There were four arts involved, two in each ofthe two primary forms of being, namely the discrete and the continuous. http://www.ucalgary.ca/commons/tlc/corecompetencies.html

Core Competencies* are a set of skills and abilities to be integrated into all curricula at the University of Calgary. Students should be competent at: Critical and creative thinking. Analysis of problems. Effective oral and written communication. Gathering and organizing information. Logical calculation. Abstract reasoning and its application. Insight and intuition in generating knowledge. Interpretive and assessment skills. *Adopted by GFC on January 1997 Cornerstone Fellow Presentation Friday February 16, 2001 Berndt Brenken, Department of Mathematics bbrenken@ucalgary.ca Core Competency: Logical Calculation and Numeracy I view this as a facility with, and an ability to apply logical reasoning in various diverse contexts and types of discourse. This includes an ability to recognize and determine the presence or absence of important logical components of arguments, for example gaps, hidden assumptions, unstated hypotheses, or fallacious conclusions. It not only is an essential component of critical thinking, but can also serve as a component that drives aspects of creative thinking. Mathematics is perhaps the subject best suited to learn this, especially at elementary levels. There it is very clear that reasoning can get results that are right, and verifiably right. Mathematics increases the ability to reason, and shows its power, all at the same time.* Because of this I have decided to concentrate mainly on how mathematics is present in accessible ways to students in many different areas.

75. OU History Of Science Leipzig) Assimilation and Transformation of the Introducto Arithmeticae bynicomachus of gerasa (2nd century AD) during the Islamic Middle Ages (9th http://www.ou.edu/cas/hsci/nwsltr93.htm

76. Welcome To Banyan Tree Book Distributors This book is the first complete translation of the Pythagorean philosophernicomachus of gerasa. It is a concise and well organized introduction to the http://www.banyantreebooks.com.au/detail.cfm?isbn=0933999437

77. Number Symbolism In The Mediterranean Before A.D. 1000: A Select Bibliography Criddle, AH The chronology of nicomachus of gerasa. Classical Quarterly, ns,48.1 (1998) McDermott WC Plotina Augusta and nicomachus of gerasa. http://students.cua.edu/16kalvesmaki/Arithmetic/Number Symbolism.htm

NUMBER SYMBOLISM IN THE MEDITERRANEAN BEFORE A.D. 1000: A SELECT BIBLIOGRAPHY Edited by Joel Kalvesmaki Updated 24 December 2004 Part of the Theology of Arithmetic website. The following books and articles deal with number symbolism in the ancient world (Europe, Africa, and Asia west of the Indus River) from prehistory to the year 1000. The cutoff date is somewhat arbitrary, but it precludes discussion of the Kabbalah and medieval number symbolism, subjects that would require their own treatment since authors from this period adopt and radically reconfigure ancient number symbolism. Nearly every study of Pythagoreanism has something to say about numbers, arithmetic, and mathematics in general. I have, however, listed only those works that have advanced historical or philological arguments concerning Pythagoreanism, specificially its number symbolism or philosophy of number. For more general or derivative articles and books on Pythagorean numbers and their integration into Pythagoreanism as a whole, see Luis E. Navia, Pythagoras: An Annotated Bibliography (New York: Garland, 1990).

78. Number Symbolism In The Mediterranean Before A.D. 1000: A Select Bibliography In this scheme, especially popularized by nicomachus of gerasa, there is thescience of quantity, and that of magnitude. Each of these subdivide further http://students.cua.edu/16kalvesmaki/Arithmetic/glossary.htm

ANCIENT NUMBER SYMBOLISM: GLOSSARY Joel Kalvesmaki Updated 4 October 2004 Part of the Theology of Arithmetic website. arithmetic The mathematical science of absolute quantity (see quadrivium ). The term is based on the Greek word arithmos , translated "number," but with plurality implied: one was for the ancient Greeks, not a number, but the source or principle of number. Arithmetic, then, treats the progression of numbers, their basic division into odd and even (the two fundamental classes of numbers in antiquity), and basic operations such as addition, subtraction, multiplication, and division. arithmology This term was introduced to modern discourse by A. Delatte, who observed it in the title of an anonymous treatise preserved in an eighteenth century manuscript. The word appears to be a hapax legomenon , and late in Greek literature, but it is useful nonetheless. Scholars apply it generally to any kind of number symbolism or numerology in the ancient world. astronomy The mathematical science of relative magnitude (see quadrivium ), more conventionally, the mathematical science of the motions and relations of the heavenly bodies. Some ancient authors combine, others separate, stereometry

79. Airlift Books Manual of Harmonics, The nicomachus of gerasa Phanes Press, 0-933999-43-7, 220pages, 152mm x 228mm, paperback, £14.99, Published 09/94 Philosophy http://www.airlift.co.uk/perl/pubdetails.pl?sessionref=&pubid=86&origpub=Phanes

80. Airlift Books of Nicomachus the Pythagorean. nicomachus of gerasa. Phanes Press. 0933999-43-7,220 pages, 152mm x 228mm, paperback, Published 09/94 http://www.airlift.co.uk/perl/showbook.pl?stockcode=MAOFHARMP

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