21. Greek And Roman Mainpage 1st Century AD) nicomachus of gerasa (c. AD 60120) O Origen (c. AD 185-254) - OrigenesAdamantius P Pausanias (c. AD 143-176) Philo (c. 20 BC - AD 45) - Philo http://www.brainfly.net/html/gkrm.htm

Greek and Roman Literature: HOME GREEK and ROMAN BABYLONIAN and EGYPTIAN Browse by Title List of Greek and Roman Authors: A Aeschines (c.389-314) Aeschylus (c.525-455 B.C.) Aesop (c. 620-560) Ambrose - Ambrosius (c. A.D. 339-397) ... Avianus (fl. c. A.D. 400) C Caesar (c. 102-44 B.C.) - Gaius Julius Caesar Cato the Elder (234 - 149 B.C.) - Marcus Porcius Cato (Cato the censor) Celsus (c. 25 B.C. - A. D. 50) - Aulus Cornelius Celsus Cicero (106-43 B.C.) - Marcus Tullius Cicero ... Cyprian (c. A.D. 200 - 258) - Thascius Caecilius Cyprianus D Demosthenes (384 - 322 B.C.) Dio Cassius (c. A.D. 40 - 110)- Cassius Dio Cocceianus Dio Chrysostom (c. A.D. 150-235) Diodorus Siculus (90-21 B.C.) ... Dionysius of Halicarnassus (c. 55 - 7 B.C.) E Epictetus (c. A.D. 60 - 135) Epicurus (c. 341-270 B.C.) Euclid (c. 300-275 B.C.) Eusebius (c. A.D. 260 - 339) ... Eutropius (fl. 4th Century A.D.) - Flavius Eutropius F Florus - Lucius Annaeus Florus Frontinus (c.A.D. 40 - 103) Sextus Julius Frontinus G Galen (c. A.D. 129-199) - Claudius Galen Gellius (c. A.D. 123-169) - Aulus Gellius H Herodian (c. A.D. 170 - 240)

22. Index Of /disciplinas/PAED/temas/nicomach/Nicomachus Of Gerasa - Britannica_com_ Parent......Index of /disciplinas/PAED/temas/nicomach/nicomachus of gerasa Britannica_com_files.Name Last modified Size http://piano.dsi.uminho.pt/disciplinas/PAED/temas/nicomach/Nicomachus Of Gerasa

Index of /disciplinas/PAED/temas/nicomach/Nicomachus Of Gerasa - Britannica_com_files Name Last modified Size Description ... Parent Directory 29-Oct-2001 18:12 0k 22-Nov-2001 01:37 12k article;pv=article;sz.. 22-Nov-2001 01:37 1k bl_corner.gif 22-Nov-2001 01:37 1k br_corner.gif 22-Nov-2001 01:37 1k britannica.css 22-Nov-2001 01:37 4k dot.gif 22-Nov-2001 01:37 1k gline.gif 22-Nov-2001 01:37 1k hdr_logo_chnl.gif 22-Nov-2001 01:37 2k onlineopinion.js 22-Nov-2001 01:37 9k red.gif 22-Nov-2001 01:37 1k standard.js 22-Nov-2001 01:37 8k tr_corner.gif 22-Nov-2001 01:37 1k ub2asdark.gif 22-Nov-2001 01:37 1k ub2homedark.gif 22-Nov-2001 01:37 1k ub2mwdark.gif 22-Nov-2001 01:37 1k ub2storedark.gif 22-Nov-2001 01:37 1k

23. Nicomachus Of Gerasa - Britannica.com ENCYCLOPÆDIA BRITANNICA. nicomachus of gerasa fl. AD 100,, Gerasa,Roman Syria now Jarash, Jordan. NeoPythagorean philosopher http://piano.dsi.uminho.pt/disciplinas/PAED/temas/nicomach/Nicomachus Of Gerasa

ENCYCLOPÆDIA BRITANNICA Nicomachus Of Gerasa fl. AD 100,, Gerasa, Roman Syria [now Jarash, Jordan] Neo-Pythagorean philosopher and mathematician who wrote Arithm e tik e eisag o g e Introduction to Arithmetic ), an influential treatise on number theory. Considered a standard authority for 1,000 years, the book sets out the elementary theory and properties of numbers and contains the earliest-known Greek multiplication table. In his Arithm e tik e Nicomachus, unlike Euclid, gave no abstract proofs of his theorems. Instead he merely enunciated the theorems and illustrated them with specific numerical examples. A Latin translation of the Arithm e tik e by Apuleius of Madaurus ( c. AD 125) is lost, but Boethius' version survived and was used as a schoolbook up to the Renaissance. Nicomachus' Encheiridion Harmonik e s ("Handbook of Harmony") is on the Pythagorean theory of music. He also wrote

24. Nicomachus Nicomachus. 60?120? nicomachus of gerasa is mentioned in a small numberof sources and we can date him fairly accurately. From his http://www.stetson.edu/~efriedma/periodictable/html/Ni.html

Nicomachus Nicomachus of Gerasa is mentioned in a small number of sources and we can date him fairly accurately. From his writings on numbers and music, it is clear that Nicomachus was a Pythagorean. Porphyry says that he was one of the leading members of the Pythagorean School. Nicomachus wrote Introduction to Arithmetic , which was the first work to treat arithmetic as a separate topic from geometry. Unlike Euclid, Nicomachus gave no abstract proofs of his theorems, merely stating theorems and illustrating them with numerical examples. The work contains elementary errors which indicate that he did not have proofs to give. An example of this, consider the results which Nicomachus quotes on perfect numbers. He states that the n th perfect number has n digits, and that all perfect numbers end in 6 and 8 alternately. These are false, but are reasonable guesses based on the four perfect numbers known during his time, namely 6, 28, 496 and 8128. The work contains the first multiplication table in a Greek text. It is also remarkable in that it contains Arabic numerals, not Greek ones. For over 1000 years Introduction to Arithmetic was the standard arithmetic text, despite the many errors and superstitous numerology. Most Arabic texts on number theory written by mathematicians were influenced by both Euclid and Nicomachus.

25. Nicomachus nicomachus of gerasa. Born about 60 in Gerasa, RomanSyria (now Jarash, Jordan) Died about 120. http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/Ncmchs.htm

Nicomachus of Gerasa Born: about 60 in Gerasa, Roman Syria (now Jarash, Jordan) Died: about 120 Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page Nicomachus wrote Arithmetike eisagoge (Introduction to Arithmetic) which was the first work to treat arithmetic as a separate topic from geometry. Unlike Euclid , Nicomachus gave no abstract proofs of his theorems, merely stating theorems and illustrating them with numerical examples. For over 1000 years it was the standard arithmetic text and it contains the first multiplication table in a Greek text. It is also remarkable in that it contains Arabic numerals, not Greek ones. He also wrote two volumes Theologoumena arithmetikes (The Theology of Numbers) which examined mystic properties of numbers. Boethius translated his Arithmetic into Latin and it was used as a school book. References (4 books/articles) A quotation by Nicomachus A page from a work by Nicomachus: Extract from a Greek multiplication table printed in 1538. 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/Nicomachus.html

26. References For Nicomachus References for nicomachus of gerasa. Biography in Dictionary of ScientificBiography (New York 19701990). Biography in Encyclopaedia Britannica. http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/~DZBCE0.htm

References for Nicomachus of Gerasa Biography in Dictionary of Scientific Biography (New York 1970-1990). Biography in Encyclopaedia Britannica. Articles: S Brentjes, Untersuchungen zum Nicomachus Arabus, Centaurus T L Heath, A History of Greek Mathematics I (Oxford, 1921), 97-112. Close this window or click this link to go back to Nicomachus 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/Nicomachus.html

27. Special Numbers The Neoplatonists nicomachus of gerasa and Iamblichus of Chalcis listed these perfectnumbers and concluded that they follow a pattern They alternately end in http://www.math.wichita.edu/history/topics/snumbers.html

Topics About Special Numbers Topic Tree Home Following are some items relating to special numbers discussed in the history of mathematics. Contents of this Page Perfect Numbers Square Numbers The Nature of Prime Numbers ... The History of Zero Perfect Numbers The Pythagoreans produced a theory of numbers comprised of numerology and scientific speculation. In their numerology, even numbers were feminine and odd numbers masculine. The numbers also represented abstract concepts such as 1 stood for reason, 2 stood for opinion, 3 stood for harmony, 4 stood for justice, and so on. Their arithmetica had a theory of special classes of numbers. There were “perfect” numbers of two kinds. The first kind included only 10, which was basic to the decimal system and the sum of the first four numbers 1 + 2 + 3 + 4 = 10. The second kind of “perfect” numbers were those equal to the sum of their proper divisors. A perfect number is a positive integer that is equal to the sum of it divisors. However, for the case of a perfect number, the number itself is not included in the sum. The Greeks called a number such as 6 or 28 a “perfect” number because the sum of the proper divisors in each case is equal to the number; the proper divisors of 6 are 1, 2, and 3, and their sum is 6. Although perfect numbers are regarded as arithmetical curiosities, their study has helped to develop the theory of numbers. Euclid proved that a number n of the form (2

28. 1120 A.D. With the birth of nicomachus of gerasa in this year, there was a breakin this dark period of mathematics. His work in mathematics http://faculty.oxy.edu/jquinn/home/Math490/Timeline/60AD.html

For sixty years after the birth of Jesus Christ, there were no prominent mathematicians. During this era, a new religion that was based on the teachings of Jesus Christ experienced rapid growth. Consequently, Christianity became the largest religion in the world today. Ironically at the same time there was no major work done in mathematics. With the birth of Nicomachus of Gerasa in this year, there was a break in this dark period of mathematics. His work in mathematics was primarily in the area of arithmetic. In " Arithmetike eisagoge ," or " Introduction to Arithmetic ," Nicomachus severed the bond between arithmetic and geometry. This was the first time in mathematical history that arithmetic was isolated from geometry. One of the important features of this book is the inclusion of multiplication tables. Nichomachus used the Arabic numerals as opposed to Greek, which was also rare. The theorems in this book were never proven, but rather stated with specific examples. Nicomachus also wrote a two volume work entitled " Theologoumena arithmetikes " or " The Theology of Numbers ," which described interesting properties about numbers. He died at the age of sixty, leaving a text that would be used in the area of arithmetic for about a thousand years, namely "

29. HighBeam Research: ELibrary Search: Results .. the presence of so many active intellectuals steeped in Greek culture in theNear East, Antiochus of Ascalon, nicomachus of gerasa, Flavius Boethus from http://www.highbeam.com/library/search.asp?FN=AO&refid=ency_refd&search_thesauru

30. FWD: Greek & Latin Texts On The Net By Antreas P. Hatzipolakis Gyula Mayer, Budapest Piliscsaba (Hungary) gam@cs.elte.hu Notes1. This Nicomachos is our =the arithmetician nicomachus of gerasa. http://mathforum.org/epigone/math-history-list/vimpzhimpblimp

reply to this message post a message on a new topic Back to math-history-list Subject: Author: xpolakis@hol.gr Date: our server The Math Forum

31. Gerasa (was: Tie Knots) By Antreas P. Hatzipolakis PELOPONNHSIOU DIA FILOTIMOU SUNDROMHS TWN OMOGENWN EN TERGESTH EK THS TUPOGRAFIASMIXAHL BAIS (MICHELE WEIS) 1832 I read about nicomachus of gerasa http://mathforum.org/epigone/math-history-list/twelfroval/v01540B00B3088FECC7B5@

Gerasa (was: Tie Knots) by Antreas P. Hatzipolakis reply to this message post a message on a new topic Back to messages on this topic Back to math-history-list Subject: Gerasa (was: Tie Knots) Author: xpolakis@otenet.gr Date: The Math Forum

32. The Manual Of Harmonics This book is the first ever complete translation of The Manual of Harmonics by thePythagorean philosopher nicomachus of gerasa (second century AD) published http://www.phanes.com/manhar.html

The Manual of Harmonics of Nicomachus the Pythagorean Translation and Commentary by Flora R. Levin In ancient Greek thought, the musical scale discovered by the philosopher Pythagoras was seen as a utopian model of the harmonic order behind the structure of the cosmos and human existence. Through proportion and harmony, the musical scale bridges the gap between two extremes. It encapsulates the most fundamental pattern of harmonic symmetry and demonstrates how the phenomena of nature are inseparably related to one another through the principle of reciprocity. Because of these relationships embodied in its structure, the musical scale was seen as an ideal metaphor of human society by Plato and other Pythagorean thinkers, for it is based on the cosmic principles of harmony, reciprocity, and proportion, whereby each part of the whole receives its just and proper share. This book is the first ever complete translation of The Manual of Harmonics by the Pythagorean philosopher Nicomachus of Gerasa (second century A.D.) published with a comprehensive, chapter-by-chapter commentary. It is a concise and well-organized introduction to the study of harmonics, the universal principles of relation embodied in the musical scale. Also included is a remarkable chapter-by-chapter commentary by the translator, Flora Levin, which makes this work easily accessible to the reader today. Dr. Levin explains the principles of Pythagorean harmony, provides extensive background information, and helps to situate Nicomachus' thought in the history of ideas. This important work constitutes a valuable resource for all students of ancient philosophy, Western cosmology, and the history of music.

33. Just Intonation: Two Definitions fl. c. 300 bc), the Manual of Harmonics by nicomachus of gerasa (b. c.60 ad), and the Harmonics by Ptolemy (c. 100–160 ad). Nicomachus http://www.chrysalis-foundation.org/just_intonation.htm

Just Intonation: Two Definitions © 2004 Cristiano M.L. Forster www.Chrysalis-Foundation.org For further discussions on the rational ratios of just intonation, see M.M. The term just intonation has two different definitions. The first is ancient and strictly mathematical. It states that just intonation is a method of tuning intervals and scales based exclusively on rational numbers. The second is modern and strictly acoustic. It states that just intonation is a method of tuning based on the intervals of the harmonic series. In the West, some of the oldest extant sources that give detailed accounts of rational or integer number ratios in music are the Division of the Canon by Euclid (fl. c b.c. ), the Manual of Harmonics by Nicomachus of Gerasa (b. c a.d. ), and the Harmonics by Ptolemy ( c. a.d. Nicomachus chronicles the discoveries of the semi-legendary Greek philosopher and mathematician Pythagoras ( c b.c.

34. A History Of Muslim Philosophy by P. Nigidus Figulus, Sotion, and particularly Apollonius of Tyana, Modera­tusof Gades, and, in later times, nicomachus of gerasa and Numenius of Apamea. http://www.muslimphilosophy.com/hmp/8.htm

Subject Index Search Announcements Feedback ... Support this Site Chapter 5 Alexandrio Syriac Thought Alexandrio Syriac Thought by C.A Qadir A Reason thus assailed could find refuge only in faith. In the period that follows we find philosophy renouncing its independence and becoming merely an instrument of theology. Ritter says, "The feeling of alienation and the yearning after a higher revelation are characteristics of the last centuries of the ancient world; this yearning was, in the first place, but an expression of consciousness of the decline of the classical nations and their cultures, the presentiment of the approach of a new era, and it called into life not only Christianity but also before it pagan and Jewish Alexandrianism and other related developments." It would be incorrect to identify the present geographical boundaries of Syria with its old ones. In Roman days, at the beginning of the Christian era Syria denoted the country west of the Euphrates and north of the Arabian Desert, including Palestine and Palmyra and extending north to the Taurus. The usual language of Syria was Aramaic, a language akin to Hebrew. The Hebrew word "Aram" is rendered as "Syria" and originally the words Aramaean and Syrian were synonymous. After the Hellenization of the country, the Greek language was used by the ruling class and the officials with very little influence on the masses who continued using their dialect. This state of affairs con­tinued till the first/seventh century when after the Muslim conquest Syriac gradually gave way vernacularly and to some extent liturgically to Arabic, though it had great influence on the vocabulary, pronunciation, and even the grammatical forms of Arabic which supplanted it.

35. Definitions Of Tuning Terms: Harmonic, (c) 1998 By Joe Monzo English translation _Fundamentals of music_ by Calvin M. Bower. Yale University Press,New Haven, 1989. nicomachus of gerasa. c. 100 AD. _Manual of Harmonics_. http://tonalsoft.com/enc/harm.htm

Definitions of tuning terms All definitions by Joe Monzo unless otherwise cited Harmonic [In ancient Greek theory,] pertaining to Harmonia and Harmonike When applied to chords or scales, it indicates that they are a section of the harmonic series The mathematical mean of two tones which produces intervals in the reverse order of the arithmetic mean is called the harmonic mean by Archytas because it was felt that this sequence was the more musical. In Western European theory, harmonic refers to harmony. [from John Chalmers , Divisions of the Tetrachord] Yahoo tuning list, message 46454 From: updated: 2003.08.19 added long addendum regarding Boethius Feedback Encyclopaedia of Tuning index Tonalsoft home

36. New Age Music: The Manual Of Harmonics Of Nicomachus The Pythagorean This book is the first complete translationof the Pythagorean philosopher nicomachus of gerasa. It is...... More Info! Book http://bookstore.newageinfo.us/n_0933999437.htm

The Newage Info Store Search: Home Connect Contact Newsletter ... The Manual of Harmonics of Nicomachus the Pythagorean by Nicomachus Click For More Info! Book Description This book is the first complete translation of the Pythagorean philosopher Nicomachus of Gerasa. It is a concise and well organized introduction to the study of harmonics and contains an extensive commentary in which Flora Levin explains the principles of Pythagorean harmony. This important work constitutes a valuable resource for all students of ancient philosophy, Western cosmology, and the history of music. From the Publisher One can see from this book why harmonics was so important to the Greeks: Like modern physics it gave entrance to the mystery of the world's construction and to the intelligence latent therein Keywords: The Manual of Harmonics of Nicomachus the Pythagorean, Books, Nicomachus, Flora R. Levin, Nicomachus,, of Gerasa, Criticism and interpretation, Music, Greek and Roman, History and criticism, New Age / Parapsychology, Music, Theory, Metaphysical Phenomena - General Click For More Info!

37. The Master Works Of Western Civilization nicomachus of gerasa, Introduction to Arithmetic. nicomachus of gerasa (fl.c. 100AD) Introduction to Arithmetic; Epictetus (c.60120) Discourses Encheiridion; http://www2.latech.edu/~bmagee/201/great_books_etexts.html

The Master Works of Western Civilization A hypertext-annotated compilation of lists of major works recommended by Drs. Adler and Eliot, Charles Van Doren, Anthony Burgess, Clifton Fadiman, the Easton Press, and many others Contents Improvements in the test stage Prufrock: an e-mail discussion on reading and writing Introduction to this Web Page The Master Works of Western Civilization A Recommended Reading List from Mortimer Adler and Charles Van Doren's How to Read a Book ... Return to Mason West's Home Page The interactive version of the Master Works of Western Civilization Web page is now in the prototype stage. Features and data are still being added, but the page is interesting and useful as it now stands. Try it out Introduction Several publishers, writers, and thinkers have drawn lists of the quintessential works of Western Civilization. This page presents several such lists along with links to the texts available on the Web. The table below contains three of the lists. Other lists are collected below the table. Maybe someday I'll collate all these lists into a single table but you know how Web page work goes maybe I won't. Dr. Mortimer Adler, who edited

38. CATHOLIC ENCYCLOPEDIA: Neo-Pythagorean Philosophy most prominently associated with this active philosophical campaign are those ofModeratus of Gades, Apollonius of Tyana, nicomachus of gerasa, Numenius, and http://www.newadvent.org/cathen/10745a.htm

Home Encyclopedia Summa Fathers ... N > Neo-Pythagorean Philosophy A B C D ... Z Neo-Pythagorean Philosophy B. C. , disappears completely from history during the fourth century, when philosophy reached the zenith of its perfection at Athens. Here and there, however, there appears a philosopher who reverts to the Pythagorean doctrine of numbers, and in a general way manifests the tendency of the school towards religious ethics and the practices of asceticism. Beginning with the middle of the first century B. C. , a more systematic attempt was made to restore the speculative philosophy of the Pythagoreans and combine it with the practice of astrology and sorcery. The first of these systematic neo-Pythagoreans was Figulus, a Roman philosopher who lived at Alexandria about the middle of the first century B. C. , and was a friend of Cicero. Other Romans also contributed to the movement, the chief of whom were Vatinius and the Sextians. It was, however, at Alexandria that the most influential of the neo-Pythagoreans taught. In the second and third centuries of the Christian era, the philosophers of the school became, so to speak, apostles of the cult, and travelled throughout the Roman Empire. The names most prominently associated with this active philosophical campaign are those of Moderatus of Gades, Apollonius of Tyana, Nicomachus of Gerasa, Numenius, and Philostratus. Like the neo-Platonists (see NEO-PLATONISM), the neo-Pythagoreans definitely placed their philosophy at the disposal of the pagan opponents of

39. Strawberry Hill Farm Studio Home Page the Lambdoma Matrix. nicomachus of gerasa recorded the process andit was picked up by Iamblichus before 350 AD We inherit the work 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?" ...

40. Pythagorean Mysteries Phanes Press This book is the first ever complete translation of The Manual ofHarmonics by the Pythagorean philosopher nicomachus of gerasa (second century http://members.aol.com/theloego/books/

Pythagorean Mysteries Click on any of the book covers below to get more information on the volume. You will also have the opportunity to purchase the volume on-line if you wish. New: Materials on Biblical Scholarship, Ancient and Modern Resource materials available: The Greek Qabalah An excellent volume with detailed charts, explanations and examples of Ancient Greek Numerology and Gematria (Alphabetic-Numeric Symbolism). Barry is a Legal and Classics scholar from New Zealand, now practicing Law in Hong Kong. Highly Recommended. Includes the passage (Book 4, chap.14) from Hippolytus of Rome's (ca. AD 170- 236) Refutation of All Heresies which clearly describes the ancient mystical "Rule of Nine" for the first time. The Pythagorean Sourcebook An excellent collections of primary texts from the Ancient Mediterranean world of Pythagoras, as well as copious notes and explanations in contemporary essays by Mystical Scholars. From the Phanes Press site: " Pythagoras (fl. 500 B.C.), the first man to call himself a philosopher or lover of wisdom, was both a brilliant mathematician and spiritual teacher. This anthology, the largest collection of Pythagorean writings ever to appear in the English language, contains the four ancient biographies of Pythagoras and over 25 Pythagorean and Neopythagorean writings from the Classical and Hellenistic periods. The Pythagorean ethical and political tractates are especially interesting for they are based on the premise that the universal principles of Harmony, Proportion, and Justice govern the physical cosmos, and these writings show how individuals and societies alike attain their peak of excellence when informed by these same principles. Indexed, illustrated, with appendices and an extensive bibliography, this acclaimed anthology also contains a foreword by Joscelyn Godwin and an introductory essay by the editor, David Fideler.

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

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