Extractions: What's new at this site on March 25, 1999 Some URLs have been updated. Abbe, Ernst Abbon [Abbo, Albo, Albon (de Fleury, Floriacensis)], St. (c. 945-1004) Abbot, Charles Greeley (1872-1973) Abbott, Francis (1799-1883) Abell, George Ogden (1927-1983) Abetti, Giorgio (1882-1982) Abney, Sir William de Wiveleslie (1843-1920) Abraham bar Hiyya Ha-Nasi [Abraham Ben Chaja [Chija]; Abraham Judaeus] (c. 1070-1136(?)) Abraham Ben Dior [Ben David, Harischon; Josophat Ben Levi] (12th c.) Abraham Zachut (15th c.)
References theon of smyrna s successive approximation of Ö2 is discussed, See the Theonof Smyrna s method on p. 77 and its possible extension to the golden http://members.tripod.com/vismath1/denes/refs.htm
Extractions: References [1] The idea of footprint- (and mind-print-) literacy was introduced by Tsion Avital; see his papers in the present issue of VM . Different linear symmetry groups (frieze groups) "printed" by animals were briefly discussed by Wolf and Wolff (1956). I should recall here the Japanese director A. Kurosawa's movie Dersu Uzala . This title is the name of an old man living in the Siberian forest. He has an extraordinary ability to "read" footprints. For example, he tells the visitors that the actual footprints are belonging to an old tiger and they should be very careful because the tiger is very hungry, etc. I am sure that this ability of Dersu Uzala was a common knowledge in the hunting and gathering society. Avital, T. Footprint Literacy: the Origins to Art and Prelude to Science and Mindprints: the Structural Shadows of Mind Reality? Wolf, K. L. and Wolff, R. (1956) , [Symmetry: An Attempt towards an Instruction in Seeing Gestalt and Meaningfully Creating Gestalt [2] Ratios of length of a vibrating string with the modern names (and notations) of intervals 1/1 - prime or unison (from C to C) 8/9 - second (from C to D) 4/5 - third (from C to E) 3/4 - forth (from C to F) 2/3 - fifth (from C to G) 3/5 - sixth (from C to A) 8/15 - seventh (from C to B) 1/2 - octave (from C to the next C) We may consider semitones and in that case we should make a clear distinction between the new minor and the original major intervals, e.g.
Extractions: One topic that is sure to cause controversy amongst astrologers is that of whether the Tropical or Sidereal zodiac is most effective in practice. A recent forum debate revealed how passionately astrologers cling to alternate views. In 1997 the Traditional Astrologer magazine asked two expert astrologers to justify their own choice by reference to history, philosophical logic and the results of their own experience. Their responses have been reproduced here and allow us to consider the historical influences upon this 'astrological complication' in-depth. This debate assumes a knowledge of the issues connected to precession. For a more detailed explanation of precession and the early refinement of zodiacal signs refer to the article Heavenly Imprints In recent years certain astrologers have made two assertions that I would like to examine and, hopefully, refute. The first is that ancient astrologers used a sidereal zodiac; the second is that this, if true, implies that we should adopt one. The best answer to the assertion that the ancient zodiac was sidereal is a question: which zodiac? The zodiac was involved in chronometry, astronomy, and divination. These make conflicting demands, for chronometry implies a tropical zodiac but astronomy a sidereal one! Reconstructing the history of the zodiac is not easy - only a fraction of ancient writings have survived and 90% of Mesopotamian texts still lie unpublished in museum basements - but the following account is probably not too far from the truth.
Bryn Mawr Classical Review 94.03.07 and theon of smyrna s Mathematical Principles Useful for the Study of Plato . this matter are those of theon of smyrna and Porphyry mentioned above. http://ccat.sas.upenn.edu/bmcr/1994/94.03.07.html
Extractions: Reviewed by Lloyd Gerson, University of Toronto. Most classicists, including those specializing in ancient philosophy, will likely know at most two facts about Thrasyllus: he was the Emperor Tiberius' astrologer and he arranged the Platonic corpus into tetralogies. Many will assume that there is not a great deal more than this to be known about him given the extant documents. For example, John Dillon's careful and thorough survey, The Middle Platonists. 80 B.C. to A.D. 220, devotes less than a page to Thrasyllus. It will also be assumed that this is not a particularly lamentable state of affairs, since Thrasyllus is likely to have been at best a minor figure in the history of Platonism. Harold Tarrant has set out to challenge these assumptions in his latest book, Thrasyllan Platonism. Tarrant believes that a careful study of the evidence reveals Thrasyllus to be a far more formidable figure than anyone has hitherto supposed. At the conclusion of his book he writes, "The influence of Thrasyllus, if my arguments have any credibility, would seem to have been immense. It falls into five main areas: philosophical influence upon (1) Neopythagoreanism, (2) Middle Platonism, and (3) Neoplatonic and early Christian thought; and influence upon Platonic interpretation down to our own times by means of (4) an arrangement of the Platonic corpus that survives and presents the material to us in a particular manner, giving an initial claim to authenticity to all that it contains and overwhelming suspicions of spuriousness to all that it does not contain, and (5) a text of Plato that Thrasyllus' interpretative hand has coloured (208)."
Bryn Mawr Classical Review 2004.08.06 a heliocentric hypothesis.9 Hipparchus is reported by theon of smyrna to have In fact, Theon, Ptolemy s older contemporary, also discusses the issue http://ccat.sas.upenn.edu/bmcr/2004/2004-08-06.html
Extractions: Almost all the substantial Hellenistic works of both Stoicism and technical astronomy have been lost. This unfortunate circumstance has caused Cleomedes' treatise on Stoic cosmology and astronomy to assume a value greater than its contents merit. For our current understanding of Stoic physical thought, however, and the dissemination of scientific ideas into the greater intellectual community, Cleomedes' work is an important source. Bowen and Todd's new translation, Cleomedes' Lectures on Astronomy , gives this key work its due. The level of scholarship in this book is of the highest caliber. The translation itself, based on Todd's edition, is quite good. The English gives the reader a close sense of the original text without being awkward or unnecessarily literal. There are, of course, a few places where I would have chosen a different idiom; nevertheless, I found no places where I thought the text could not support the reading which is given. This book, however, is more than a reader's text of Cleomedes for an English speaking audience. The introduction and commentary by Bowen and Todd situate Cleomedes' work in the context of what we know about Stoic physics and ancient technical astronomy. A series of modern diagrams also helps the reader follow the many arguments which are based on the geometric configurations of the Stoic cosmos.
Holy Number Diagrams 10 Kenneth Sylvan Guthrie, cited above, quoting theon of smyrna, Theon ofSmyrna, the second century CE author of Mathematics Useful for http://www.recoveredscience.com/const129holynumberdiagrams.htm
Extractions: recoveredscience .com We offer surprises about and numerals and their ancient religious uses in our e-book Ancient Creation Stories told by the Numbers by H. Peter Aleff Site Contents NUMERALS Numerals Introduction Horus Eye Fractions Creation by numerals ... Reader responses Visit our other Sections: Prime Patterns Board Games Astronomy Medicine Store Stuff Home Page Footnotes : André Pichot: La naissance de la science, Gallimard, Paris, 1991, translation consulted Die Geburt der Wissenschaft Von den Babyloniern zu den frühen Griechen, Wissenschaftliche Buchgesellschaft, Darmstadt, 1995, see subchapter: Die Zahlenmystik, pages 92 to 94. Simo Parpola: The Assyrian Tree of Life: Tracing the Origins of Jewish Monotheism and Greek Philosophy, Journal of Near Eastern Studies, Volume 52, July 1993, Number 3, pages 161-208. David R. Fideler, in his Introduction to Kenneth Sylvan Guthrie, compiler and translator: The Pythagorean Sourcebook and Library, Phanes Press, Grand Rapids Michigan , 1988, page 29.
Perceptions Of Numbers and translator The Pythagorean Sourcebook and Library, Phanes Press, GrandRapids , Michigan , 1988, page 21 bottom, quoting theon of smyrna. http://www.recoveredscience.com/const304numberviews.htm
Extractions: recoveredscience .com We offer surprises about and numerals and their ancient religious uses in our e-book Ancient Creation Stories told by the Numbers by H. Peter Aleff Site Contents NUMERALS Numerals Introduction Horus Eye Fractions Creation by numerals ... King Solomon's Pi Number perceptions Golden ratio properties Golden ratio prehistory Woman Wisdom Constant ... Reader responses Visit our other Sections: Prime Patterns Board Games Astronomy Medicine Store Stuff Home Page Erik Temple Bell: The Magic of Numbers, 1946 and 1974, edition consulted Dover, New York, 1991, pages 20 and 21. Bonnie Gold: Review of Social Constructivism as a Philosophy of Mathematics by Paul Ernest and of What is Mathematics, Really by Reuben Hersh, The American Mathematical Monthly, April 1999, pages 373 to 380. For instance, Paul Ernest in: Social Constructivism as a Philosophy of Mathematics, State University of New York Press, 1998, per Bonnie Gold in the above review, page 375. See, for instance, the biblical king Hezekiahs stamp on jar handles mentioned in Frank Moore Cross: King Hezekiahs Seal Bears Phoenician Imagery, Biblical Archaeology Review, March/April 1999, pages 42 to 45 and 60, see page 45 left.
Utterpants Writers Community :: View Topic - Bartenders Interestingly, theon of smyrna (often called the father of mathematics ) had amost remarkable daughter Hypatia, who was not only stunningly beautiful http://www.utterpants.co.uk/pantsbb/viewtopic.php?p=14247&
Order Of Nazorean Essenes theon of smyrna. 1 The Importance Of The Quaternary Obtained By Addition Is GreatIn Music Because All The Consonances Are Found In It. http://essenes.net/scrolls/64sspythagoras.html
Pythagoreans Theon of Smyna. theon of smyrna. The Importance Of The Quaternary Obtained ByAddition Is Great In Music Because All The Harmonies Are Found In It. http://essenes.net/theonsay.html
Extractions: Th eon of Smy na Theon Of Smyrna The Importance Of The Quaternary Obtained By Addition Is Great In Music Because All The Harmonies Are Found In It. 2 But It Is Not Only For This Reason That All Pythagorean-Theanoians Hold It In Highest Esteem, It Is Also Because It Seems To Symbolize The Entire Nature Of The Universe. 3 It Is For This Reason That The Formula Of Their Oath Was: I Swear By The Ones Who Have Bequeathed The Tetraktys, The Source Of Eternal Nature, Into Our Souls And Unto Future Generations. 4 The Ones Who Bestowed It Were Pythagoras And Theano, And It Has Been Said The Tetraktys Appears Indeed To Have Been Discovered By Them. 5 The First Quaternary Is The One Which We Have Just Spoken: It Is Formed By Addition Of The First Four Numbers. 6 The Second Is Formed By Multiplication, Of Even And Odd Numbers, Starting From Unity. 7 Of These Numbers, Unity Is The First, Because As We Have Said, It Is The Principle Of All The Even Numbers, The Odd Numbers And Of All The Odd-Even Numbers, And Its Essence Is Simple. 8 Next Comes Three Numbers From The Odd As Well As The Even Series.
Euclid - Books I-IX As is well known, theon of smyrna (pp. 43, 44, ed. Hiller) describes this systemof numbers. The unit, being the beginning of all things, http://www.headmap.org/unlearn/euclid/notes/note-II10-Side.htm
Extractions: @import url(../../../ul-css/3-col-nn4-new-main.css); PROPOSITIONS Euclids elements BOOKS I-IX translated by T.L. Heath GEOMETRICAL ALGEBRA book II identities gemetrical solution of quadratics application of areas transformation of areas ... Book V notes Book VII notes Book VIII notes Book IX notes HEADMAP home unlearning EUCLID BOOK I BOOK II BOOK III BOOK IV ... BOOK IX OVERVIEW book 1, triangles book 2, quadratics books 3 and 4, circles book 5, theory of proportion book 6, geometry and the theory of proportion books 7, 8 and 9 ,number theory BACKGROUND euclid and the traditions about him. euclid's other works. greek commentators on the elements ... modern algebraic interpretations [see also: equations - Diophantus; conics - Appolonius] Side and Diameter numbers "Side" and "diagonal " numbers giving successive approximations to Zeuthen pointed out (Die Lehre von den Kegelschnitten im Alterum, 1886, pp. 27, 28) that 11. 9, 10 have great interest in connexion with a problem of indeterminate analysis which received much attention from the ancient Greeks. If we take the straight line AB divided at C and D as in II. 9, and if we put CD = x, DB = y, the result obtained by Euclid, namely: becomes the. formula
History Of Magic Squares was invented by FuhHi, the mythical founder of Chinese civilisation;Greek writings dating from about 1300 BC; the works of theon of smyrna in 130 AD http://www.markfarrar.co.uk/msqhst01.htm
Extractions: History Of Magic Squares Magic Squares have fascinated mankind throughout the ages, with examples being found in: Chinese literature dating from as early as 2800 B.C., when a Magic Square known as the "Loh-Shu", or "scroll of the river Loh" (see above), was invented by Fuh-Hi, the mythical founder of Chinese civilisation Greek writings dating from about 1300 B.C. the works of Theon of Smyrna in 130 A.D. use by Arabian astrologers in the ninth century when drawing up horoscopes Arabic literature, written by Abraham ben Ezra, dating from the eleventh century India, dating from the eleventh or twelfth century, where the earliest fourth order magic square was found, in Khajuraho the writings of the Greek mathematician, Emanuel Moschopulus, whose works now reside in the National Library in Paris more recently, magic squares appeared in Chinese literature during the latter part of the posterior Chou dynasty (951 - 1126 A.D.) or the beginning of the Southern Sung dynasty (1127 - 1333 A.D.) the works of Cornelius Agrippa, a German physician and theologian from the sixteenth century, who constructed seven magic squares, of orders three to nine inclusive, which he associated with the seven planets then known (including both the Sun and the Moon)
Extractions: Posted by Just a visitor on January 16, 2003 at 10:21:21: In Reply to: Re: Isidoros and Anthemios - Great Buildings Online posted by Kevin Matthews on November 23, 1999 at 00:22:59: Dear Mr. Matthews, I would like to support what Mrs. Grigoris said about the unfortunate way in which Anthemios And Isidoros are presented. One gets a very strong impression, that those architects were of Turkish origin, after reading the biography of them presented in http://www.greatbuildings.com/architects/Isidoros_and_Anthemios.html I would like to provide you with a few references that should help you correct this:
Alibris: Robert Lawlor by Lawlor, Robert (Translated by), and theon of smyrna, and Toulis, Christos buyused from $184.90! 7. The bicentennial book more books like this http://www.alibris.com/search/books/author/Lawlor, Robert
Extractions: Explore a truly astonishing range of interests, philosophies, religions, and cultures from alchemy to angels, Buddhism to Hinduism, myth to magic. The distinguished authors bring a wealth of knowledge, visionary thinking, and accessible writing to each intriguing subject in these lavishly illustrated, large-format paperback books.
Smyrna: Weather And Much More From Answers.com theon of smyrna Polycarp, Saint (Christian martyr). Smyrna River Seven Churchesin Asia (in the Bible). Smyrna, New York George Horton http://www.answers.com/topic/smyrna-georgia
Extractions: A city of northwest Georgia, a residential suburb of Atlanta. Population: 45,600. Encyclopedia Smyrna, city (1990 pop. 30,981), Cobb co., NW Ga., a residential suburb of Atlanta; inc. 1872. Manufactures include computer equipment, building materials, plastics, ordnance, and chemicals. Originally a religious camp-meeting ground, the city grew with the coming of the railroad. It has a bird sanctuary and is noted for its jonquils. The city was almost totally destroyed during the Civil War. Weather AccuWeather Current Conditions for
Smyrna: Definition And Much More From Answers.com Smyrna (disambiguation), theon of smyrna Smyrna (city of northwest Georgia),Polycarp, Saint (Christian martyr). Smyrna River Seven Churches in Asia (in http://www.answers.com/topic/smyrna-1
Extractions: Smyrna Izmir , Turkey) was settled at the beginning of the 3rd millennium BCE . Throughout Antiquity it was the early leading city-state of Greek Ionia , on the Aegean shores and islands of Asia Minor. Smyrna was among the cities that claimed Homer as a resident. Modern Turkish interpretations emphasize Smyrna's earlier connections with the Hittite empire of central Anatolia Smyrna is said to have been a city of the autochthonous Leleges before the Greek colonists settled in the coast of Asia Minor. The name, which Greek myth derived from an eponymous Amazon named Smyrna, was applied also to a quarter of
Sacred Mathematics theon of smyrna put together a handbook for philosophy students of Plato whichshowed how prime numbers, geometrical numbers such as squares, progressions, http://www.halexandria.org/dward010.htm
Extractions: Sacred Mathematics, by way of definition, refers to the concepts which, according to ancient (and a few modern) scholars, encompassed all of creation in mathematical terms. It includes numerical ratios of the most profound significance (literally Transcendental Numbers ), the nature of numbers themselves ( Numerology ), their mutual relationship ( Astrology ), strange beasts such as Magic Squares and Infinite Series , those astounding aspects of geometrical relationships in Sacred Geometry which seem to defy logical or rational explanation, and the manner in which all of these aspects describe the universe. Sacred Mathematics represents a wholly contained and internally consistent philosophy a philosophy which describes physical reality, its cosmogony and every aspect of its science The Greek Philosopher, Plato, has said: Geometry is knowledge of the eternally existent. Numbers are the highest degree of knowledge. It is knowledge itself. This profoundly philosophical interpretation or Mathematical Theory is echoed in many spiritual traditions.
Studies In Occult Philosophy, Purucker, Q & A (#10) Did the fifth degree of the Mysteries as described by theon of smyrna include theon of smyrna speaks of this fifth degree as friendship and interior http://www.theosociety.org/pasadena/soph/sopqa10.htm
Extractions: Meaning of the Term Chaldean Why is it necessary to have seven principles? Cannot Divinity work through one good vehicle? Perfection does not produce imperfection. Therefore between the perfection of the Divine Unity and the imperfection of the manifested universe, that dark and somber place, there must be a virtually infinite range of intermediary stages running from Divinity to the utmost dregs of materiality. Thus we call these the seven principles in man from the Atman, corresponding to the Divine in the universe, to the physical body, corresponding to the lowest manifested plane. Man obviously is not divine, neither in devotion nor in thought, nor in any characteristic, for if it were so men would be gods. But men are imperfect and it is this range from the perfect to the imperfect in the universe that corresponds to the seven principles of man. I have always considered Egyptians as a very religious people, but at
Lunar Republic : Craters Greek mathematician and astronomer; son of theon of smyrna (qv). Theon Senior.0.8S. 15.4E. 18. ~ Of Smyrna (c. 70?c. 135? http://www.lunarrepublic.com/gazetteer/crater_t.shtml
Extractions: Craters (T) Craters A B C D ... Return To Gazetteer Index Common Name Lat Long Diam Origin T. Mayer Johann Tobias ~ (1723-1762), German astronomer, cartographer and mathematician; first to determine the libration of the Moon. Tacchini Pietro ~ (1838-1905), Italian astronomer; director of the observatories at Modena, Palermo and the Collegio Romano. Tacitus Cornelius ~ (c. 55-120?), Roman politician, philosopher and historian. Tacquet André ~, S.J. (1612-1660), Belgian Jesuit and mathematician; his work helped pave that way for the discovery of the calculus. Taizo Japanese male name.
Math Words Page 13 theon of smyrna extends the idea to the difference between any two figurate numbers.The difference between the pentagonal numbers, for example, http://www.pballew.net/arithm13.html
Extractions: Back to Math Words Alphabetical Index Aliquot parts of a number are proper divisors of the number that are smaller than the number. The aliquot parts of six are one, two, and three. The word joins two unlikely partners, the Latin ali for "other" and quot for how many. Together they came to mean a part of something, in this case, a part of the number of which it is a factor. The "other" meaning of ali remains today in words like alius, alibi, and alien. The quot root remains in quotient. Aliquot chains, sometimes called sociable chains , are formed by taking the sum of the aliquot parts and adding them to form a new number, then repeating this process on the next number. For some numbers, the result will bring you directly back to the original number. In that case the two numbers are called amicable numbers . For example, 220 and 284 are amicable numbers. The divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110 and if you add all these numbers together, you can see they sum to 284. The aliquot parts of 284 are 1, 2, 4, 71, 142 and these sum to 220. The relationship between 220 and 284 was known at least as far back as Pythagorus (500 BC). Sam Kutler has written to tell me that the first use of a term like "friend" for the pair was in a commentary on the work of Nicomachus by Iamblichus, around 300 AD. He also thought the Greek term was
