Extractions: A n early Copernican, Keplerian, and defender of Galileo, Boulliau was the most noted astronomer of his generation. Although his career reflects many of the movements associated with the Scientific Revolution, Boulliau was widely known in the Republic of Letters as an historian, classical scholar, and philologist. Arguably his correspondence network (which rivals the combined efforts of Mersenne and Oldenburg) marks the transition from to homme de science , from intelligencer to state-sponsored science. B intelligencer to matters of science. B oulliau's first book, De natura lucis (1638), grew out of an ongoing conversation on the nature of light with his friend Pierre Gassendi (15921655). Against Gassendi's atomist claims, Boulliau defended Kepler's punctiform analysis but argued, against Kepler, that light behaved three dimensionally (Prop. 7) and could be understood as a mean proportional between corporeal and incorporeal substance' (Theorem I). With a smile, Descartes somehow missed the point by reading between substance and accident.' Later in the volume Boulliau provided one of the first statements of the law of illumination (Prop. 27). I n the following year Boulliau published his Philolaus (1639), which had circulated in manuscript in the years following Galileo's condemnation. Thoroughly Copernican, there was perhaps little remarkable about the book except, as Descartes noted, that it was published at all. Boulliau's purpose was to provide new geometrical and optical arguments for the motion of the earth. Although he was attacked by J-B Morin (15831656) and several Italian astronomers, Boulliau continued to embrace Kepler's central claim, that nature loves simplicity, she loves unity...she uses one cause for many effects' (
Springer-Verlag - Computer Science Precession, Comets, etc. Ptolemy and theon of smyrna. The First Few Definitionsin Euclid s Elements. 11 The Age-Long Recovery. The Early Renaissances. http://www.springeronline.com/sgw/cda/frontpage/0,10735,5-146-22-24191434-detail
Extractions: Select a discipline Biomedical Sciences Chemistry Computer Science Engineering Environmental Sciences Geosciences Law Life Sciences Materials Mathematics Medicine Statistics preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,10885,5-0-17-900120-0,00.gif'); preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,10885,5-0-17-900180-0,00.gif'); preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,10885,5-0-17-900170-0,00.gif'); preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,10885,5-0-17-900190-0,00.gif'); preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,10885,5-0-17-900200-0,00.gif'); preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,10885,5-0-17-900160-0,00.gif');
History Of Magic Squares Greek writings dating from about 1300 BC; the works of theon of smyrna in 130 AD;use by Arabian astrologers in the ninth century when drawing up horoscopes; 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)
CHAPTER3 and Pope Urban VIII and all who protested without letup against the realismof thinkers like Adrastus of Aphrodisias and theon of smyrna, the Arab http://www.hcc.hawaii.edu/~pine/Thesis/CHAPTER3.htm
Extractions: Duhem An alternative framing of the relativist-anti-relativist debate often revolves around the notions of empirical equivalence and underdetermination. In its simplest gloss, according to the relativist, a rational decision regarding the competition between two theories is radically underdetermined because these theories are empirically equivalent or can be made so with enough effort and ingenuity in terms of auxiliary patching. Pierre Duhem's To Save the Phenomena and The Aim and Structure of Physical Theory have been massively influential in this regard. In Aim and Structure Duhem hammers home the possibility of auxiliary patching in blocking allegiance to a naive falsificationism. In Save the Phenomena he highlights the continuity, from Plato to the Renaissance, of the importance of empirical adequacy, destroying with massive historical detail the modernist myth of the "scientific night of the Middle Ages," that empirical inductive science began with Copernicus, Galileo, and Kepler. By showing the progressive continuity of the evolution of astronomy and physics from the ancient Greeks, through the Middle Ages, to the Renaissance, Duhem makes his famous plea that the aim of science should acknowledge the wisdom of Plato, Geminus, Ptolemy, Proclus, Posidonius, Simplicius, Maimonides, Aquinas, Bonaventura, John of Jandun, Lefevre d'Etaples, Osiander, and of course Bellarmine and Pope Urban VIII and all who "protested without letup against the realism of thinkers like Adrastus of Aphrodisias and Theon of Smyrna, the Arab physicists, the Italian Averroists and Ptolemaists, Copernicus and Rheticus themselves."
Esoteric Science theon of smyrna declares that this array of ten dots, the tetractys of Pythagoras,was a symbol of the greatest importance, to the discerning mind it revealed http://www.prs.org/gallery-science.htm
Extractions: By far the most remarkable conception of the atom evolved during the last century is that produced by the genius of Dr. Edwin D. Babbitt. MPH The Problem of Diversity From Kircher's Ars Magna Sciendi In this diagram Kircher arranges 18 objects in two vertical columns and then determines the number of arrangements in which they can be combined. By the same method Kircher further estimates that fifty objects may be arranged in 1,273, 726,838,815,420,339, 851,343,083, 767,005,515,293, 749,454,795,473,408,000,000, 000,000 combinations. From this it will be evident that infinite diversity is possible, for the countless parts of the universe may be related to each other in an in-calculable number of ways. MPH Pythagoras, the First Philosopher
New Page 3 70 BC); Clepcosmological work On the Cyclic motions of the celestial bodies; andtheon of smyrna (first half of second century AD), who wrote the Manual of http://jrider.web.wesleyan.edu/wescourses/2001f/fren234/01/handbooktradition.htm
Extractions: contemporary Home Excerpts pertaining to the history of the handbook tradition From pages 11-12, and 14 of Foundations of Modern Science in the Middle Ages by Edward Grant. Any "bold faced" words were not bold faced in the original text. "The achievements of the first six centuries of the Christian era were typical of the manner in which Greek science and natural philosophy had developed and advanced. Always the product of a small number of gifted scholars concentrated in a few centers, Greek science was a fragile enterprise, able to advance and preserve itself just so long as the intellectual environment was favorable, or at least not overtly antagonistic. Greek science at its traditional best in the Roman Empire was but a continuation of the progress already made in the physical and biological sciences of classical Greece and the Hellenistic world, when the works of Plato, Aristotle, Hipparchus, Eudoxus, Euclid, Archimedes, Appollonius of Perga, Hipparchus, Theophrastus, Herophilus, and Erastistratus established the highest levels of achievement.
The Christ By John E. Remsberg (Chapter 2) Arrian Petronius Dion Pruseus Paterculus Appian theon of smyrna Phlegon Pompon MelaQuintius Curtius Lucian Pausanias Valerius Flaccus Florus Lucius Favorinus http://www.positiveatheism.org/hist/rmsbrg02.htm
Extractions: Another proof that the Christ of Christianity is a fabulous and not a historical character is the silence of the writers who lived during and immediately following the time he is said to have existed. That a man named Jesus, an obscure religious teacher, the basis of this fabulous Christ, lived in Palestine about nineteen hundred years ago, may be true. But of this man we know nothing. His biography has not been written. A Renan and others have attempted to write it, but have failed have failed because no materials for such a work exist. Contemporary writers have left us not one word concerning him. For generations afterward, outside of a few theological epistles, we find no mention of him. The following is a list of writers who lived and wrote during the time, or within a century after the time, that Christ is said to have lived and performed his wonderful works: Josephus
A Gilded Lapse Of Time - Gjertrud Schnackenberg but other sources still defeat the reader The speculation that the concentricspheres must exist is quoted from theon of smyrna, Expositio rerum http://www.complete-review.com/reviews/poetryus/schnackj4.htm
Extractions: Review Summaries Source Rating Date Reviewer Antioch Review Fall/1993 Daniel McGuiness Antioch Review Summer/2001 Carol Moldaw The New Republic Glyn Maxwell The New Republic A Rosanna Warren The NY Rev. of Books Daniel Mendelsohn The NY Times Book Rev. William Logan The NY Times Book Rev. Adam Kirsch Poetry Christian Wiman TLS A Ruth Fainlight "Here's a book for people who don't exist anymore. It would have been a bestseller in the Renaissance. (...) These are poems of terrific intelligence, terrific belief, terrific technique, terrific learning, But we also know what the hitch always is: are we too terrified to afford their kind of comfort, too sick of the trees to see the forest that ails us ?" -
Nuptial Arithmetic introduces the Florentine s commentary and explores its context, sources, and difficulties,especially its debts to Plato s Timaeus and to theon of smyrna. http://englishwww.humnet.ucla.edu/RecentPubs/Nupt.html
Extractions: Marsilio Ficino's Commentary on the Fatal Number in Book VIII of Plato's Republic The latest of Michael Allen's distinguished studies of the leading Renaissance Neoplatonist, Marsilio Ficino (1433-1499), presents for the first time a difficult and fascinating text. Very late in his career Ficino wrote a commentary on the mathematical passage in Book VIII of Plato's Republic that concerns the mysterious geometric or "fatal" number. Since antiquity no one had interpreted this famous enigma; in doing so, Ficino addressed a variety of wide-ranging philosophical, psychological, numerological, astrological, and prophetic themes that are central to our understanding of his thought and of the mentalité of his age. In the first part of Nuptial Arithmetic, Allen introduces the Florentine's commentary and explores its context, sources, and difficulties, especially its debts to Plato's Timaeus and to Theon of Smyrna. He then analyzes Ficino's Pythagorean approach to figured numbers and their progressions and Ficino's determination of the fatal and the nuptial numbers. Allen next turns to Ficino's arresting speculations on eugenics, man's habitus
Pythagoras - Number stones. Composites were further distinguished as plane or solid. Heathquotes theon of smyrna (1st century AD) as writing of composite http://www.mathgym.com.au/history/pythagoras/pythnum.htm
Extractions: Introduction: The Pythagorean view of the universe rested squarely on the belief that Natural (counting) number was the key to the various qualities of mankind and matter. Since in their view everything was composed of number, the explanation for an objects existence could only be found in number. Elsewhere about this time, number existed for utilitarian purposes only, as a device for solving problems in calendar construction, building and commerce. It was the Pythagoreans who saw number as important in itself, the numbers themselves having "personality in a rustic landscape". The distinction was made between logistic (art of computation) and arithmetic (number theory). Kline [6 ] quotes the famous Pythagorean Philolaus (425 B.C.E.), as writing: "Were it not for number and its nature, nothing that exists would be clear to anybody either in itself or in its relation to other things...You can observe the power of number exercising itself ... in all acts and the thoughts of men, in all handicrafts and music." Pythagoras and the early Order initially treated number concretely, as patterns with pebbles, but over time the Pythagoreans developed and refined their concept of number into the same abstract entity which still exists today. Though it is difficult to separate fact from fancy in some of the surviving references to the Pythagoreans, it is generally conceded that they began number theory, and were responsible for the introduction and development of number mysticism in Western Society.
Extractions: Abstract. Martin Euser researches the factor root-(2N - 1) and its interesting relations between musical proportions and Pythagorean triangles. The simple scheme N +/- root-N is also interesting as a generative set of pairs of numbers. This set looks like a prototype for the generative set of pairs of numbers discussed in a previous article by the author. The findings are presented summarily and it is left to the reader to elaborate upon them. Pythagorean Triangles and Musical Proportions Martin Euser S ince writing a previous article on Sacred Geometry I have done a little research on the factor root-(2N - 1) and found some interesting relations between musical proportions and Pythagorean triangles. Furthermore, I have looked into the matter of the 'root-factor' scheme a bit further and found that the simple scheme N +/- root-N is also interesting as a generative set of pairs of numbers. This set looks like a prototype for the generative set of pairs of numbers I have discussed in a previous article. I will present these findings summarily and leave it to the reader to elaborate upon them.
Extractions: Abstract. Mathematician Jay Kappraff discusses a pair of tables of integers found in the Nicomachus's Introduction to Arithmetic and shows how they lead to a general theory of proportion. He shows how the system of musical proportions developed by the neo-Platonic Renaissance architects Leon Battista Alberti and Andrea Palladio, the Roman system of proportions described by Theon of Smyrna, and the Modulor of Le Corbusier are derived naturally from the Nicomachus tables. The Arithmetic of Nicomachus of Gerasa N icomachus of Gerasa (Figure 1, at left) has gained a position of importance in the history of ancient mathematics due in great measure to his Introduction to Arithmetic [1]. This book is one of the only surviving documentations of Greek number theory. Little is known about the life of Nicomachus, and the period of his life can only be estimated to lie between the middle of the first century and the middle of the second century AD, making him contemporary with Theon of Smyrna and Ptolemy. I will discuss a pair of tables of integers found in the
Extractions: Music and the Power of Sound : the influence and tuning and interval on consciousness / Alain Danielou Music, above all other arts, has always been esteemed for its power to speak directly to our higher consciousness. Based on unchanging laws of number and proportion, music also embodies the fundamental metaphysical principles underlying everyday reality. How do these two aspects of music's power, its twin roots in consciousness and mathematics, relate to one another? And why does each of the world's music systems seem to have its own unique effects on consciousness? These are questions this book addresses.
Extractions: Computing, Information Systems and Mathematics 87 Rodenhurst Road South Bank University London, SW4 8AF, England London, SE1 0AA, England Tel/fax: 0181-674 3676 Tel: 0171-815 7411 Fax: 0171-815 7499 E-mail: ZINGMAST@VAX.SBU.AC.UK last Web revision:December 22, 1998 Mario Velucchi's Web Index visitors since Dec. 22, 1998 Web page processed by Web Master - Mario Velucchi velucchi@bigfoot.com Mario Velucchi / Via Emilia, 106 / I-56121 Pisa - Italy
PHILTAR - Compendium Of Philosophers/T and work. Theodorus of Cyrene (465398 BC) A brief introduction tohis life and work. theon of smyrna (c70-c135) An introduction to http://philtar.ucsm.ac.uk/compendium_of_philosophers/t/
Extractions: Links to materials by and/or about over a thousand philosophers from thousands of years from all over the world from A to Z This compendium contains entries large and small, single or multiple, on hundreds of philosophers. Links vary in size from a few lines of biography to the whole of the Summa Theologica. Sometimes you are directed to a site which has further links. In that case there is no guarantee that all the further links will work, but enough work to make a visit worthwhile. This compendium does not provide links to philosophers own home pages. A list of them can be found here A B C ... Z Tagore, Rabindranath (1861-1941) A small Tagore website with a few links
Kairouz We observe, too, the Pythagorean diatonism clearly described in thesecond century by Nicomachus of Gerasa and theon of smyrna. http://www.keyrouz.com/engmelkite.html
Extractions: CD SACRED MELKITE CHANT 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. the sound is never rigidly set; like a cell,As if sister Marie Keyrouz were following the treatise of Porphirius of Tyre (Bar Malkan, 3rd cent.), it expands, contracts, varies in color.
Freethought Today, March 1996, "Christ Killers"?, Hayes PhiloJudaeus, Pliny the Elder, Seutonius, Juvenal, Martial, Arrian, Petronius,Dion Pruseus, Paterculus, Appian, Phlegon, theon of smyrna, Persius, Plutarch http://www.ffrf.org/fttoday/march96/hayes.html
Extractions: Anyone who has read a lot of books about the history of the Roman Catholic Church will necessarily have read a lot of books about anti-Semitism. The Catholic Church's centuries-long persecution of the Jews has always been accompanied by cries of the epithet, "Christ-killers!" Those words are still spit out, even today, by hateful bigots. The Jews, accused of killing Jesus, and therefore killing God, were guilty of the most horrible crime imaginabledeicide. Just think. They killed God. This charge demands some scrutiny. The first thought that should spring to mind is: How can you kill a God?! Isn't that by definition an impossibility? But setting aside this major assault on logic, anyone even slightly familiar with ancient Hebrew law knows that if the Jews had wanted to kill Jesus, they would have stoned him to death. The Jews did not crucify people. The Romans did. That undeniable fact is skirted by claiming that the Jews arranged for Jesus' death and were therefore responsible for it, but they turned him over to the Roman authorities to do the actual killing. But how likely is this? Even if the Jews were screaming for Jesus' blood, why would Pilate automatically do their bidding? Who ruled JudeaPilate or the Jews? History leaves no doubt about that, so what was Pilate's motivation? Well, they say that Pilate was afraid that this Jesus might somehow start an insurrection, so he'd best be got rid of. But if that's true, then we're going to have to rewrite history.
Marsilio Ficino of other ancient texts into Latin including the works of Synesius, Psellus, Iamblichus On the Mysteries of the Egyptians , Porphyry and theon of smyrna. http://www.renaissanceastrology.com/ficino.html
Extractions: Introduction TOP M arsilio Ficino, one of the greatest figures of the Italian Renaissance, was born in Florence, on October 19, 1433. He died in October of 1499. He was a priest, a doctor and musician, but is best known for his work as a translator of classic works, author and philosopher. Ficino, in contrast to Cornelius Agrippa , was fortunate in finding such exemplary patrons as the Medici family of Florence.
Extractions: Previous SOURCES BOOK REVIEWS Ideas of Space, by Jeremy Gray (Joan L. Richards) ................................................ 9597 by Emmanuel Poulle (Bernard R. Goldstein) ............................................ 9799 Two Decades of Mathematics in the Netherlands 19201940. A Retrospection on the Occasion of the Bicentennial of the Wiskundig Genootschap , edited by E. M. J. Bertin, H. J. M. Bos, and A. W. Grootendors (Dirk J. Struik) ................................................. 99100 Theon of Smyrna. Mathematics Useful for Understanding Plato, by J. Dupuis, translated by Robert and Deborah Lawlor and edited by Christos Toulis and others (Richard D. McKirahan, Jr.) ..................................... 100104 R. A. Fisher. The Life of a Scientist, by Joan Fisher Box (N. T. Gridgeman) ............................................... 104106 The Library of Isaac Newton , by John Harrison (I. Bernard Cohen) .............................................. 106109
Spring 2003 Sectional Meeting Of The Allegheny Mountain Section Of In the first century AD, the Introduction to Arithmetic, by Nicomachus of Gerasaand Mathematics Useful for Understanding Plato by theon of smyrna were one the http://www.math.psu.edu/sellersj/alleghenymtn/annual_meeting_2003/tattersall.htm
