Crowley's Greek Qabalah From
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0.GEMATRIA DATABASE.Pages
GEMATRIA - DATABASE ! Bavarian Illuminati Est. May 1st, 1776} 5/01/1776 ! Scottish Rite Est. May 31, 1801 } 5/31/1801 Knights Templar ARRESTED on Oct. 13, 1307 } 10/12/1307 ! Knights Templar FOUNDED in Jerusalem, Israel: 1119 ! Skull & Bones 322 FOUNDED in 1832 at Yale University) (Russell Trust Association - Parent Organization) 322 references 322 BC ! Vatican City Est. February 11, 1929 (109 acres) ! One legend is that the numbers in the society's emblem ("322") represent "founded in '32, 2nd corps", referring to a first Corps in an unknown German university.[22][23] ! Convocation founded in 1539 (3rd Papal Bull) Jesuits founded in 1541 Copernicus of 1543 (Ball Earth) The Council of Trent founded in 1545 ! (Christopher Columbus) America discovered in 1492 (2 Papal Bulls) 1912 = Titanic sank 1913 = Federal Reserve Established 1914 = First World War 1917 = Bolshevik Communist Invasion ! Jewish Bolshevism, also known as Judeo-Bolshevism, is an antisemitic and anti-communist canard [citation needed] which alleges that the Jews were at the origin of the Russian Revolution and held the primary power among Bolsheviks. Similarly, the Jewish Communism theory implies that Jews have been dominating the Communist movements in the world. It is similar to the ZOG conspiracy theory, which asserts that Jews control world politics. The expressions have been used as a catchword for the assertion that Communism is a Jewish conspiracy. ! Hexagram = Star of David ! Pythagoras the Samian or Pythagoras of Samos (570-495 BC) was a mathematician, Ionian Greek -
Indirect Proof
95698_ch02_067-120.qxp 9/5/13 4:53 PM Page 76 76 CHAPTER 2 ■ PARALLEL LINES In Exercises 28 to 30, write a formal proof of each theorem. 34. Given: Triangle MNQ with M obtuse ∠MNQ 28. If two parallel lines are cut by a transversal, then the pairs Construct: NE Ќ MQ, with E of alternate exterior angles are congruent. on MQ. N Q 29. If two parallel lines are cut by a transversal, then the pairs 35. Given: Triangle MNQ with of exterior angles on the same side of the transversal are Exercises 34, 35 obtuse ∠MNQ supplementary. Construct: MR Ќ NQ 30. If a transversal is perpendicular to one of two parallel lines, (HINT: Extend NQ.) then it is also perpendicular to the other line. 36. Given: A line m and a point T not on m 31. Suppose that two lines are cut by a transversal in such a way that the pairs of corresponding angles are not congruent. T Can those two lines be parallel? 32. Given: Line ᐍ and point P P m not on ᐍ —! Suppose that you do the following: Construct: PQ Ќ ᐍ i) Construct a perpendicular line r from T to line m. ii) Construct a line s perpendicular to line r at point T. 33. Given: Triangle ABC with B three acute angles What is the relationship between lines s and m? Construct: BD Ќ AC, with D on AC. A C 2.2 Indirect Proof KEY CONCEPTS Conditional Contrapositive Indirect Proof Converse Law of Negative Inverse Inference Let P S Q represent the conditional statement “If P, then Q.” The following statements are related to this conditional statement (also called an implication). -
Grcriddles Documentation Release 1A
GRCRiddles Documentation Release 1a Marko Manninen Jul 30, 2019 Contents 1 Processing Greek corpora for the riddle solver3 1.1 Focus of the study............................................3 1.1.1 Natural language processing..................................5 1.1.2 Statistics.............................................8 1.2 Table data................................................. 10 1.3 Bar chart................................................. 11 1.4 Optional live chart............................................ 11 1.4.1 Unique words database..................................... 11 1.5 Longest words.............................................. 15 1.6 Highest isopsephy............................................ 17 2 Isopsephical riddles in Greek Pseudo Sibylline hexameter poetry 21 2.1 Introduction............................................... 21 2.1.1 Riddle 1............................................. 23 2.1.2 Riddle 2............................................. 23 2.1.3 Riddle 3............................................. 24 3 Study of the results of the riddle solver 33 4 Appendix 1 - Store database 35 5 Appendix 2 - Solve riddles 37 i ii GRCRiddles Documentation, Release 1a In the following chapters, I’m guiding through the process of solving some enigmatic alphanumeric riddles in the Greek Pseudo Sibylline oracles. In the first chapter, I will download and preprocess freely available open source Greek corpora. In the second chapter, I will use the processed unique word database to solve some specific riddles in the Sibylline oracles. The third chapter is reserved more for the speculative analysis of the results. The reader may download all material and code for the interactive exploration from the GitHub project: https://github. com/markomanninen/grcriddles Contents: Contents 1 GRCRiddles Documentation, Release 1a 2 Contents CHAPTER 1 Processing Greek corpora for the riddle solver Pseudo-Sibylline1 oracles contain hexametric poems written in Ancient Greek. These oracula were mainly composed in 150BC - 700AD to twelve distinct extant books. -
The Idea of Στοιχεῖον in Grammar and Cosmology: from Antique Roots to Medieval Systems
The Idea of Στοιχεῖον in Grammar and Cosmology: From Antique Roots to Medieval Systems Angel Eduardo Juan Acevedo A dissertation submitted in fulfilment of the requirements for the degree of Doctor of Philosophy in Combined Historical Studies The Warburg Institute University of London 2018 1 I declare that the work presented in this dissertation is my own. Signed: Date: 2 Abstract This thesis defines and follows the development of the concept expressed by theGreek στοιχεῖον and the Latin elementum. From approximately the sixth century bc to the twelfth century ad, these words had three simultaneous meanings: letter, number and element, corresponding respectively to the disciplines of grammar, arithmetic and cosmology. The first part of the thesis, in two chapters, draws primarily onGreek philosophical, grammatical and arithmetical sources to delineate this polysemy, with particular attention to Pythagorean number cosmology and the foundational and lasting role of Plato’s Timaeus. Once the triple concept is established, the second part, in four chapters, tracks it through late Antiquity in Hellenistic religious texts and in Abrahamic scriptural sources and exegetical literature, identifying semantic analogues in Hebrew and Arabic. The third part of the thesis studies particular casesof alphanumeric cosmology in doctrinal systems of major Jewish, Christian and Islamic authors of the High Middle Ages, namely in the Sefer Yetsirah, in Aquinas and Ibn ʿArabī. In the conclusion I gather the comparative evidence to situate the concept of the alphanumeric element in its relations to the broader metaphysical, theological and cosmological heritage of the International Mediterranean Middle Ages. 3 Contents Abstract 3 Acknowledgements 9 Notes to the Reader 10 Transliterations ................................. -
Icons of Mathematics an EXPLORATION of TWENTY KEY IMAGES Claudi Alsina and Roger B
AMS / MAA DOLCIANI MATHEMATICAL EXPOSITIONS VOL 45 Icons of Mathematics AN EXPLORATION OF TWENTY KEY IMAGES Claudi Alsina and Roger B. Nelsen i i “MABK018-FM” — 2011/5/16 — 19:53 — page i — #1 i i 10.1090/dol/045 Icons of Mathematics An Exploration of Twenty Key Images i i i i i i “MABK018-FM” — 2011/5/16 — 19:53 — page ii — #2 i i c 2011 by The Mathematical Association of America (Incorporated) Library of Congress Catalog Card Number 2011923441 Print ISBN 978-0-88385-352-8 Electronic ISBN 978-0-88385-986-5 Printed in the United States of America Current Printing (last digit): 10987654321 i i i i i i “MABK018-FM” — 2011/5/16 — 19:53 — page iii — #3 i i The Dolciani Mathematical Expositions NUMBER FORTY-FIVE Icons of Mathematics An Exploration of Twenty Key Images Claudi Alsina Universitat Politecnica` de Catalunya Roger B. Nelsen Lewis & Clark College Published and Distributed by The Mathematical Association of America i i i i i i “MABK018-FM” — 2011/5/16 — 19:53 — page iv — #4 i i DOLCIANI MATHEMATICAL EXPOSITIONS Committee on Books Frank Farris, Chair Dolciani Mathematical Expositions Editorial Board Underwood Dudley, Editor Jeremy S. Case Rosalie A. Dance Tevian Dray Thomas M. Halverson Patricia B. Humphrey Michael J. McAsey Michael J. Mossinghoff Jonathan Rogness Thomas Q. Sibley i i i i i i “MABK018-FM” — 2011/5/16 — 19:53 — page v — #5 i i The DOLCIANI MATHEMATICAL EXPOSITIONS series of the Mathematical As- sociation of America was established through a generous gift to the Association from Mary P. -
Simple Andi Complete K-Points in Continuous and in Modular Projective Spaces
SIMPLE ANDI COMPLETE K-POINTS IN CONTINUOUS AND IN MODULAR PROJECTIVE SPACES by Beulah Armstrong Submitted to the Department of Mathematica and the faculty of the Graduate School of the University of Kansas in partial fulfillment.of I the requirements for the degree of Master of Arts. · Approved . 'UI/;~ _ Depar.tment of~ B I B L I ·o G R A P H Y. Allman, G.J. - Greek Geometry from Thales to Euclid - Longmans, Green & Co., London - 1889. Beman, W.W. and Smith, D.E. - Kls.in's Famous. Problems in ·Elementary Geometry - Ginn & Co., Boston - 1897. , , n Cantor, Moritz - Vorlesungen Uber Geschichte der Math- ematik - B.G. !l:eubner - Leipzig - 1894. Daviesf Iviathematical Dictionary and Cyclopedia of Math- ematical ~cieilce - A.s. Barnes & Co., New. York - 1855. Eisenlohr, Augu.st - Mathematisches Hendbuch der Alten Aegypter, Erst er Band - j. c. Hinrich, Le~pzig - 1877/ . _ Gow, James - A Short History of Greek Mathematics, University Press, Cambridge - 1884. Heath, T.L. - The i;chirteen Books of Euclid 1 s Elements, University Press; Cambridge - 1908. Lachlan, R. :.. Modern Pure Geometry - MacMillan & Co., New York - 1893. Tropfke, Johannes, Gesohichte der E1ementar Mathematik, Veit und Comp, Leipzig, 1903. Veblen and Young - Projective Geometry - Ginn & Co., New York - 1910. Young, J.W.A. - Monographs on Modern Mathematics, ·Longmans, Green & Co., New York - 1911. 1. INTRODUCTION. It is the pil:rpose of this paper, (1) ¥0 trace the development of the concepts of the simple· k-point ·and the complete k-point as they appear in mathematical literature and to £ormulate their definitions in a modular or an ordinary projective n-space (Se.ctioris 1 and 2); and (2) To determine the number of complete k-points in a modular projective plane (Section 3). -
Polygrammal Symmetries in Bio-Macromolecules: Heptagonal Poly D(As4t) . Poly D(As4t) and Heptameric -Hemolysin
Polygrammal Symmetries in Bio-macromolecules: Heptagonal Poly d(As4T) . poly d(As4T) and Heptameric -Hemolysin A. Janner * Institute for Theoretical Physics, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen The Netherlands Polygrammal symmetries, which are scale-rotation transformations of star polygons, are considered in the heptagonal case. It is shown how one can get a faithful integral 6-dimensional representation leading to a crystallographic approach for structural prop- erties of single molecules with a 7-fold point symmetry. Two bio-macromolecules have been selected in order to demonstrate how these general concepts can be applied: the left-handed Z-DNA form of the nucleic acid poly d(As4T) . poly d(As4T) which has the line group symmetry 7622, and the heptameric transmembrane pore protein ¡ -hemolysin. Their molecular forms are consistent with the crystallographic restrictions imposed on the combination of scaling transformations with 7-fold rotations. This all is presented in a 2-dimensional description which is natural because of the axial symmetry. 1. Introduction ture [4,6]. In a previous paper [1] a unifying general crystallography has The interest for the 7-fold case arose from the very nice axial been de®ned, characterized by the possibility of point groups of view of ¡ -hemolysin appearing in the cover picture of the book in®nite order. Crystallography then becomes applicable even to on Macromolecular Structures 1997 [7] which shows a nearly single molecules, allowing to give a crystallographic interpre- perfect 7-fold scale-rotation symmetry of the heptamer. In or- tation of structural relations which extend those commonly de- der to distinguish between law and accident, nucleic acids have noted as 'non-crystallographic' in protein crystallography. -
L-G-0008528105-0017872237.Pdf
Wissenschaftliche Untersuchungen zum Neuen Testament Herausgeber / Editor Jörg Frey (Zürich) Mitherausgeber / Associate Editors Markus Bockmuehl (Oxford) · James A. Kelhoffer (Uppsala) Hans-Josef Klauck (Chicago, IL) · Tobias Nicklas (Regensburg) J. Ross Wagner (Durham, NC) 363 Book of Seven Seals The Peculiarity of Revelation, its Manuscripts, Attestation, and Transmission Edited by Thomas J. Kraus and Michael Sommer Mohr Siebeck Thomas J. Kraus, born 1965; studied Catholic Theology and English linguistics & lite- rature; 1999 Dissertation at the Faculty of Catholic Theology, Regensburg University; since 1999 teacher at a grammar school in Bavaria/Germany; since 2013 lecturer at Zurich University, Switzerland. Michael Sommer, born 1984; studied Catholic Theology at the Faculty of Catholic Theology, Regensburg University; 2013 Dissertation; since 2014 Junior Professor of Biblical Theology, Martin-Luther-University Wittenberg-Halle. e-ISBN PDF 978-3-16-154268-8 ISBN 978-3-16-152741-8 ISSN 0512-1604 (Wissenschaftliche Untersuchungen zum Neuen Testament) Die Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliogra- phie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2016 by Mohr Siebeck, Tübingen, Germany. www.mohr.de This book may not be reproduced, in whole or in part, in any form (beyond that permitted by copyright law) without the publisher’s written permission. This applies particularly to reproductions, translations, microfilms and storage and processing in electronic systems. The book was printed by Gulde Druck in Tübingen on non-aging paper and bound by Buch binderei Spinner in Ottersweier. Printed in Germany. Preface The idea to bring together scholars to write about manuscripts and text- critical issues of the Book of Revelation, the last book of the Canon of the New Testament, came up during a conference in Lausanne, Switzerland, in 2011. -
“This Cabal Guy Could Be Right”: Numeric Correlations in Maury Yeston's in the Beginning
e Interdisciplinary Journal of Popular Culture and Pedagogy “This Cabal Guy Could Be Right”: Numeric Correlations in Maury Yeston’s In the Beginning Leonard Vandegrift Cal Poly Pomona Pomona, California, USA [email protected] Abstract: The study of gematria and isopsephy, the numeric conversion of Hebrew and Greek words, yields an abundant harvest of biblical insight. Though applying this method to more secular literature is rare, we have a unique set of circumstances in Maury Yeston’s musical In the Beginning that renders its use appropriate. Derived from Hebrew and Greek, the names of the show’s principal characters can be converted to numeric values, all of which share at least one of three common factors. Moreover, the names are often connected thematically, and their factors reflect key elements in the first five books of the Bible. Along with contributions from fellow collaborators Larry Gelbart and David Hahn, Yeston appears to be the most likely candidate to have included these numeric features, the intention of which is expressed in the words of the antagonist Romer, who draws particular attention to Kabbalah’s use of numbers: “There is something about the number forty. This Cabal guy could be right” (2.4.65; emphasis added). The character only skims the surface of the number 40’s implications and misses entirely the deeper meanings that further reflection offers, but having drawn some attention to the matter, the script seems to have left the question open for any observant director, performer, or audience member familiar with such things and with sufficient interest to investigate further. -
Crowley's Greek Qabalah From
The Greek Qabalah LIBER MCCCLXV A.'. A.'. Publication in Class C By Frater Apollonius f 4° = 7 AN CV 2009 e.v. Preface Simply beginning my research of the Greek Qabalah proved rewarding right from the start. This is a project that has been slowly put together over several years as I‟ve found interesting tid-bits when surfing the net; usually looking for something else. Add to this my general dissatisfaction when first coming across what has proved to be the incomplete work of Aleister Crowely, transliterating the letters and words of the Greek language into a numerically listed compendium that in the format presented was almost completely worthless. And even calling it the „Greek Qabalah‟ either was almost a joke, or in itself simply a scratch start to a project that he never really even began. As my research begain in ernest, I also began returning the letters in Crowley‟s work back to their original Greek, only to discover that only one of the ancient Gnostic documents was actually written in Greek; the rest being in Coptic, generally. And I decided to discount these, even though a Qabalah is utterly dependent on „holy‟ or „praeternatural‟ scriptures to have any authenticity. Still, one is at least enough, but I would discover there‟s a world to itself, simply in the alphabet and the ideas that were being incorporated from the measure of the planets in our solar system along with the geometry that forms the basis in number of our Western culture. And for that matter, these numbers are incorporated to some degree, in the Apocalypose of John, which was written long before the Jews thought of putting a Qabalah together. -
The Logarithmic Spiral by Donald G
THE PENTAGON Volume XVI SPRING, 1957 Number 2 CONTENTS Page National Officers 66 The Logarithmic Spiral By Donald G. Johnson 67 Consequences of A* + B8 = Ca By Alfred Moessner 76 Paradox Lost—Paradox Regained By Peggy Steinbeck •— 78 Watch That Check—It Might Bounce! By Dana R. Sudborough 84 Construction of the Circle of Inversion By Shirley T. Loeven 85 Mathematical Notes By Merl Kardatzke 86 Creating Interest for Gifted Students By Ati R. Amir-Moez „ 88 Order Among Complex Numbers By Merl Kardatzke 91 Problem Corner , 94 The Mathematical Scrapbook 97 The Book Shelf 101 Installation of New Chapter 109 Kappa Mu EpsOon News . ._ 110 Program Topics 112 National Officers C. C. Richtmeyer President Central Michigan College, Mt. Pleasant, Michigan R. G. Smith Vice-President Kansas State Teachers College, Pittsburg, Kansas Laura Z. Greene Secretary Washburn Municipal University, Topeka, Kansas M. Leslie Madison Treasurer Colorado A&M College, Port Collins, Colorado Frank Hawthorne .... - Historian The State Education Department, Albany, N.Y. Charles B. Tucker -- - Past President Teachers College, Emporia, Kansas Kappa Mu Epsilon, national honorary mathematics society, was founded in 1931. The object of the fraternity is fourfold: to further the interests of mathematics in those schools which place their primary emphasis on the undergraduate program; to help the undergraduate realize the important role that mathematics has played in the develop ment of western civilization; to develop an appreciation of the power and beauty possessed by mathematics, due, mainly, to its demands for logical and rigorous modes of thought; and to provide a society for the recognition of outstanding achievements in the study of mathe matics at the undergraduate leveL The official journal, THE PENTA GON, is designed to assist in achieving these objectives as well as to aid in establishing fraternal ties between the chapters. -
Tessellated and Stellated Invisibility
Tessellated and stellated invisibility Andr´eDiatta,1 Andr´eNicolet,2 S´ebastien Guenneau,1 and Fr´ed´eric Zolla2 September 20, 2021 1Department of Mathematical Sciences, Peach Street, Liverpool L69 3BX, UK Email addresses: [email protected]; [email protected] 2Institut Fresnel, UMR CNRS 6133, University of Aix-Marseille III, case 162, F13397 Marseille Cedex 20, France Email addresses: [email protected]; [email protected]; Abstract We derive the expression for the anisotropic heterogeneous matrices of per- mittivity and permeability associated with two-dimensional polygonal and star shaped cloaks. We numerically show using finite elements that the forward scat- tering worsens when we increase the number of sides in the latter cloaks, whereas it improves for the former ones. This antagonistic behavior is discussed using a rigorous asymptotic approach. We use a symmetry group theoretical approach to derive the cloaks design. Ocis: (000.3860) Mathematical methods in physics; (260.2110) Electromagnetic the- ory; (160.3918) Metamaterials; (160.1190) Anisotropic optical materials 1 Introduction Back in 2006, a team led by Pendry and Smith theorized and subsequently experimen- tally validated that a finite size object surrounded by a spherical coating consisting of a metamaterial might become invisible for electromagnetic waves [1, 2]. Many authors have since then dedicated a fast growing amount of work to the invisibility cloak- arXiv:0912.0160v1 [physics.optics] 1 Dec 2009 ing problem. However, there are alternative approaches, including inverse problems’s methods [3] or plasmonic properties of negatively refracting index materials [4]. It is also possible to cloak arbitrarily shaped regions, and for cylindrical domains of arbi- trary cross-section, one can generalize [1] to linear radial geometric transformations [5] ′ r = R1(θ)+ r(R2(θ) R1(θ))/R2(θ) , 0 r R2(θ) , ′ − ≤ ≤ θ = θ , 0 < θ 2π , (1) ′ ≤ x = x , x IR , 3 3 3 ∈ ′ ′ ′ where r , θ and x3 are “radially contracted cylindrical coordinates” and (x1, x2, x3) is the Cartesian basis.