LEADER 01509nam2 2200337 i 450 001 SUN0089661 005 20130801125216.449 010 $a88-17-16653-7 100 $a20120606d1989 |0grcc50 ba 101 $agrc$aITA 102 $aIT 105 $a|||| ||||| 200 1 $aCimone$aLucullo$fPlutarco$gintroduzione, traduzione e note [di Cimone] di Stefania Fuscagni$gintroduzione e note [di Lucullo] di Barbara Scardigli$gtraduzione [di Lucullo] di Beatrice Mugelli 210 $aMilano$cRizzoli$d1989 215 $a513 p.$cill.$d18 cm. 410 1$1001SUN0093936$12001 $aBUR. 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Waterloo, Ont., Canada : Wilfrid Laurier University Press, c1987. 300 $a"Incorporates ... a new preface and a section of 'Corrections and additions,' both prepared specially for this edition by the author"--T.p. verso. 311 $a0-486-40007-7 320 $aIncludes bibliographical references (p. 180-195). 327 $aCover; Title Page; Copyright Page; Contents; Preface to the Dover Edition; Foreword; A Guide for Readers; A. Internal Organization; B. Bibliographical Details; C. Abbreviations; D. Symbols; E. Dates; F. Quotations from Primary Sources; Introduction; Chapter I. The Euclidean Text; Section 1. The Text; Section 2. An Examination of the Euclidean Text; A. Preliminary Observations; B. A Proposal Concerning the Origin of DEMR; C. Theorem XIII,8; D. Theorems XIII,1-5; E. Stages in the Development of DEMR in Book XIII; Chapter II. Mathematical Topics; Section 3. Complements and the Gnomon 327 $aSection 4. Transformation of AreasSection 5. Geometrical Algebra, Application of Areas, and Solutions of Equations; A. Geometrical Algebra-Level 1; B. Geometrical Algebra-Level 2; C. Application of Areas-Level 3; D. Historical References; E. Setting Out the Debate; F. Other Interpretations in Terms of Equations; G. Problems in Interpretation; H. Division of Figures; I. Theorems VI,28,29 vs 11,5,6; J. Euclid's Data; K. Theorem II,11; L. II,11-Application of Areas, Various Views; i. Szabo?; ii. Junge; iii. Valabrega-Gibellato; Section 6. Side and Diagonal Numbers; Section 7. Incommensurability 327 $aSection 8. The Euclidean Algorithm, Anthyphairesis, and Continued FractionsChapter III. Examples of The Pentagon, Pentagram, and Dodecahedron Before -400; Section 9. Examples before Pythagoras (before c. -550); A. Prehistoric Egypt; B. Prehistoric Mesopotamia; C. Sumerian and Akkadian Cuneiform Ideograms; i. Fuy?e's Theory; D. A Babylonian Approximation for the Area of the Pentagon; i. Stapleton's Theory; E. Palestine; Section 10. From Pythagoras until -400; A. Vases from Greece and its Italian Colonies , Etruria (Italy); B. Shield Devices on Vases; C. Coins; D. Dodecahedra 327 $aE. Additional MaterialConclusions; Chapter IV. The Pythagoreans; i. Pythagoras; ii. Hippasus; iii. Hippocrates of Chios; iv. Theodorus of Cyrene; v. Archytas; Section 11. Ancient References to the Pythagoreans; A. The Pentagram as a Symbol of the Pythagoreans; B. The Pythagoreans and the Construction of the Dodecahedron; C. Other References to the Pythagoreans; Section 12. Theories Linking DEMR with the Pythagoreans; i. The Pentagram; ii. Scholia Assigning Book IV to the Pythagoreans; iii. Equations and Application of Areas; iv. The Dodecahedron 327 $av. A Marked Straight-Edge Construction of the Pentagonvi. A Gnomon Theory; vii. Allman's Theory: The Discovery of Incommensurability; viii. Fritz-Junge Theory: The Discovery of Incommensurability; ix. Heller's Theory: The Discovery of DEMR; x. Neuenschwander's Analysis; xi. Stapleton; Chapter V. Miscellaneous Theories; Section 13. Miscellaneous Theories; i. Michel; ii. Fowler: An Anthyphairesis Development of DEMR; iii. Knorr: Anthyphairesis and DEMR; iv. Itard: Theorem IX,15; Section 14. Theorems XIII,1-5; i. Bretschneider; ii. Allman; iii. Michel; iv. Dijksterhuis and Van der Waerden 327 $av. Lasserre 330 $a
A comprehensive study of the historic development of division in extreme and mean ratio (""the golden number""), this text traces the concept's development from its first appearance in Euclid's Elements through the 18th century. The coherent but rigorous presentation offers clear explanations of DEMR's historical transmission and features numerous illustrations.
410 0$aDover Books on Mathematics 606 $aRatio and proportion$xHistory 606 $aGeometry 615 0$aRatio and proportion$xHistory. 615 0$aGeometry. 676 $a512.7 700 $aHerz-Fischler$b Roger$f1940-$01514906 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910782070503321 996 $aA mathematical history of the golden number$93750371 997 $aUNINA