DOCSLIB.ORG

Chap 1-3 Final

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Chap 1-3 Final Dreams in Homer, Heraclitus, and Plato Item Type text; Electronic Thesis Authors Novikova, Aleksandra Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 30/09/2021 14:28:04 Link to Item http://hdl.handle.net/10150/628164 DREAMS IN HOMER, HERACLITUS, AND PLATO by Aleksandra Novikova ____________________________ Copyright © Aleksandra Novikova 2018 A Thesis Submitted to the Faculty of the DEPARTMENT OF RELIGIOUS STUDIES AND CLASSICS In Partial Fulfillment of the Requirements For the Degree of MASTER OF ARTS In the Graduate College THE UNIVERSITY OF ARIZONA 2018 Novikova !1!2 Novikova !3 Table of Contents Abstract 4 Introduction 5 Chapter 1: Dreams as Messages of the Divine 10 Chapter 2: Dreams as Lack of True Knowledge 24 Chapter 3: Dreams as the Void of True Perception 35 Conclusion 53 Works Cited 54 Novikova !4 Abstract My thesis examines the connection between dreams, knowledge, and perception in the works of Homer, Heraclitus and Plato. Although the perception is not a topic thoroughly discussed in the Iliad and the Odyssey, Homeric view on dreams will serve as a basis for comparison with Heraclitus and Plato. In Homer, dreams are generally messages from a supernatural force imparting some divine knowledge to the sleeper in order to fulfill their own will. As a reaction to the traditionally accepted views of the epics, Heraclitus asserts that dreams, because they are created by specific individuals and are cut off from the shared world fire, are a poor source of the true logos, true knowledge. Furthermore, Plato expands upon Heraclitus’ idea by stating that dreaming is a form of perception that is too unstable to be able to provide true knowledge. By exploring how people perceive dreams while asleep, we can get a better understanding of the sort of knowledge that is obtained in dreams. Novikova !5 Introduction The subject of dreams is an interesting topic because of our own human desire to understand what we experience while asleep. On the one hand, with the advancement of medicine and neurological sciences in the last century, we now know the physiological needs of sleep and its essential part in our daily routine. Nowadays even the simplest sleep tracker can tell us how long we sleep and what stages of sleep we experience. We can also identify that most of dreaming happens during the rapid eye movement (REM) sleep stage (Mendelson 2017: 14-15). However, dreams themselves have not been so easily defined and understood. Many of us try to assign some psychological explanations to what we dream in order to better understand our own subconscious mind, hoping that dreams could reveal some hidden knowledge about ourselves. The significance of dream interpretation goes at least as far back as second and first millennium BCE to Babylonia and Assyria (Lewis 1996). Many cultures had their own dream interpreters who would record and help them interpret their dreams. Although the first comprehensive “dream-book” appeared in the second century CE in the Oneirocritica of Artemidorus (Walde 1999), in Greek culture dreams already had an irreplaceable role in curing various aliments through the process known as sleep incubation. Healing sanctuaries were common throughout Greece and, although the most important sanctuary at Epidaurus of the god Asclepius was not fully developed until the late 4th century BCE, there are many inscriptions dating back to the 5th century which reference this manner of curing various sicknesses (Holowchak 2002: 151-156). It was a religious ritual in which the diseased sleeper would be granted the cure or other means by which the illness could be resolved through a visitation of a god. Additionally, by the late 5th century a collection of medical writings called the Hippocratic Novikova !6 Corpus, usually attributed to Hippocrates despite its questionable authorship, introduced the idea that sleep is necessary and the interpretation of whatever one sees asleep can lead to a better understanding of one’s health. The underlying assumption for all those seeking to understand one’s dreams is that there is some knowledge to be gained from their interpretation. The earliest written record of dreams in Ancient Greece can be seen in Homer’s epic poems the Iliad and the Odyssey. In both of these works, the terms “to sleep” ("ὕ$"%&) and “dream” (ὄν"%()* or ὄν+() are generally used in conjunction with one another. Even though one asleep does not always dream, one has to be asleep in order to dream. The two states, though technically different, share the same requirement of being unconscious. Nevertheless, a dream comes into the narrative following a specific pattern (Morris 1983): a supernatural deity approaches the unsuspecting sleeper, stands above their head, and speaks to the recipient of the dream. In Homer, dreams are generally in association with some sort of divine or supernatural power and are a way for those powers to utter a message into the sleeper’s mind. The messages themselves are not merely words of wisdom or simple predictions of the future: they carry the will of whatever otherworldly power that created them. In many cases, it is some kind of knowledge which would lead the dreamer into accomplishing the will of the divine being. Sometimes the knowledge imparted upon the sleeper is relatively straightforward. In Book 23 of the Iliad, the ghost of Patroclus1 appears to Achilles in a dream urging the Greek hero to bury his friend as quickly as possible so that he could finally rest in peace. This interjection from the supernatural world immediately propels the grieving man into finally burying his lost comrade. Similarly, this visit serves as a parallel to his mistreatment of Hector’s 1 In the first chapter, I will further explain why I consider this particular episode a dream. Novikova !7 corpse and a reminder to respect the laws of the dead. Other times, however, the knowledge imparted upon the sleeper is deliberately misleading to its recipient (both with positive and negative results). It is evident in Book 6 of the Odyssey, where Nausicaa under the subconscious suggestions of Athena that she would encounter her husband inadvertently meets Odysseus and organize his return home. Regardless of the intention of the supernatural beings, in the epic poems it is only in the dreams provided by the divine that any knowledge can be attained. For the ancient Greeks, the Homeric epics were not only literary works but also poems which represented a past that they otherwise did not have preserved in any other easily accessible form. They were a source of both a historical and a mythical past—a model to follow in many facets of their everyday lives (Scodel 2004; Osborne 2004). As the Greek world experienced economical, cultural, and geographic growth, so did writing and literature that the ancients began to produce. All of these factors facilitated the emergence of curious thinkers (the “pre- Socratics”—more specifically, the early philosophers before the time of Plato) who, instead of accepting the commonly accepted views provided by Homer, pursued the “study of the nature, origin and processes of the natural world” (Warren 2007: 2).2 These early thinkers explored many aspects of the world; some of which were dreams and sleep. The earliest thinker of this period to discuss dreams was Heraclitus in the late 6th to early 5th centuries BCE. Although the fragmentary nature of the texts is problematic, the fragments 2There were several different camps of thought sprawled all over the Mediterranean. The earliest (dating back to the first half of the sixth century BCE) of these scientist-philosophers were the Milesians on the Ionian coast. One of these was Thales whose main interest was to find the principal element from which all things in the universe are made and who is recorded as having accurately predicted a solar eclipse that occurred in 585 BCE (O’Grady 2005). Following was Xenophanes who, aside from composing lyric poetry, was also avidly questioning the epics and how the world works. Then, there were the so-called Eleatic philosophers (named after the Greek colony of Elea in Italy) whose leading philosopher Parmenides (late 6th/early 5th century) claimed that only one thing existed. The list does not end here; however, this extremely brief introduction gives a good overview of the topics that they tended to discuss. Novikova !8 provide a general overview of Heraclitus’ philosophy. Even though the fragments do not necessarily use the exact vocabulary (ὄν"%()* or ὄν+(), Heraclitus discusses dreams while exploring sleep and whatever happens while one is asleep. However, unlike in Homer, dreams are seen as an insignificant part of sleep which does not impart any true knowledge upon the sleeper. Heraclitus, like many of his predecessors, disliked and rejected the traditional views of the divine presented in Homer. Most of all, his main argument was that men only assume to know what is the nature of the gods and not that they actually know. Thus, anything that Homer discussed concerning the divine should not be taken seriously—in this case, the dream-messages from the divine. In his first fragment, Heraclitus attempts to explain that men have the tendency to not understand the logos, the fundamental principle that governs the nature of the universe, even though they have the potential for it. The philosopher also point out that one’s senses, like eyesight, which are used to gather information about the outside world are extremely important.
Load more

Recommended publications
  • The Ordered Distribution of Natural Numbers on the Square Root Spiral
    The Ordered Distribution of Natural Numbers on the Square Root Spiral - Harry K. Hahn - Ludwig-Erhard-Str. 10 D-76275 Et Germanytlingen, Germany ------------------------------ mathematical analysis by - Kay Schoenberger - Humboldt-University Berlin ----------------------------- 20. June 2007 Abstract : Natural numbers divisible by the same prime factor lie on defined spiral graphs which are running through the “Square Root Spiral“ ( also named as “Spiral of Theodorus” or “Wurzel Spirale“ or “Einstein Spiral” ). Prime Numbers also clearly accumulate on such spiral graphs. And the square numbers 4, 9, 16, 25, 36 … form a highly three-symmetrical system of three spiral graphs, which divide the square-root-spiral into three equal areas. A mathematical analysis shows that these spiral graphs are defined by quadratic polynomials. The Square Root Spiral is a geometrical structure which is based on the three basic constants: 1, sqrt2 and π (pi) , and the continuous application of the Pythagorean Theorem of the right angled triangle. Fibonacci number sequences also play a part in the structure of the Square Root Spiral. Fibonacci Numbers divide the Square Root Spiral into areas and angle sectors with constant proportions. These proportions are linked to the “golden mean” ( golden section ), which behaves as a self-avoiding-walk- constant in the lattice-like structure of the square root spiral. Contents of the general section Page 1 Introduction to the Square Root Spiral 2 2 Mathematical description of the Square Root Spiral 4 3 The distribution
    [Show full text]
  • The Spiral of Theodorus and Sums of Zeta-Values at the Half-Integers
    The spiral of Theodorus and sums of zeta-values at the half-integers David Brink July 2012 Abstract. The total angular distance traversed by the spiral of Theodorus is governed by the Schneckenkonstante K introduced by Hlawka. The only published estimate of K is the bound K ≤ 0:75. We express K as a sum of Riemann zeta-values at the half-integers and compute it to 100 deci- mal places. We find similar formulas involving the Hurwitz zeta-function for the analytic Theodorus spiral and the Theodorus constant introduced by Davis. 1 Introduction Theodorus of Cyrene (ca. 460{399 B.C.) taught Plato mathematics and was himself a pupil of Protagoras. Plato's dialogue Theaetetus tells that Theodorus was distinguished in the subjects of the quadrivium and also contains the following intriguing passage on irrational square-roots, quoted here from [12]: [Theodorus] was proving to us a certain thing about square roots, I mean of three square feet and of five square feet, namely that these roots are not commensurable in length with the foot-length, and he went on in this way, taking all the separate cases up to the root of 17 square feet, at which point, for some reason, he stopped. It was discussed already in antiquity why Theodorus stopped at seventeen and what his method of proof was. There are at least four fundamentally different theories|not including the suggestion of Hardy and Wright that Theodorus simply became tired!|cf. [11, 12, 16]. One of these theories is due to the German amateur mathematician J.
    [Show full text]
  • A Short History of Greek Mathematics
    Cambridge Library Co ll e C t i o n Books of enduring scholarly value Classics From the Renaissance to the nineteenth century, Latin and Greek were compulsory subjects in almost all European universities, and most early modern scholars published their research and conducted international correspondence in Latin. Latin had continued in use in Western Europe long after the fall of the Roman empire as the lingua franca of the educated classes and of law, diplomacy, religion and university teaching. The flight of Greek scholars to the West after the fall of Constantinople in 1453 gave impetus to the study of ancient Greek literature and the Greek New Testament. Eventually, just as nineteenth-century reforms of university curricula were beginning to erode this ascendancy, developments in textual criticism and linguistic analysis, and new ways of studying ancient societies, especially archaeology, led to renewed enthusiasm for the Classics. This collection offers works of criticism, interpretation and synthesis by the outstanding scholars of the nineteenth century. A Short History of Greek Mathematics James Gow’s Short History of Greek Mathematics (1884) provided the first full account of the subject available in English, and it today remains a clear and thorough guide to early arithmetic and geometry. Beginning with the origins of the numerical system and proceeding through the theorems of Pythagoras, Euclid, Archimedes and many others, the Short History offers in-depth analysis and useful translations of individual texts as well as a broad historical overview of the development of mathematics. Parts I and II concern Greek arithmetic, including the origin of alphabetic numerals and the nomenclature for operations; Part III constitutes a complete history of Greek geometry, from its earliest precursors in Egypt and Babylon through to the innovations of the Ionic, Sophistic, and Academic schools and their followers.
    [Show full text]
  • Welcome to the Complete Pythagoras
    Welcome to The Complete Pythagoras A full-text, public domain edition for the generalist & specialist Edited by Patrick Rousell for the World Wide Web. I first came across Kenneth Sylvan Guthrie’s edition of the Complete Pythagoras while researching a book on Leonardo. I had been surfing these deep waters for a while and so the value of Guthrie’s publication was immediately apparent. As Guthrie explains in his own introduction, which is at the beginning of the second book (p 168), he was initially prompted to publish these writings in the 1920’s for fear that this information would become lost. As it is, much of this information has since been published in fairly good modern editions. However, these are still hard to access and there is no current complete collection as presented by Guthrie. The advantage here is that we have a fairly comprehensive collection of works on Pythagoras and the Pythagoreans, translated from the origin- al Greek into English, and presented as a unified, albeit electronic edition. The Complete Pythagoras is a compilation of two books. The first is entitled The Life Of Py- thagoras and contains the four biographies of Pythagoras that have survived from antiquity: that of Iamblichus (280-333 A.D.), Porphry (233-306 A.D.), Photius (ca 820- ca 891 A.D.) and Diogenes Laertius (180 A.D.). The second is entitled Pythagorean Library and is a complete collection of the surviving fragments from the Pythagoreans. The first book was published in 1920, the second a year later, and released together as a bound edition.
    [Show full text]
  • Euclidean Geometry
    Euclidean Geometry Rich Cochrane Andrew McGettigan Fine Art Maths Centre Central Saint Martins http://maths.myblog.arts.ac.uk/ Reviewer: Prof Jeremy Gray, Open University October 2015 www.mathcentre.co.uk This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. 2 Contents Introduction 5 What's in this Booklet? 5 To the Student 6 To the Teacher 7 Toolkit 7 On Geogebra 8 Acknowledgements 10 Background Material 11 The Importance of Method 12 First Session: Tools, Methods, Attitudes & Goals 15 What is a Construction? 15 A Note on Lines 16 Copy a Line segment & Draw a Circle 17 Equilateral Triangle 23 Perpendicular Bisector 24 Angle Bisector 25 Angle Made by Lines 26 The Regular Hexagon 27 © Rich Cochrane & Andrew McGettigan Reviewer: Jeremy Gray www.mathcentre.co.uk Central Saint Martins, UAL Open University 3 Second Session: Parallel and Perpendicular 30 Addition & Subtraction of Lengths 30 Addition & Subtraction of Angles 33 Perpendicular Lines 35 Parallel Lines 39 Parallel Lines & Angles 42 Constructing Parallel Lines 44 Squares & Other Parallelograms 44 Division of a Line Segment into Several Parts 50 Thales' Theorem 52 Third Session: Making Sense of Area 53 Congruence, Measurement & Area 53 Zero, One & Two Dimensions 54 Congruent Triangles 54 Triangles & Parallelograms 56 Quadrature 58 Pythagoras' Theorem 58 A Quadrature Construction 64 Summing the Areas of Squares 67 Fourth Session: Tilings 69 The Idea of a Tiling 69 Euclidean & Related Tilings 69 Islamic Tilings 73 Further Tilings
    [Show full text]
  • Galileo, Ignoramus: Mathematics Versus Philosophy in the Scientific Revolution
    Galileo, Ignoramus: Mathematics versus Philosophy in the Scientific Revolution Viktor Blåsjö Abstract I offer a revisionist interpretation of Galileo’s role in the history of science. My overarching thesis is that Galileo lacked technical ability in mathematics, and that this can be seen as directly explaining numerous aspects of his life’s work. I suggest that it is precisely because he was bad at mathematics that Galileo was keen on experiment and empiricism, and eagerly adopted the telescope. His reliance on these hands-on modes of research was not a pioneering contribution to scientific method, but a last resort of a mind ill equipped to make a contribution on mathematical grounds. Likewise, it is precisely because he was bad at mathematics that Galileo expounded at length about basic principles of scientific method. “Those who can’t do, teach.” The vision of science articulated by Galileo was less original than is commonly assumed. It had long been taken for granted by mathematicians, who, however, did not stop to pontificate about such things in philosophical prose because they were too busy doing advanced scientific work. Contents 4 Astronomy 38 4.1 Adoption of Copernicanism . 38 1 Introduction 2 4.2 Pre-telescopic heliocentrism . 40 4.3 Tycho Brahe’s system . 42 2 Mathematics 2 4.4 Against Tycho . 45 2.1 Cycloid . .2 4.5 The telescope . 46 2.2 Mathematicians versus philosophers . .4 4.6 Optics . 48 2.3 Professor . .7 4.7 Mountains on the moon . 49 2.4 Sector . .8 4.8 Double-star parallax . 50 2.5 Book of nature .
    [Show full text]
  • |||GET||| Geometry Theorems and Constructions 1St Edition
    GEOMETRY THEOREMS AND CONSTRUCTIONS 1ST EDITION DOWNLOAD FREE Allan Berele | 9780130871213 | | | | | Geometry: Theorems and Constructions For readers pursuing a career in mathematics. Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed Geometry Theorems and Constructions 1st edition theorem Intercept theorem Pons asinorum Pythagorean theorem Thales's theorem Theorem of the gnomon. Then the 'construction' or 'machinery' follows. For example, propositions I. The Triangulation Lemma. Pythagoras c. More than editions of the Elements are known. Euclidean geometryelementary number theoryincommensurable lines. The Mathematical Intelligencer. A History of Mathematics Second ed. The success of the Elements is due primarily to its logical presentation of most of the mathematical knowledge available to Euclid. Arcs and Angles. Applies and reinforces the ideas in the geometric theory. Scholars believe that the Elements is largely a compilation of propositions based on books by earlier Greek mathematicians. Enscribed Circles. Return for free! Description College Geometry offers readers a deep understanding of the basic results in plane geometry and how they are used. The books cover plane and solid Euclidean geometryelementary number theoryand incommensurable lines. Cyrene Library of Alexandria Platonic Academy. You can find lots of answers to common customer questions in our FAQs View a detailed breakdown of our shipping prices Learn about our return policy Still need help? View a detailed breakdown of our shipping prices. Then, the 'proof' itself follows. Distance between Parallel Lines. By careful analysis of the translations and originals, hypotheses have been made about the contents of the original text copies of which are no longer available.
    [Show full text]
  • Mathematical Methods for Cad: the Method of Proportional Division of the Whole Into Two Unequal Parts
    UDC 621; 511.176; 511.41; 511.13; 004.89 + 612.82; 510.6; 378.016:510:004; 519; 615.84 P. Kosobutskyy, Department of Computer-Aided Design (CAD) M. Karkulovska*, *Department of Physics (DP) A. Morgulis** ** The City University of New York, Mathematics Department, USA MATHEMATICAL METHODS FOR CAD: THE METHOD OF PROPORTIONAL DIVISION OF THE WHOLE INTO TWO UNEQUAL PARTS © Kosobutskyy P., Karkulovska M., Morgulis A., 2018 In this paper an analysis of the laws of quadratic irrationality of the roots of the quadratic equation x2 =р x + q with modulus coefficients is described р = q , which describes the proportional division of the whole into two unequal parts and the characteristic equation of the second order recurrence relation. It is shown that in the phase diagram р,q there exists a set of irrational values of the roots with properties similar to those of the classical 1 1 “golden” numbers j + =( -1 + 5) = + 0.618... and F+ =(1 + 5) = + 1.618... 2 2 Key words: golden ratio (GR), proportional division, the quadratic irrational МАТЕМАТИЧНІ МЕТОДИ САПР: МЕТОД ПРОПОРЦІЙНОГО ПОДІЛУ ЦІЛОГО НА ДВІ НЕРІВНІ ЧАСТИНИ © Кособуцький П., Каркульовська M., Моргуліс A., 2018 Подано аналіз законів квадратичної ірраціональності коренів квадратного рівняння x2 =р x + q з коефіцієнтами р = q , що описують пропорційний розподіл цілого числа на дві нерівні частини та характеристичне рівняння рекурентного співвідношення другого порядку. Показано, що на фазовій діаграмі р, q існує безліч ірраціональних значень коренів з властивостями, подібними до властивостей класичних “золотих” 1 1 чисел j + =( -1 + 5) = + 0.618... і F+ =(1 + 5) = + 1.618.... 2 2 Ключові слова: золота пропорція (ЗП), пропорційний розподіл, квадратична ірраціональність.
    [Show full text]
  • Spiral of Theodorus Making Kit
    Making Math Lesson Spiral of Theodorus Making Kit What is it? The Spiral of Theodorus is a series of right triangles formed together in a spiral. The triangles in the spiral have one side length of 1 unit long and two irrational side lengths in the form of consecutive square root numbers. The first starter piece is a 1 x 1 square cut on the diagonal to make the first triangle. In other words, this is an isosceles right triangle with the legs as 1 unit long. Each triangle after has the diagonal from the previous piece as a base. Use the corner of the original 1 x 1 starter piece to get a perpendicular and measure a height 1, then draw the new diagonal. The Pythagorean Theorem tells us the length of the resulting diagonals. a + b2 = c2 1 x 1 has hypotenuse of length √2 1 x √2 has hypotenuse of length √3 1 x √3 has hypotenuse of length √4 and so on ... What do we learn by making it? We start with the Pythagorean Theorem. From this first definition of √2 as the diagonal of a 1 x 1, we can show that every natural number has a square root and that we can construct them physically even though the value is an irrational number. Like Pi, which is in every circle, √2 is in every square. What’s fun? The spiral is made using an iterative process that makes different triangles at each step. The final spiral can then be used as a drawstart in creative ways.
    [Show full text]
  • Analysis of Mathematical Fiction with Geometric Themes
    ANALYSIS OF MATHEMATICAL FICTION WITH GEOMETRIC THEMES Jennifer Rebecca Shloming Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy under the Executive Committee of the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2012 © 2012 Jennifer Rebecca Shloming All rights reserved ABSTRACT Analysis of Mathematical Fiction with Geometric Themes Jennifer Rebecca Shloming Analysis of mathematical fiction with geometric themes is a study that connects the genre of mathematical fiction with informal learning. This study provides an analysis of 26 sources that include novels and short stories of mathematical fiction with regard to plot, geometric theme, cultural theme, and presentation. The authors’ mathematical backgrounds are presented as they relate to both geometric and cultural themes. These backgrounds range from having little mathematical training to advance graduate work culminating in a Ph.D. in mathematics. This thesis demonstrated that regardless of background, the authors could write a mathematical fiction novel or short story with a dominant geometric theme. The authors’ pedagogical approaches to delivering the geometric themes are also discussed. Applications from this study involve a pedagogical component that can be used in a classroom setting. All the sources analyzed in this study are fictional, but the geometric content is factual. Six categories of geometric topics were analyzed: plane geometry, solid geometry, projective geometry, axiomatics, topology, and the historical foundations of geometry. Geometry textbooks aligned with these categories were discussed with regard to mathematical fiction and formal learning. Cultural patterns were also analyzed for each source of mathematical fiction. There were also an analysis of the integration of cultural and geometric themes in the 26 sources of mathematical fiction; some of the cultural patterns discussed are gender bias, art, music, academia, mysticism, and social issues.
    [Show full text]
  • A History of Greek Mathematics
    CORNELL UNIVERSITY LBRAaY Cornell University Library QA 22.H43 V.1 A history of Greek mathematics, 3 1924 008 704 219 A HISTORY OF GREEK MATHEMATICS VOLUME I A HISTORY OF GKEEK MATHEMATICS BY SIR THOMAS HEATH K.C.B., K.C.V.O.. F.R.S. Se.D. CAMI). ; HON. D.SC. OXFORD HONORARV FEt.r.OW (FORMFRLV FELLOw) OF TRI>fITY COLI.FHF, CAAIBRIDGE ' . An independent world, Created out of pnre intelligence.' Wordsworth. VOLUME I FROM THALES 'JO EUCIJD OXFORD AT THE CLARENDON PRESS 1921 OXFORD UNIVERSITY PRESS London Edinburgh Glasgow Copenhagen New York Toronto Melbourne Cape Town Bombay Calcutta Madras Shanghai HUMPHREY MILFORD Publisher to the University PREFACE The idea may seem quixotic, but it is nevertheless the author's confident hope that this book will give a fresh interest to the story of Greek mathematics in the eyes both of mathematicians and of classical scholars. For the mathematician the important consideration is that the foundations of mathematics and a great portion of its content are Greek. The Greeks laid down the first principles, invented the methods ah initio, and fixed the terminology. Mathematics in short is a Greek science, whatever new developments modern analysis has brought or may bring. The interest of the subject for the classical scholar is no doubt of a different kind. Greek mathematics reveals an important aspect of the Greek genius of which the student of Greek culture is apt to lose sight. Most people, when they think of the Greek genius, naturally call to mind its master- pieces in literature and art with their notes of beauty, truth, freedom and humanism.
    [Show full text]
  • HISTORY of MATH CONCEPTS Essentials, Images and Memes
    HISTORY OF MATH CONCEPTS Essentials, Images and Memes Sergey Finashin Modern Mathematics having roots in ancient Egypt and Babylonia, really flourished in ancient Greece. It is remarkable in Arithmetic (Number theory) and Deductive Geometry. Mathematics written in ancient Greek was translated into Arabic, together with some mathematics of India. Mathematicians of Islamic Middle East significantly developed Algebra. Later some of this mathematics was translated into Latin and became the mathematics of Western Europe. Over a period of several hundred years, it became the mathematics of the world. Some significant mathematics was also developed in other regions, such as China, southern India, and other places, but it had no such a great influence on the international mathematics. The most significant for development in mathematics was giving it firm logical foundations in ancient Greece which was culminated in Euclid’s Elements, a masterpiece establishing standards of rigorous presentation of proofs that influenced mathematics for many centuries till 19th. Content 1. Prehistory: from primitive counting to numeral systems 2. Archaic mathematics in Mesopotamia (Babylonia) and Egypt 3. Birth of Mathematics as a deductive science in Greece: Thales and Pythagoras 4. Important developments of ideas in the classical period, paradoxes of Zeno 5. Academy of Plato and his circle, development of Logic by Aristotle 6. Hellenistic Golden Age period, Euclid of Alexandria 7. Euclid’s Elements and its role in the history of Mathematics 8. Archimedes, Eratosthenes 9. Curves in the Greek Geometry, Apollonius the Great Geometer 10. Trigonometry and astronomy: Hipparchus and Ptolemy 11. Mathematics in the late Hellenistic period 12. Mathematics in China and India 13.
    [Show full text]