Euclid's Elements
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Euclid's Elements - Wikipedia, the Free Encyclopedia
Euclid's Elements - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Euclid's_Elements Euclid's Elements From Wikipedia, the free encyclopedia Euclid's Elements (Ancient Greek: Στοιχεῖα Stoicheia) is a mathematical and geometric treatise Elements consisting of 13 books written by the ancient Greek mathematician Euclid in Alexandria c. 300 BC. It is a collection of definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of the propositions. The thirteen books cover Euclidean geometry and the ancient Greek version of elementary number theory. The work also includes an algebraic system that has become known as geometric algebra, which is powerful enough to solve many algebraic problems,[1] including the problem of finding the square root of a number.[2] With the exception of Autolycus' On the Moving Sphere, the Elements is one of the oldest extant Greek mathematical treatises,[3] and it is the oldest extant axiomatic deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science. The name 'Elements' comes from the plural of 'element'. The frontispiece of Sir Henry Billingsley's first According to Proclus the term was used to describe a English version of Euclid's Elements, 1570 theorem that is all-pervading and helps furnishing proofs of many other theorems. The word 'element' is Author Euclid, and translators in the Greek language the same as 'letter'. This Language Ancient Greek, translations suggests that theorems in the Elements should be seen Subject Euclidean geometry, elementary as standing in the same relation to geometry as letters number theory to language. -
Cotton Mather's Relationship to Science
Georgia State University ScholarWorks @ Georgia State University English Theses Department of English 4-16-2008 Cotton Mather's Relationship to Science James Daniel Hudson Follow this and additional works at: https://scholarworks.gsu.edu/english_theses Part of the English Language and Literature Commons Recommended Citation Hudson, James Daniel, "Cotton Mather's Relationship to Science." Thesis, Georgia State University, 2008. https://scholarworks.gsu.edu/english_theses/33 This Thesis is brought to you for free and open access by the Department of English at ScholarWorks @ Georgia State University. It has been accepted for inclusion in English Theses by an authorized administrator of ScholarWorks @ Georgia State University. For more information, please contact [email protected]. COTTON MATHER’S RELATIONSHIP TO SCIENCE by JAMES DANIEL HUDSON Under the Direction of Dr. Reiner Smolinski ABSTRACT The subject of this project is Cotton Mather’s relationship to science. As a minister, Mather’s desire to harmonize science with religion is an excellent medium for understanding the effects of the early Enlightenment upon traditional views of Scripture. Through “Biblia Americana” and The Christian Philosopher, I evaluate Mather’s effort to relate Newtonian science to the six creative days as recorded in Genesis 1. Chapter One evaluates Mather’s support for the scientific theories of Isaac Newton and his reception to natural philosophers who advocate Newton’s theories. Chapter Two highlights Mather’s treatment of the dominant cosmogonies preceding Isaac Newton. The Conclusion returns the reader to Mather’s principal occupation as a minister and the limits of science as informed by his theological mind. Through an exploration of Cotton Mather’s views on science, a more comprehensive understanding of this significant early American and the ideological assumptions shaping his place in American history is realized. -
University of Pennsylvania Press
University of Pennsylvania Press Newtonian Science, Miracles, and the Laws of Nature Author(s): Peter Harrison Source: Journal of the History of Ideas, Vol. 56, No. 4 (Oct., 1995), pp. 531-553 Published by: University of Pennsylvania Press Stable URL: http://www.jstor.org/stable/2709991 Accessed: 30-10-2015 01:34 UTC Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://www.jstor.org/page/ info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. University of Pennsylvania Press is collaborating with JSTOR to digitize, preserve and extend access to Journal of the History of Ideas. http://www.jstor.org This content downloaded from 130.102.42.98 on Fri, 30 Oct 2015 01:34:15 UTC All use subject to JSTOR Terms and Conditions NewtonianScience, Miracles, andthe Laws ofNature PeterHarrison Introduction "Newton,"writes Richard Westfall, "both believed in and did not believe in miracles."It can onlybe concluded,Westfall continues, that the greatscientist, unwilling to relinquishhis beliefin a providentialand inter- posingDeity, "abandoned himself to ambiguitiesand inconsistencies,which gave theappearance of divine participation in nature,but not the substance."' Newton'sapparent ambivalence -
The Book and Printed Culture of Mathematics in England and Canada, 1830-1930
Paper Index of the Mind: The Book and Printed Culture of Mathematics in England and Canada, 1830-1930 by Sylvia M. Nickerson A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Institute for the History and Philosophy of Science and Technology University of Toronto © Copyright by Sylvia M. Nickerson 2014 Paper Index of the Mind: The Book and Printed Culture of Mathematics in England and Canada, 1830-1930 Sylvia M. Nickerson Doctor of Philosophy Institute for the History and Philosophy of Science and Technology University of Toronto 2014 Abstract This thesis demonstrates how the book industry shaped knowledge formation by mediating the selection, expression, marketing, distribution and commercialization of mathematical knowledge. It examines how the medium of print and the practices of book production affected the development of mathematical culture in England and Canada during the nineteenth and early twentieth century. Chapter one introduces the field of book history, and discusses how questions and methods arising from this inquiry might be applied to the history of mathematics. Chapter two looks at how nineteenth century printing technologies were used to reproduce mathematics. Mathematical expressions were more difficult and expensive to produce using moveable type than other forms of content; engraved diagrams required close collaboration between author, publisher and engraver. Chapter three examines how editorial decision-making differed at book publishers compared to mathematical journals and general science journals. Each medium followed different editorial processes and applied distinct criteria in decision-making about what to publish. ii Daniel MacAlister, Macmillan and Company’s reader of science, reviewed mathematical manuscripts submitted to the company and influenced which ones would be published as books. -
Mathematical Language and Mathematical Progress by Eberhard Knobloch
Mathematical language and mathematical progress By Eberhard Knobloch In 1972 the space probe Pioneer 10 was launched, carrying a plaque which contains the first message of mankind to leave our solar system1: The space probe is represented by a circular segment and a rectangle designed on the same scale as that of the man and the woman. This is not true of the solar system: sun and planets are represented by small circles and points. We do not know whether there are other intelligent beings living on stars in the universe, or whether they will even understand the message. But the non-verbal, the symbolical language of geometry seemed to be more appropriate than any other language. The grammar of any ordinary language is so complicated that still every computer breaks down with regards to it. 1 Karl Märker, "Sind wir allein im Weltall? Kosmos und Leben", in: Astronomie im Deutschen Museum, Planeten - Sterne - Welteninseln, hrsg. von Gerhard Hartl, Karl Märker, Jürgen Teichmann, Gudrun Wolfschmidt (München: Deutsches Museum, 1993), p. 217. [We reproduce the image of the plaque from: http://en.wikipedia.org/wiki/Pioneer_plaque ; Karine Chemla] 1 The famous Nicholas Bourbaki wrote in 19482: "It is the external form which the mathematician gives to his thought, the vehicle which makes it accessible to others, in short, the language suited to mathematics; this is all, no further significance should be attached to it". Bourbaki added: "To lay down the rules of this language, to set up its vocabulary and to clarify its syntax, all that is indeed extremely useful." But it was only the least interesting aspect of the axiomatic method for him. -
Horner Versus Holdred
Historia Mathematica 26 (1999), 29–51 Article ID hmat.1998.2214, available online at http://www.idealibrary.com on Horner versus Holdred: An Episode in the History View metadata, citation and similar papers at core.ac.uk of Root Computation brought to you by CORE provided by Elsevier - Publisher Connector A. Thomas Fuller Hillcrest, The Common, Woodgreen, Fordingbridge, Hants SP6 2BQ, England It is well known that Horner’s method for the computation of a real root of a polynomial equa- tion was anticipated in Italy by Ruffini. In the present paper it is shown that in England the method was published by Holdred, before Horner. The resulting controversy over priority is discussed, and related letters from contemporary mathematicians are reproduced. It is concluded that the dissemi- nation of the algorithm under the inappropriate designation “Horner’s method” is mainly due to De Morgan. C 1999 Academic Press Il est bien connu que la m´ethodede Horner pour calculer une racine re´elled’une ´equationpolynˆome avait ´et´eanticip´eeen Italie par Ruffini. Dans ce papier il est d´emontr´equ’en Angleterre la m´ethodefut publi´eepar Holdred avant Horner. La controverse sur la priorit´eest discut´ee,et des lettres de math´e- maticiens contemporains sont reproduites. Il est conclu que la diss´eminationde l’algorithme sous la d´esignation inappropri´ee“m´ethodede Horner” est principalement duea ` De Morgan. C 1999 Academic Press MSC 1991 subject classifications: 01A55; 01A70; 01A80; 65-03. Key Words: root computation; synthetic division; Horner; Holdred; De Morgan. 1. INTRODUCTION The algorithm for the computation of a real root of a polynomial equation with given numerical coefficients known as “Horner’s method” is described in many textbooks, for example Herbert Turnbull [73, 25–26, 30–33, 83–88] and James Uspensky [74, 151–169]. -
Watson-The Rise of Pilo-Semitism
The Rise of Philo-Semitism and Premillenialism during the Seventeenth and Eighteenth Centuries By William C. Watson, Colorado Christian University Let me therefore beg of thee not to trust to the opinion of any man… But search the scriptures thyself… understanding the sacred prophecies and the danger of neglecting them is very great and the obligation to study them is as great may appear by considering the case of the Jews at the coming of Christ. For the rules whereby they were to know their Messiah were the prophecies of the old Testament… It was the ignorance of the Jews in these Prophecies which caused them to reject their Messiah… If it was their duty to search diligently into those Prophecies: why should we not think that the Prophecies which concern the latter times into which we have fallen were in like manner intended for our use that in the midst of Apostasies we might be able to discern the truth and be established in the faith…it is also our duty to search with all diligence into these Prophecies. If God was so angry with the Jews for not searching more diligently into the Prophecies which he had given them to know Christ by: why should we think he will excuse us for not searching into the Prophecies which he had given us to know Antichrist by? … They will call you a Bigot, a Fanatic, a Heretic, and tell thee of the uncertainty of these interpretations [but] greater judgments hang over the Christians for their remises than ever the Jews felt. -
Where, Oh Waring? the Classic Problem and Its Extensions
Where, Oh Waring? The Classic Problem and its Extensions Brian D. Beasley Presbyterian College, Clinton, SC Brian Beasley (B.S., Emory University; M.S., University of North Carolina; Ph.D., University of South Carolina) has taught at Pres- byterian College since 1988. He became a member of the Mathe- matical Association of America in 1989 and joined ACMS in 2007. Outside the classroom, Brian enjoys family time with his wife and two sons. He is an enthusiastic Scrabble player, a not-so-avid jog- ger, and a very shaky unicyclist. In the 2009-2010 academic year, one of our mathematics majors, Olivia Hightower, became interested in the history of Edward Waring and his famous conjecture about expressing positive integers as the sum of kth powers. Olivia's investigation eventually led to her honors project on Waring's Problem, in which she focused on the history of the conjecture, the eventual proof that all positive integers may be written as the sum of at most nine cubes, and the work of Hardy and Wright in establishing lower bounds in the case of sufficiently large integers. Her research renewed her professor's own interest in Waring, leading to the following article. This paper will sketch brief outlines of Waring's life and the history behind the eventual solution to his problem. In addition, it will present some of the related questions currently being studied, such as expressing sufficiently large integers as sums of powers, sums of powers of primes, and sums of unlike powers. We begin with a short summary of the biography of Edward Waring. -
The Project Gutenberg Ebook #31061: a History of Mathematics
The Project Gutenberg EBook of A History of Mathematics, by Florian Cajori This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: A History of Mathematics Author: Florian Cajori Release Date: January 24, 2010 [EBook #31061] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK A HISTORY OF MATHEMATICS *** Produced by Andrew D. Hwang, Peter Vachuska, Carl Hudkins and the Online Distributed Proofreading Team at http://www.pgdp.net transcriber's note Figures may have been moved with respect to the surrounding text. Minor typographical corrections and presentational changes have been made without comment. This PDF file is formatted for screen viewing, but may be easily formatted for printing. Please consult the preamble of the LATEX source file for instructions. A HISTORY OF MATHEMATICS A HISTORY OF MATHEMATICS BY FLORIAN CAJORI, Ph.D. Formerly Professor of Applied Mathematics in the Tulane University of Louisiana; now Professor of Physics in Colorado College \I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history."|J. W. L. Glaisher New York THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., Ltd. 1909 All rights reserved Copyright, 1893, By MACMILLAN AND CO. Set up and electrotyped January, 1894. Reprinted March, 1895; October, 1897; November, 1901; January, 1906; July, 1909. Norwood Pre&: J. S. Cushing & Co.|Berwick & Smith. -
Arianism in English Nonconformity, 1700-1750
Perichoresis Volume 17. Single Author Supplement 1 (2019): 21–36 DOI: 10.2478/perc-2019-0002 ARIANISM IN ENGLISH NONCONFORMITY, 1700-1750 DINU MOGA * Emanuel University of Oradea ABSTRACT. During the time of English Nonconformity, Arianism was not only embraced, but openly acknowledged by most of the Presbyterian ministers. That generation of ministers, who contended so zealously for the orthodox faith, had finished their labours, and received from their Lord a dismissal into eternal rest. Those champions among the laity who, at the begin- ning of the controversy, stood up so firmly for the truth, had entered as well into the joy of their Lord. Though their children continued Dissenters, too many of them did not possess the same sentiments or spirit. Among those who succeeded these ministers were too many who embraced the Arian creed. To this unhappy change contributed the example and conversation as well of many from the younger Presbyterian ministers. In consequence Arianism spread far and wide in the Presbyterian congregations, both among the ministers and the people. This unhappy controversy proved the grave of the Presbyterian congregations, and of those of the General Baptists. The effects of Arianism, though at first scarcely visible, gradually produced desolation and death. KEYWORDS: Arianism, controversy, nonconformity, creeds, consubstantiality Introduction The apostolic teaching about Christ was relatively simple. But what the apostle taught about Christ also contained ideas that some people found difficult to understand. While the history progresses after the time of the apostles, we learn that prior to the beginning of the fourth century all creeds and summaries of faith were local in character. -
Arianism 1 Arianism
Arianism 1 Arianism "Arian" redirects here. For other uses, see Arian (disambiguation). Not to be confused with "Aryanism", which is a racial theory. Part of a series of articles on Arianism History and theology • Arius • Acacians • Anomoeanism • Arian controversy • First Council of Nicaea • Lucian of Antioch • Gothic Christianity Arian leaders • Acacius of Caesarea • Aëtius • Demophilus of Constantinople • Eudoxius of Antioch • Eunomius of Cyzicus • Eusebius of Caesarea • Eusebius of Nicomedia • Eustathius of Sebaste • George of Laodicea • Ulfilas Other Arians • Asterius the Sophist • Auxentius of Milan • Auxentius of Durostorum • Constantius II • Wereka and Batwin • Fritigern • Alaric I • Artemius • Odoacer • Theodoric the Great Modern semi-Arians • Samuel Clarke • Isaac Newton • William Whiston Opponents • Peter of Alexandria • Achillas of Alexandria Arianism 2 • Alexander of Alexandria • Hosius of Cordoba • Athanasius of Alexandria • Paul I of Constantinople Christianity portal • v • t [1] • e Arianism is the theological teaching attributed to Arius (c. AD 250–336), a Christian presbyter in Alexandria, Egypt, concerning the relationship of God the Father to the Son of God, Jesus Christ. Arius asserted that the Son of God was a subordinate entity to God the Father. Deemed a heretic by the Ecumenical First Council of Nicaea of 325, Arius was later exonerated in 335 at the regional First Synod of Tyre,[2] and then, after his death, pronounced a heretic again at the Ecumenical First Council of Constantinople of 381. The Roman Emperors Constantius II (337–361) and Valens (364–378) were Arians or Semi-Arians. The Arian concept of Christ is that the Son of God did not always exist, but was created by—and is therefore distinct from—God the Father. -
Unpublished Letters of James Joseph Sylvester and Other New Information Concerning His Life and Work Author(S): Raymond Clare Archibald Source: Osiris, Vol
Unpublished Letters of James Joseph Sylvester and Other New Information concerning His Life and Work Author(s): Raymond Clare Archibald Source: Osiris, Vol. 1 (Jan., 1936), pp. 85-154 Published by: The University of Chicago Press on behalf of The History of Science Society Stable URL: http://www.jstor.org/stable/301603 . Accessed: 06/03/2014 07:56 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. The University of Chicago Press and The History of Science Society are collaborating with JSTOR to digitize, preserve and extend access to Osiris. http://www.jstor.org This content downloaded from 159.237.12.82 on Thu, 6 Mar 2014 07:56:26 AM All use subject to JSTOR Terms and Conditions UnpublishedLetters of JamesJoseph Sylvesterand othernew Information concerninghis Life and Work CONTENTS 1. - Introductory. II. -Curriculum Vitae. III. Publications dealing with SYLVEsTER'sLife and Work. IV. SyLv1EsTER'sFirst Mathematical Publication. V. -SYLvESTER and the Universityof Virginia. VI. SYLVESTER, i842-I855. VII. SYLVEsTER'S Poetry. VIII. Letters of SyLvEsTER. I. - INTRODUCTORY In yesteryearsthere were two gloriously inspiring centers of mathematical study in America. One of these was at -the University of Chicago, when BOLZA, and MASCHKE and E.