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SIMON STEVIN (1548 – 1620) by HEINZ KLAUS STRICK, Germany
SIMON STEVIN (1548 – 1620) by HEINZ KLAUS STRICK, Germany The Flemish mathematician, physicist and engineer SIMON STEVIN is one of the lesser-known personalities in the history of science. However, his work has left many traces. We do not even know his exact date of birth and death; his birthplace was Bruges; where he died is uncertain: either Leiden or the Hague. Raised in the Calvinist tradition, he grew up in Flanders, became an accountant and cashier for a trading firm in Antwerp, travelled for several years through Poland, Prussia and Norway until he took a job at the tax office in Bruges in 1577. Around this time, the 17 provinces of the Netherlands, which also include the area of present-day Belgium, Luxembourg and parts of northern France, belong to the Spanish dominion. Large parts of the population, especially in the northern provinces, converted to the Calvinist faith. In 1567 King PHILIP II OF SPAIN appointed the DUKE OF ALBA as governor. When ALBA carried out a punitive expedition against the Protestants, a war began which only ended in 1648 with the Peace Treaty of Münster (partial treaty of the Peace of Westphalia). In 1579 the Protestant provinces in the north of the Netherlands united to form the Union of Utrecht and declared their independence as the Republic of the United Netherlands; they elected WILLIAM THE SILENT or WILLIAM OF ORANGE as regent. As the political situation came to a head, SIMON STEVIN's life situation also changed: although he was already 33 years old, he still attended a Latin school and then took up studies at the newly founded University of Leiden. -
Great Physicists
Great Physicists Great Physicists The Life and Times of Leading Physicists from Galileo to Hawking William H. Cropper 1 2001 1 Oxford New York Athens Auckland Bangkok Bogota´ Buenos Aires Cape Town Chennai Dar es Salaam Delhi Florence HongKong Istanbul Karachi Kolkata Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi Paris Sao Paulo Shanghai Singapore Taipei Tokyo Toronto Warsaw and associated companies in Berlin Ibadan Copyright ᭧ 2001 by Oxford University Press, Inc. Published by Oxford University Press, Inc. 198 Madison Avenue, New York, New York 10016 Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Cropper, William H. Great Physicists: the life and times of leadingphysicists from Galileo to Hawking/ William H. Cropper. p. cm Includes bibliographical references and index. ISBN 0–19–513748–5 1. Physicists—Biography. I. Title. QC15 .C76 2001 530'.092'2—dc21 [B] 2001021611 987654321 Printed in the United States of America on acid-free paper Contents Preface ix Acknowledgments xi I. Mechanics Historical Synopsis 3 1. How the Heavens Go 5 Galileo Galilei 2. A Man Obsessed 18 Isaac Newton II. Thermodynamics Historical Synopsis 41 3. A Tale of Two Revolutions 43 Sadi Carnot 4. On the Dark Side 51 Robert Mayer 5. A Holy Undertaking59 James Joule 6. Unities and a Unifier 71 Hermann Helmholtz 7. The Scientist as Virtuoso 78 William Thomson 8. -
Curren T Anthropology
Forthcoming Current Anthropology Wenner-Gren Symposium Curren Supplementary Issues (in order of appearance) t Humanness and Potentiality: Revisiting the Anthropological Object in the Anthropolog Current Context of New Medical Technologies. Klaus Hoeyer and Karen-Sue Taussig, eds. Alternative Pathways to Complexity: Evolutionary Trajectories in the Anthropology Middle Paleolithic and Middle Stone Age. Steven L. Kuhn and Erella Hovers, eds. y THE WENNER-GREN SYMPOSIUM SERIES Previously Published Supplementary Issues December 2012 HUMAN BIOLOGY AND THE ORIGINS OF HOMO Working Memory: Beyond Language and Symbolism. omas Wynn and Frederick L. Coolidge, eds. GUEST EDITORS: SUSAN ANTÓN AND LESLIE C. AIELLO Engaged Anthropology: Diversity and Dilemmas. Setha M. Low and Sally Early Homo: Who, When, and Where Engle Merry, eds. Environmental and Behavioral Evidence V Dental Evidence for the Reconstruction of Diet in African Early Homo olum Corporate Lives: New Perspectives on the Social Life of the Corporate Form. Body Size, Body Shape, and the Circumscription of the Genus Homo Damani Partridge, Marina Welker, and Rebecca Hardin, eds. Ecological Energetics in Early Homo e 5 Effects of Mortality, Subsistence, and Ecology on Human Adult Height 3 e Origins of Agriculture: New Data, New Ideas. T. Douglas Price and Plasticity in Human Life History Strategy Ofer Bar-Yosef, eds. Conditions for Evolution of Small Adult Body Size in Southern Africa Supplement Growth, Development, and Life History throughout the Evolution of Homo e Biological Anthropology of Living Human Populations: World Body Size, Size Variation, and Sexual Size Dimorphism in Early Homo Histories, National Styles, and International Networks. Susan Lindee and Ricardo Ventura Santos, eds. -
A Brief History of Microwave Engineering
A BRIEF HISTORY OF MICROWAVE ENGINEERING S.N. SINHA PROFESSOR DEPT. OF ELECTRONICS & COMPUTER ENGINEERING IIT ROORKEE Multiple Name Symbol Multiple Name Symbol 100 hertz Hz 101 decahertz daHz 10–1 decihertz dHz 102 hectohertz hHz 10–2 centihertz cHz 103 kilohertz kHz 10–3 millihertz mHz 106 megahertz MHz 10–6 microhertz µHz 109 gigahertz GHz 10–9 nanohertz nHz 1012 terahertz THz 10–12 picohertz pHz 1015 petahertz PHz 10–15 femtohertz fHz 1018 exahertz EHz 10–18 attohertz aHz 1021 zettahertz ZHz 10–21 zeptohertz zHz 1024 yottahertz YHz 10–24 yoctohertz yHz • John Napier, born in 1550 • Developed the theory of John Napier logarithms, in order to eliminate the frustration of hand calculations of division, multiplication, squares, etc. • We use logarithms every day in microwaves when we refer to the decibel • The Neper, a unitless quantity for dealing with ratios, is named after John Napier Laurent Cassegrain • Not much is known about Laurent Cassegrain, a Catholic Priest in Chartre, France, who in 1672 reportedly submitted a manuscript on a new type of reflecting telescope that bears his name. • The Cassegrain antenna is an an adaptation of the telescope • Hans Christian Oersted, one of the leading scientists of the Hans Christian Oersted nineteenth century, played a crucial role in understanding electromagnetism • He showed that electricity and magnetism were related phenomena, a finding that laid the foundation for the theory of electromagnetism and for the research that later created such technologies as radio, television and fiber optics • The unit of magnetic field strength was named the Oersted in his honor. -
J. Wallis the Arithmetic of Infinitesimals Series: Sources and Studies in the History of Mathematics and Physical Sciences
J. Wallis The Arithmetic of Infinitesimals Series: Sources and Studies in the History of Mathematics and Physical Sciences John Wallis was appointed Savilian Professor of Geometry at Oxford University in 1649. He was then a relative newcomer to mathematics, and largely self-taught, but in his first few years at Oxford he produced his two most significant works: De sectionibus conicis and Arithmetica infinitorum. In both books, Wallis drew on ideas originally developed in France, Italy, and the Netherlands: analytic geometry and the method of indivisibles. He handled them in his own way, and the resulting method of quadrature, based on the summation of indivisible or infinitesimal quantities, was a crucial step towards the development of a fully fledged integral calculus some ten years later. To the modern reader, the Arithmetica Infinitorum reveals much that is of historical and mathematical interest, not least the mid seventeenth-century tension between classical geometry on the one hand, and arithmetic and algebra on the other. Newton was to take up Wallis’s work and transform it into mathematics that has become part of the mainstream, but in Wallis’s text we see what we think of as modern mathematics still 2004, XXXIV, 192 p. struggling to emerge. It is this sense of watching new and significant ideas force their way slowly and sometimes painfully into existence that makes the Arithmetica Infinitorum such a relevant text even now for students and historians of mathematics alike. Printed book Dr J.A. Stedall is a Junior Research Fellow at Queen's University. She has written a number Hardcover of papers exploring the history of algebra, particularly the algebra of the sixteenth and 159,99 € | £139.99 | $199.99 ▶ seventeenth centuries. -
Who Invented the Calculus? - and Other 17Th Century Topics Transcript
Who invented the calculus? - and other 17th century topics Transcript Date: Wednesday, 16 November 2005 - 12:00AM Location: Barnard's Inn Hall WHO INVENTED THE CALCULUS? Professor Robin Wilson Introduction We’ve now covered two-thirds of our journey ‘From Caliphs to Cambridge’, and in this lecture I want to try to survey the mathematical achievements of the seventeenth century – a monumental task. I’ve divided my talk into four parts – first, the movement towards the practical sciences, as exemplified by the founding of Gresham College and the Royal Society. Next, we’ll gravitate towards astronomy, from Copernicus to Newton. Thirdly, we visit France and the gradual movement from geometry to algebra (with a brief excursion into some new approaches to pi) – and finally, the development of the calculus. So first, let’s make an excursion to Gresham College. Practical science The Gresham professorships arose from the will of Sir Thomas Gresham, which provided for £50 per year for each of seven professors to read lectures in Divinity, Astronomy, Music, Geometry, Law, Physic and Rhetoric. As the Ballad of Gresham College later described it: If to be rich and to be learn’d Be every Nation’s cheifest glory, How much are English men concern’d, Gresham to celebrate thy story Who built th’Exchange t’enrich the Citty And a Colledge founded for the witty. From its beginning, Gresham College encouraged the practical sciences, rather than the Aristotelian studies still pursued at the ancient universities: Thy Colledg, Gresham, shall hereafter Be the whole world’s Universitie, Oxford and Cambridge are our laughter; Their learning is but Pedantry. -
John Napier's Life Napier's Logarithms KYLIE BRYANT & PAUL SCOTT
KYLIE BRYANT & PAUL SCOTT John Napier’s life Napier’s logarithms John Napier was born in 1550 in the Tower of Napier’s idea in inventing the logarithm was to Merchiston, near Edinburgh, Scotland. His save mathematicians from having to do large father, Archibald Napier, was knighted in 1565 calculations. These days, calculations and was appointed Master of the Mint in 1582. involving large numbers are done using calcu- His mother, Janet Bothwell, was the sister of lators or computers; however before these were the Bishop of Orkney. Napier’s was an impor- invented, large calculations meant that much tant family in Scotland, and had owned the time was taken and mistakes were made. Merchiston estate since 1430. Napier’s logarithm was not defined in terms Napier was educated at St Salvator’s of exponents as our logarithm is today. College, graduating in 1563. He was just 13 Instead Napier thought of his logarithm in years old when his mother died and he was terms of moving particles, distances and veloc- sent to St Andrew’s University where he ities. He considered two lines, AZ of fixed studied for two years. This is where he gained length and A'Z' of infinite length and points X his interest in theology. He did not graduate, and X' starting at A and A' moving to the right however, instead leaving to travel around with the same initial velocity. X' has constant Europe for the next five years. During this velocity and X has a velocity proportional to time he gained knowledge of mathematics and the distance from X to Z. -
The Knowledge Bank at the Ohio State University Ohio State Engineer
The Knowledge Bank at The Ohio State University Ohio State Engineer Title: A History of the Slide Rule Creators: Derrenberger, Robert Graf Issue Date: Apr-1939 Publisher: Ohio State University, College of Engineering Citation: Ohio State Engineer, vol. 22, no. 5 (April, 1939), 8-9. URI: http://hdl.handle.net/1811/35603 Appears in Collections: Ohio State Engineer: Volume 22, no. 5 (April, 1939) A HISTORY OF THE SLIDE RULE By ROBERT GRAF DERRENBERGER HE slide rule, contrary to popular belief, is not in 1815 made a rule with scales specially adapted for a modern invention but in its earliest form is the calculations involved in chemistry. T several hundred years old. As a matter of fact A very important improvement was made by Sir the slide rule is not an invention, but an outgrowth of Isaac Newton when he devised a method of solving certain ideas in mathematics. cubic equations by laying three movable slide rule scales Leading up to the invention of the slide rule was the side by side 'and bringing them together or in line by- invention of logarithms, in 1614, by John Napier. laying a separate straight edge across them. This is Probably the first device having any relation to the now known as a runner. It was first definitely attached slide rule was a logarithmic scale made by Edmund to the slide rule by John Robertson in 1775. Gunter, Professor of Astronomy at Gresham College, About 1780 William Nicholson, publisher and editor in London, in 1620. This scale was used for multi- of "Nicholson's Journal", a kind of technical journal, plication and division by measuring the sum or differ- began to devote most of his time to the study and im- ence of certain scale lengths. -
Simon Stevin
II THE PRINCIPAL WORKS OF SIMON STEVIN E D IT E D BY ERNST CRONE, E. J. DIJKSTERHUIS, R. J. FORBES M. G. J. MINNAERT, A. PANNEKOEK A M ST E R D A M C. V. SW ETS & Z E IT L IN G E R J m THE PRINCIPAL WORKS OF SIMON STEVIN VOLUME II MATHEMATICS E D IT E D BY D. J. STRUIK PROFESSOR AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE (MASS.) A M S T E R D A M C. V. SW ETS & Z E IT L IN G E R 1958 The edition of this volume II of the principal works of SIMON STEVIN devoted to his mathematical publications, has been rendered possible through the financial aid of the Koninklijke. Nederlandse Akademie van Wetenschappen (Royal Netherlands Academy of Science) Printed by Jan de Lange, Deventer, Holland The following edition of the Principal Works of SIMON STEVIN has been brought about at the initiative of the Physics Section of the Koninklijke Nederlandse Akademie van Weten schappen (Royal Netherlands Academy of Sciences) by a committee consisting of the following members: ERNST CRONE, Chairman of the Netherlands Maritime Museum, Amsterdam E. J. DIJKSTERHUIS, Professor of the History of Science at the Universities of Leiden and Utrecht R. J. FORBES, Professor of the History of Science at the Municipal University of Amsterdam M. G. J. M INNAERT, Professor of Astronomy at the University of Utrecht A. PANNEKOEK, Former Professor of Astronomy at the Municipal University of Amsterdam The Dutch texts of STEVIN as well as the introductions and notes have been translated into English or revised by Miss C. -
A Probabilistic Proof of Wallis's Formula for Π
A PROBABILISTIC PROOF OF WALLIS’S FORMULA FOR ¼ STEVEN J. MILLER There are many beautiful formulas for ¼ (see for example [4]). The purpose of this note is to introduce an alternate derivation of Wallis’s product formula, equation (1), which could be covered in a first course on probability, statistics, or number theory. We quickly review other famous formulas for ¼, recall some needed facts from probability, and then derive Wallis’s formula. We conclude by combining some of the other famous formulas with Wallis’s formula to derive an interesting expression for log(¼=2) (equation (5)). Often in a first-year calculus course students encounter the Gregory-Leibniz for- mula, ¼ 1 1 1 X1 (¡1)n = 1 ¡ + ¡ + ¢ ¢ ¢ = : 4 3 5 7 2n + 1 n=0 The proof uses the fact that the derivative of arctan x is 1=(1 + x2), so ¼=4 = R 1 2 0 dx=(1 + x ). To complete the proof, expand the integrand with the geometric series formula and then justify interchanging the order of integration and summa- tion. Another interesting formula involves Bernoulli numbers and the Riemann zeta function. The Bernoulli numbers Bk are the coefficients in the Taylor series t t X1 B tk = 1 ¡ + k ; et ¡ 1 2 k! k=2 P1 ¡s each Bk is rational. The Riemann zeta function is ³(s) = n=1 n , which converges for real part of s greater than 1. Using complex analysis one finds (see for instance [10, p. 365] or [18, pp. 179–180]) that (¡4)kB ³(2k) = ¡ 2k ¢ ¼2k; 2 ¢ 2k! 1 2 P ¡2 yielding formulas for ¼ to any even power. -
Geometry and Mathematical Symbolism of the 16Th Century Viewed Through a Construction Problem
THE TEACHING OF MATHEMATICS 2016, Vol. XIX, 1, pp. 32–40 GEOMETRY AND MATHEMATICAL SYMBOLISM OF THE 16TH CENTURY VIEWED THROUGH A CONSTRUCTION PROBLEM Milana Dabi´c Abstract. This paper represents a construction problem from Problematum geometricorum IV written by Simon Stevin from Bruges in 1583. The problem is used for illustrating the geometry practice and mathematical language in the 16th century. The large impact of Euclid and Archimedes can be noted. In one part of the construction, Stevin expressed the need for using numbers for greater clarity. Hence, the link with the work of Descartes and the further geometry development is pointed out. MathEduc Subject Classification: A35 MSC Subject Classification: 97A30 Key words and phrases: 16th century mathematics; mathematical symbolism; Simon Stevin; construction problems 1. Introduction From the times of Ancient Greece until the 16th century there was no signif- icant geometrical contribution that would expand the existing geometrical knowl- edge. Only in the second half of the 16th century we can find geometry works of Simon Stevin from Bruges (1548–1620). It is believed that his influence was neglected in the history of mathematics and that his name should be mentioned together with the name of his contemporary Galileo Galilei, from whom Stevin was a whole generation older (16 years) [8]. It is considered that Stevin, as a predecessor of Descartes, prepared a path for introducing correspondence between numbers and points on the line by studying the 10th book of Euclid’s Elements and translating it to numbers [9]. Besides his work on the Problematum geometricorum libri V, he wrote Tomus secundus de geometriae praxi (in 1605) which is: ::: different from the Problemata geometrica and inferior to it; it is also a collection of geometrical problems but it is not arranged as logically as the former; it was chiefly made to complete the Prince’s geometrical training [6, p. -
The Book As Instrument: Craft and Technique in Early Modern Practical Mathematics
BJHS Themes (2020), 5, 111–129 doi:10.1017/bjt.2020.8 RESEARCH ARTICLE The book as instrument: craft and technique in early modern practical mathematics Boris Jardine* Department of History and Philosophy of Science, University of Cambridge, Free School Lane, CB2 3RH, UK *Email: [email protected] Abstract Early modern books about mathematical instruments are typically well illustrated and contain detailed instructions on how to make and use the tools they describe. Readers approached these texts with a desire to extract information – and sometimes even to extract illustrations which could be repurposed as working instruments. To focus on practical approaches to these texts is to bring the category of ‘making’ to the fore. But here care needs to be taken about who could make what, about the rhetoric of craft, and about the technique of working with diagrams and images. I argue that we should read claims about making instruments cautiously, but that, con- versely, we should be inquisitive and open-minded when it comes to the potential uses of printed diagrams in acquiring skill and knowledge: these could be worked on directly, or cut out or copied and turned into working instruments. Books were sites of mathematical practice, and in certain disciplines this was central to learning through doing. One of the more surprising things a sixteenth-century owner of an expensive folio volume might do was to take a sharp knife and cut it to pieces. John Blagrave’s 1585 The Mathematical Jewel, in fact, demands nothing less. This book, which introduced an elaborate instrument of Blagrave’s design for performing astronomical calculations, included wood- cuts that were specifically intended to be cut out and used as surrogates for the brass original: ‘get very fine pastboord … and then spred your paste very fine thereon, & quickly laying on this picture & clappe it streight into a presse’.1 ‘This picture’ refers to the full- page diagram printed near the front of the book, which can, as Blagrave says, be compiled with other diagrams to make a functioning instrument.