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Grove Press. 1967. In-12. Broché. Bon état, Couv. légèrement passée, Dos plié, Intérieur acceptable. 256 pages. Dos des plats jaunis.. . . . Classification Dewey : 420-Langue anglaise. Anglo-saxon
Reference : RO60111353
Grove Press, B 171. By the author of 'City of Night'. Classification Dewey : 420-Langue anglaise. Anglo-saxon
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5 book(s) with the same title
The Making of Index Numbers - A Study of Their Varieties, Tests, and Reliability
Augustus M. Kelley , Reprints of Economic Classics Malicorne sur Sarthe, 72, Pays de la Loire, France 1967 Book condition, Etat : Bon hardcover, editor's blue printed binding, no dust-jacket grand In-8 1 vol. - 571 pages
61 black and white tables reprint,1967 "Contents, Chapitres : Prefatory note, Prefaces, Suggestions to readers, Table of contents, Contents of appendices, List of tables, List of charts, xxxiii, Text, Appendices, Index, 538 pages - Six types of index numbers compared - Four methods of weighting - Two great reversal tests - Erratic, biased, and freakish index numbers - The two reversal tests as finders of formulae - Rectifying formulae by "" crossing "" them - Rectifying formulae by crossing their weights - The enlarged series of formulae - What simple index number is best ? - What is the best index number ? - Comparing all the index numbers with the "" ideal "", formula 353 - The so-called circular test - Blending the apparently inconsistent results - Speed of calculation - Other practical considerations - Summary and outlook - Appendices : Notes to text - The influence of weighting - An index number an average of ratios rather than a ratio of averages - Landmarks in the history of index numbers - List of formulae for index numbers - Numerical data and examples - Index numbers by 134 formulae for prices by the fixed base system and, in note-worthy cases, the chain system - Selcted bibliography - Review of literature since the first edition" near fine copy, the editor's binding is fine, inside is fine, clean and unmarked, without dust-jacket
De la Controverse entre Mrs. Leibnitz & Bernouilli sur les Logarithmes des Nombres Negatifs e Imaginaires. (Controversy between Mr Leibniz and Mr Bernouilli on the logarithms of negative and imaginary numbers).
(Berlin, Haude et Spener, 1751). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome V, pp. 139-179.
First edition of this importent paper on the logarithms of complex numbers, where Euler clarified such functions. He disagreed with Leibniz that a special function was only applicable for positive numbers, and showed that i was applicable for both negative and positive numbers, only with a difference of a constant. When Euler here (the offered item) came out with the correct form for the logarithm, it was not generally accepted. - Enestrom, Euler Bibliography E 168.
Numbers, Measures, and the Transfer of Goods in Prehistory
, Brepols, 2024 Paperback, 122 pages, Size:216 x 280 mm, Illustrations:10 b/w, 25 col., 12 tables b/w., 1 maps b/w, 5 maps color, Language: English. ISBN 9782503610689.
Summary Numbers, weights, and measurements, and the systems underpinning them, have always been a fundamental part of human society. Developed in different ways and at different times, such systems have provided a foundation for science, technology, economics, and new ways of engaging with and understanding the world. This volume aims to explore the background to numbers and measurements in more detail by drawing together specialists from a growing field of research. The contributions gathered here offer new and interdisciplinary insights into how the development of mathematical ideas and systems evolved, early metrological systems, the exchange of goods and their impact, the standardization of measuring tools, and the impact of such concepts. This unique volume is deliberately set broad, both geographically and chronologically, in order to compare and contrast changes over time and between peoples, and in doing so it sheds new light on the social and scientific developments among both prehistoric and early historic societies. TABLE OF CONTENTS List of Illustrations Foreword 1. How to Open the Gift Box? Archaeology and the Transfer of Goods Christophe Darmangeat 2. Between East and West. The Measurement of Linearity as the Forerunner of Weighing Aleksander Dzby?ski 3. Feasting and Burial Rites in Pre-Hispanic Honduras. Comparing Archaeological and Ethnographic Evidence Franziska Fecher 4. Development and Functioning of Numeral Systems Jadranka Gvozdanovi? 5. Some Further Thoughts on Commodity and Gift Exchange in Tribal Societies Ju?rg Helbling 6. The Early Bronze Age Rib Ingot Hoard from Oberding (Upper Bavaria) Sabrina Kutscher 7. Numbers and Measures in the Iberian Peninsula during the Iron Age. Evidence from the Archaeological and Textual Records Thibaud Poigt and Coline Ruiz Darasse 8. Highly Composite Numbers and the Early Use of Weights Lorenz Rahmstorf 9. The Functions of Number in Early Greek Text Richard Seaford
[Church:] A note on the Entscheidungsproblem (+) Correction to A note on the Entscheidungsproblem (+) Review of ""A. M. Turing. On Computable numbers, with an application to the Entscheidungsproblem"" (+) [Post:] Finite combinatory processes-formulation... - [LANDMARK VOLUME IN THE HISTORY OF LOGIC]
[No place], The Association for Symbolic Logic, 1936 & 1937. Royal8vo. Bound in red half cloth with gilt lettering to spine. In ""Journal of Symbolic Logic"", Volume 1 & 2 bound together. Barcode label pasted on to back board. Small library stamp to lower part of 16 pages. A very fine copy. [Church:] Pp. 40-1" Pp. 101-2. [Post:] Pp. 103-5. [Turing:] Pp. 153-163" 164. [Entire volume: (4), 218, (2), IV, 188 pp.]
First edition of this collection of seminal papers within mathematical logic, all constituting some of the most important contributions mathematical logic and computional mathematics. A NOTE ON THE ENTSCHEIDUNGSPROBLEM (+) CORRECTION TO A NOTE ON THE ENTSCHEIDUNGSPROBLEM (+) REVIEW OF ""A. M. TURING. ON COMPUTABLE NUMBERS, WITH AN APPLICATION TO THE ENTSCHEIDUNGSPROBLEM"":First publication of Church's seminal paper in which he proved the solution to David Hilbert's ""Entscheidungsproblem"" from 1928, namely that it is impossible to decide algorithmically whether statements within arithmetic are true or false. In showing that there is no general algorithm for determining whether or not a given statement is true or false, he not only solved Hilbert's ""Entscheidungsproblem"" but also laid the foundation for modern computer logic. This conclusion is now known as Church's Theorem or the Church-Turing Theorem (not to be mistaken with the Church-Turing Thesis). The present paper anticipates Turing's famous ""On Computable Numbers"" by a few months. ""Church's paper, submitted on April 15, 1936, was the first to contain a demonstration that David Hilbert's 'Entscheidungsproblem' - i.e., the question as to whether there exists in mathematics a definite method of guaranteeing the truth or falsity of any mathematical statement - was unsolvable. Church did so by devising the 'lambda-calculus', [...] Church had earlier shown the existence of an unsolvable problem of elementary number theory, but his 1936 paper was the first to put his findings into the exact form of an answer to Hilbert's 'Entscheidungsproblem'. Church's paper bears on the question of what is computable, a problem addressed more directly by Alan Turing in his paper 'On computable numbers' published a few months later. The notion of an 'effective' or 'mechanical' computation in logic and mathematics became known as the Church-Turing thesis."" (Hook & Norman: Origins of Cyberspace, 250) Church coined in his review of Turing's paper the phrase 'Turing machine'.FINITE COMBINATORY PROCESSES-FORMULATION I: The Polish-American mathematician Emil Post made notable contributions to the theory of recursive functions. In the 1930s, independently of Turing, Post came up with the concept of a logic automaton similar to a Turing machine, which he described in the present paper (received on October 7, 1936). Post's paper was intended to fill a conceptual gap in Alonzo Church's paper on 'An unsolvable problem of elementary number theory'. Church had answered in the negative Hilbert's 'Entscheidungsproblem' but failed to provide the assertion that any such definitive method could be expressed as a formula in Church's lambda-calculus. Post proposed that a definite method would be one written in the form of instructions to mind-less worker operating on an infinite line of 'boxes' (equivalent to the Turing machines 'tape'). The range of instructions proposed by Post corresponds exactly to those performed by a Turing machine, and Church, who edited the Journal of Symbolic Logic, felt it necessary to insert an editorial note referring to Turing's ""shortly forthcoming"" paper on computable numbers, and asserting that ""the present article ... although bearing a later date, was written entirely independently of Turing's"". (Hook & Norman: Origins of Cyberspace, 356).COMPUTABILITY AND LAMBDA-DEFINABILITY (+) THE Ø-FUNCTION IN LAMBDA-K-CONVERSION: The volume also contains Turing's influential ""Computability and lambda-definability"" in which he proved that computable functions ""are identical with the lambda-definable functions of Church and the general recursive functions due to Herbrand and Gödel and developed by Kleene"". (Hook & Norman: Origins of Cyberspace, 395).
Equal Temperament in the Eighteenth Century. The Ear versus Numbers
, Brepols, 2023 Hardback, xiv + 186 pages, Size:210 x 270 mm, Illustrations:13 b/w, 12 musical examples, Language: English. ISBN 9782503606750.
Summary Today, many have urged early music specialists to adopt a historical unequal temperament for keyboards and harps, and even for instruments whose frets produce equal temperament naturally. Equal temperament, however, played a significant role during this period, but most writing today has stressed the numbers from early mathematicians who believed that the more just intervals a temperament has, the better it will be. Major writers, however, pressed for equal temperament because it enabled full use of the keyboard, transposition, and enharmonic notes. In contrast, the major and minor semitones of unequal temperaments, and their flats pitched higher than sharps, limited the keyboard's usable compass and made enharmonic notes and transposition impossible. As advanced thinkers were aware, performers with pitch flexibility did not follow the theorists' numbers. An accompaniment in equal temperament offered them free rein to find the best intonation because its ratios for fourths and fifths are closest to the natural ones. Among the many writers who supported equal temperament was Jakob Adlung, who observed that the theorists' calculations gave rise to the argument: ?Whether the ear or the numbers should judge if music sounds in or out of tune?. TABLE OF CONTENTS Foreword Glossary of terms Abbreviation of journal Abbreviaton of refence works CHAPTER ONE: 'EARS TO HEAR, BUT DO NOT HEAR' Introduction Late Renaissance Intonation Later Intonation Standards Eighteenth-Century Views Theory vs. Practice Tuners and the Monochord CHAPTER TWO: FUNDAMENTALS Measurement The Construction of Meantone Temperament The Monochord The Ear's Tolerance for Pitch Discrepancies The Meaning of 'Diatonic' Equal Temperament in Practice CHAPTER THREE: TEMPERAMENT IN ITALY AND FRANCE Equal Temperament in Italy Equal Temperament in France Marin Mersenne Equal Temperament and Instruments Jean-Philippe Rameau Reaction The Francophile Marpurg Temperament Requirements in French Music CHAPTER FOUR: CLARIFYING THE ISSUES The Necessity for Equal Temperament Does an Unequal Temperament Make All Keys Usable? Werckmeister and Equal Temperament Well-Tempered Neidhardt and Equal Temperament CHAPTER FIVE: TEMPERAMENT IN GERMANY The Acceptance of Equal Temperament Key Characteristics Kirnberger and Temperament CHAPTER SIX: INTONATION Flexible Intonation Eighteenth-Century Intonation The Curious Story of the Prelleur Violin Chart The Influence of Traditional Theory Differentiating between Theory and Practice Orchestral Intonation Tuning and Intonation CHAPTER SEVEN: ORGAN TEMPERAMENT AND J.S. BACH Equal Temperament and the Organ Musical Scores Equal Temperament in Bach's Area Builders and Temperament Bach's Harmonic Tequirements Postscript CHAPTER EIGHT: EXPRESSIVE INTONATION Equal Temperament and Expressive Intonation Mathematicians' Reaction CONCLUSION BIBLIOGRAPHY INDEX OF NAMES
