This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1902 Excerpt: ...earth. r' = radius of moon, or other body. P = moon's horizontal parallax = earth's angular semidiameter as seen from the moon. f = moon's angular semidiameter. Now = P (in circular measure), r'-r = r (in circular measure);.'. r: r':: P: P', or (radius of earth): (radios of moon):: (moon's parallax): (moon's semidiameter). Examples. 1. Taking the moon's horizontal parallax as 57', and its angular diameter as 32', find its radius in miles, assuming the earth's radius to be 4000 miles. Here moon's semidiameter = 16';.-. 4000::: 57': 16';.-. r = 400 16 = 1123 miles. 2. The sun's horizontal parallax being 8"8, and his angular diameter 32V find his diameter in miles. ' Am. 872,727 miles. 3. The synodic period of Venus being 584 days, find the angle gained in each minute of time on the earth round the sun as centre. Am. l"-54 per minute. 4. Find the angular velocity with which Venus crosses the sun's disc, assuming the distances of Venus and the earth from the sun are as 7 to 10, as given by Bode's Law. Since (fig. 50) S V: VA:: 7: 3. But Srhas a relative angular velocity round the sun of l"-54 per minute (see Example 3); therefore, the relative angular velocity of A V round A is greater than this in the ratio of 7: 3, which gives an approximate result of 3"-6 per minute, the true rate being about 4" per minute. Annual ParaUax. 95. We have already seen that no displacement of the observer due to a change of position on the earth's surface could apparently affect the direction of a fixed star. However, as the earth in its annual motion describes an orbit of about 92 million miles radius round the sun, the different positions in space from which an observer views the fixed stars from time to time throughout the year must be separated ...
Zum Verständnis der intellektuellen Auseinandersetzungen und Friktionen im 3. Jahrhundert v.u.Z. bis Zerfall des Imperium Romanum wollen wir zunächst wesentliche Merkmale des gesellschaftlichen Diskurses politisch, wirtschaftlich, militärisch, religiös, sozial und bildungspolitisch betrachten. Dadurch sollen Meinungen und geäußerte Einstellungen zu den τέχναί einen "Sitz im Leben" bekommen. Der spezifische Beitrag zu diesem Diskurs und Alternative ist die "Vita contemplativa". Wir rufen einige für eine spieltheoretische Untersuchung wichtige Merkmale der hellenistischen und der römischen Zeit in Erinnerung und werfen einen Blick auf den sozioökonomischen Hintergrund in Alexandria (4.1.1) und Rom (4.1.2.) und einem Blick auf die Entwicklung der Spezialwissenschaften in beiden Herrschaftsbereichen. Erst dann können wir die Einstellungen der philosophischen Schulen (4.2), der Redner und Sophisten, in der Bildung und die Spiegelungen in der Literatur, gegliedert nach ihren Zweigen, (4.3.) betrachten.
Die Wissenschaft arbeitet kumulativ. In der Mathematik und in den Naturwissenschaften gibt es keine unvollendeten Sympho nien. über Jahrhunderte hinweg können thematische Problem kreise ihre Dynamik behalten; im historischen Rückblick erschei nen dann lange, zusammenhängende Problemketten von einer faszinierenden Kontinuität des menschlichen Denkens. Es ist die Befriedigung grundlegender materieller und geistiger Bedürfnisse der Menschheit, die dem weitgespannten Bogen zwischen Ver gangenheit und Gegenwart Stabilität verleiht. Zugleich und andererseits liegt hierin der Umstand begründet, daß wissenschaftliche Fragestellungen der Vergangenheit in die Gegenwart und Zukunft hineinwirken können. Gerade die führen den 'Wissenschaftler waren sich der Fruchtbarkeit historischen Selbstverständnisses für ihre eigenen Forschungen bewußt. Die Abhandlungen von LAGRANGE zum Beispiel gehören zu den Kost barkeiten auch der mathematik-historischen Literatur. Und wie wären die Leistungen von EULER und GAUSS, von EINSTEIN und v. LAUE möglich gewesen ohne die von ihnen selbst vorgenommene Einordnung in eine wissenschaftliche Tradition? Auch die durch greifenden Revolutionen in der 'Vissenschaft bedeuten nichts an deres als die dialektische überwindung eines zuvor bestätigten wissenschaftlichen Tatbestandes. In diesem Sinne stellt die hier dargestellte Geschichte der Dio phantischen Analysis geradezu einen klassischen Fall aktueller Geschichte der Mathematik dar. Der historische Bogen spannt sich über mehr als 17 Jahrhunderte, vom Ausgang der Antike bis zum Beginn des 20. Jahrhunderts, ohne daß eine künstliche Reaktivierung der Leistungen von DIOPHANT notwendig geworden wäre. 1* 4 Geleitwort Die Autorin des vorgelegten Büchleins ist eine erfahrene und er folgreiche Historikerin der Mathematik. Frau Prof. Dr. I. G.
This is a selection of expository essays by Paulo Ribenboim, the author of such popular titles as "The New Book of Prime Number Records" and "The Little Book of Big Primes". The book contains essays on Fibonacci numbers, prime numbers, Bernoulli numbers, and historical presentations of the main problems pertaining to elementary number theory, such as for instance Kummer's work on Fermat's Last Theorem. The essays are written in a light and humorous language without secrets and are thoroughly accessible to everyone with an interest in numbers.
Volume 2 of an authoritative two-volume set that covers the essentials of mathematics and features every landmark innovation and every important figure, including Euclid, Apollonius, and others.
Facts101 is your complete guide to Heart of Mathematics, An Invitation to Effective Thinking. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.
Facts101 is your complete guide to A Survey of Mathematics. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.
Facts101 is your complete guide to A Problem Solving Approach to Mathematics. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.
Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines—linear algebra, abstract algebra, and number theory—into one comprehensive and fluid presentation, facilitating a deeper understanding of the topic and improving readers' retention of the main concepts. The book begins with an introduction to the elements of set theory. Next, the authors discuss matrices, determinants, and elements of field theory, including preliminary information related to integers and complex numbers. Subsequent chapters explore key ideas relating to linear algebra such as vector spaces, linear mapping, and bilinear forms. The book explores the development of the main ideas of algebraic structures and concludes with applications of algebraic ideas to number theory. Interesting applications are provided throughout to demonstrate the relevance of the discussed concepts. In addition, chapter exercises allow readers to test their comprehension of the presented material. Algebra and Number Theory is an excellent book for courses on linear algebra, abstract algebra, and number theory at the upper-undergraduate level. It is also a valuable reference for researchers working in different fields of mathematics, computer science, and engineering as well as for individuals preparing for a career in mathematics education.
Originally published: Oxford: Clarendon Press, 1931; previously published by Dover Publications in 1963.
Volume 2 of an authoritative two-volume set that covers the essentials of mathematics and features every landmark innovation and every important figure, including Euclid, Apollonius, and others.
This edition of Books IV to VII of Diophantus' Arithmetica, which are extant only in a recently discovered Arabic translation, is the outgrowth of a doctoral dissertation submitted to the Brown University Department of the History of Mathematics in May 1975. Early in 1973, my thesis adviser, Gerald Toomer, learned of the existence of this manuscript in A. Gulchln-i Macanl's just-published catalogue of the mathematical manuscripts in the Mashhad Shrine Library, and secured a photographic copy of it. In Sep tember 1973, he proposed that the study of it be the subject of my dissertation. Since limitations of time compelled us to decide on priorities, the first objective was to establish a critical text and to translate it. For this reason, the Arabic text and the English translation appear here virtually as they did in my thesis. Major changes, however, are found in the mathematical com mentary and, even more so, in the Arabic index. The discussion of Greek and Arabic interpolations is entirely new, as is the reconstruction of the history of the Arithmetica from Diophantine to Arabic times. It is with the deepest gratitude that I acknowledge my great debt to Gerald Toomer for his constant encouragement and invaluable assistance.

Best Books