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Download The Origins of the Infinitesimal Calculus (Dover Classics of Science and Mathematics) eBook

by Margaret E. Baron

Download The Origins of the Infinitesimal Calculus (Dover Classics of Science and Mathematics) eBook
ISBN:
0486653714
Author:
Margaret E. Baron
Category:
Mathematics
Language:
English
Publisher:
Dover Pubns (July 1, 1987)
Pages:
304 pages
EPUB book:
1530 kb
FB2 book:
1703 kb
DJVU:
1979 kb
Other formats
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Rating:
4.2
Votes:
263


This book is marginally useful at best. The argument is this: since the circumference of the circle with the same area as the ellipse is 2 pi sqrt(ab), the circumference of the circle must be somewhat greater (since the circle has the least possible perimeter for a given area).

This book is marginally useful at best. It consists almost entirely of convoluted and muddled exposition of sample theorems and proofs of one mathematician after another without much cohesion.

The History of the Calculus and Its Conceptual Development (Dover Books on Mathematics) by Carl B. Boyer .

Baron's tendency to obscure or even severely distort the point of an argument may be illustrated by the following example, where she is in addition promoting the modern propaganda myth that 17th century mathematicians committed numerous mistakes and were guided by "a happy instinct" (p. 109) rather than reason.

ISBN 10: 1483233545 ISBN 13: 9781483233543 Publisher: Pergamon, 2014 Softcover. Customers who bought this item also bought.

The publication first ponders on Greek mathematics, transition to Western Europe, and some center of gravity determinations in. .

The publication first ponders on Greek mathematics, transition to Western Europe, and some center of gravity determinations in the later 16th century. Discussions focus on the growth of kinematics in the West, latitude of forms, influence of Aristotle, axiomatization of Greek mathematics, theory of proportion and means, method of exhaustion, discovery method of Archimedes, and curves, normals, tangents, and curvature.

Subsequent chapters discuss the arithmetization of integration methods, the role of investigation of special curves, concepts of tangent and arc, the composition of motions, more. Categories: Mathematics\Analysis.

Results from Google Books. Dr. Baron provides an enlightening view of the Greek, Hindu, and Arabic sources that constituted the framework for the development of infinitesimal methods in the seventeenth century.

Download books for free. DOVER CLASSICS OF SCIENCE AND MA THEMA TICS DE RE METALLICA, Georgius Agricola

Download books for free. DOVER CLASSICS OF SCIENCE AND MA THEMA TICS DE RE METALLICA, Georgius Agricola. ori- gins of the infinitesimal calculus lie, not only in the significant contributions of Newton and Leibniz, but also in the centuries-long struggle to investigate area, volume, tangent and arc by purely geometric methods, To understand the important changes in proof structure, method, technique and means of presentation which emerged in the later seventeenth century it is necessary to go back to.

Start by marking The Origins of the Infinitesimal Calculus as Want to.Published January 26th 2004 by Dover Publications (first published June 1969).

Start by marking The Origins of the Infinitesimal Calculus as Want to Read: Want to Read savin. ant to Read. Few among the numerous studies of calculus offer the detailed and fully documented historical perspective of this text. It begins with an enlightening view of the Greek, Hindu, and Arabic sources that constituted the framework for the development of infinitesimal methods in the seventeenth century. Origins of the Infinitesimal Calculus. 0486495442 (ISBN13: 9780486495446).

Mathematics includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and change (mathematical analysis). It has no generally accepted definition. Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature

This historical account begins with the Greek, Hindu, and Arabic sources that constituted the framework for the development of infinitesimal methods in the 17th century. Subsequent chapters discuss the arithmetization of integration methods, the role of investigation of special curves, concepts of tangent and arc, the composition of motions, more. 1969 edition.
  • Blacknight
This book is marginally useful at best. It consists almost entirely of convoluted and muddled exposition of sample theorems and proofs of one mathematician after another without much cohesion. Baron's tendency to obscure or even severely distort the point of an argument may be illustrated by the following example, where she is in addition promoting the modern propaganda myth that 17th century mathematicians committed numerous mistakes and were guided by "a happy instinct" (p. 109) rather than reason.

"When [Kepler] argued by analogy he sometimes made mistakes. Unable to determine theoretically the length of an elliptic arc he argues that, since the area of an ellipse is equal to that of a circle, the radius of which is the geometric mean of the major and minor axes (area = pi ab = pi r^2, where a/r = r/b), then the circumference of the ellipse should correspondingly be equal to the circumference of a circle the radius of which is the arithmetic mean of the semi-axes, i.e. pi (a+b)." (p. 109)

The only one making a "mistake" here is Baron. What Baron portrays as a crackpot "analogy" is in fact a perfectly sound and intelligent argument. The argument is this: since the circumference of the circle with the same area as the ellipse is 2 pi sqrt(ab), the circumference of the circle must be somewhat greater (since the circle has the least possible perimeter for a given area). Kepler then proposes to use the *approximation* pi (a+b) for the circumference, being fully aware and completely explicit that it is an approximation only ("elliptica circumferentia est proxime...", we read on the very page of the Opera Omnia referred to by Baron)---and indeed a very good and very convenient approximation at that for ellipses of small eccentricity (such as the orbit of Mars, which is Kepler's interest).
  • Danrad
EXCELLENT...