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Titlebook: Redefining Geometrical Exactness; Descartes’ Transform Henk J. M. Bos Book 2001 Springer-Verlag New York, Inc. 2001 Canon.Discard.Mathemati

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书目名称Redefining Geometrical Exactness
副标题Descartes’ Transform
编辑Henk J. M. Bos
视频video
丛书名称Sources and Studies in the History of Mathematics and Physical Sciences
图书封面Titlebook: Redefining Geometrical Exactness; Descartes’ Transform Henk J. M. Bos Book 2001 Springer-Verlag New York, Inc. 2001 Canon.Discard.Mathemati
描述In his "Géométrie" of 1637 Descartes achieved a monumental innovation of mathematical techniques by introducing what is now called analytic geometry. Yet the key question of the book was foundational rather than technical: When are geometrical objects known with such clarity and distinctness as befits the exact science of geometry? Classically, the answer was sought in procedures of geometrical construction, in particular by ruler and compass, but the introduction of new algebraic techniques made these procedures insufficient. In this detailed study, spanning essentially the period from the first printed edition of Pappus‘ "Collection" (1588, in Latin translation) and Descartes‘ death in 1650, Bos explores the current ideas about construction and geometrical exactness, noting that by the time Descartes entered the field the incursion of algebraic techniques, combined with an increasing uncertainty about the proper means of geometrical problem solving, had produced a certain impasse. Hethen analyses how Descartes transformed geometry by a redefinition of exactness and by a demarcation of geometry‘s proper subject and procedures in such a way as to incorporate the use of algebraic me
出版日期Book 2001
关键词Canon; Discard; Mathematica; analytic geometry; arithmetic; construction; development; equation; field; form;
版次1
doihttps://doi.org/10.1007/978-1-4613-0087-8
isbn_softcover978-1-4612-6521-4
isbn_ebook978-1-4613-0087-8Series ISSN 2196-8810 Series E-ISSN 2196-8829
issn_series 2196-8810
copyrightSpringer-Verlag New York, Inc. 2001
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Henk J. M. Boshniques like the factorization method, Lie algebras, matrix elements and quantum control at the Reader’s disposal. For this purpose a comprehensive description is provided of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in t
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hniques like the factorization method, Lie algebras, matrix elements and quantum control at the Reader’s disposal. For this purpose a comprehensive description is provided of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in t
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Henk J. M. Bostorization method in quantum mechanics at an advanced level with an aim to put mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the Reader’s disposal. For this purpose a comprehensive description is provided of the
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1588: Pappus’ “Collection”s for finding the solutions of problems. At the same time Pappus’ practice of problem solving was often inconsistent with the rules and aims he professed. As a result the influence of the book on the subsequent ideas about construction was strong but undogmatic.
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