標題: Titlebook: Redefining Geometrical Exactness; Descartes’ Transform Henk J. M. Bos Book 2001 Springer-Verlag New York, Inc. 2001 Canon.Discard.Mathemati [打印本頁] 作者: papyrus 時間: 2025-3-21 19:06
書目名稱Redefining Geometrical Exactness影響因子(影響力)
作者: BANAL 時間: 2025-3-21 23:58 作者: BOLT 時間: 2025-3-22 03:15
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作者: 時間等 時間: 2025-3-22 08:09 作者: DEAF 時間: 2025-3-22 12:38
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作者: Employee 時間: 2025-3-22 16:27
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 作者: 極端的正確性 時間: 2025-3-22 19:58 作者: pester 時間: 2025-3-22 23:20 作者: 獨裁政府 時間: 2025-3-23 03:40 作者: admission 時間: 2025-3-23 09:27
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.作者: FUME 時間: 2025-3-23 13:09
Early modern methods of analysisons were analysis called “synthesis.” Moreover, a few classical sources. spoke in general about this arrangement. The most important of these texts was the opening of the seventh book of Pappus’ .; I quote this passage here in full:作者: 口味 時間: 2025-3-23 17:02
Using algebra — Viète’s analysis or to non-numerical quantities (such as line segments or other geometrical magnitudes), thus legitimizing the use of algebra in geometry while retaining the conviction that geometrical magnitude and number were essentially different. Viète called this system “new algebra” or “specious logistics.”作者: 高射炮 時間: 2025-3-23 21:42 作者: justify 時間: 2025-3-23 22:58
Keplere of algebra. For Kepler the issue was of central philosophical importance, and for that reason his analysis of constructional exactness in geometry was both more detailed and more critical than any in his period.作者: 通知 時間: 2025-3-24 04:32 作者: incredulity 時間: 2025-3-24 10:32
General introductionheir science in order to meet more appropriate and higher standards of exactness. Several such endeavors have been highly successful. Exploring the intricacies of incommensurability and the infinite, Greek mathematicians created theories whose rigor is still impressive to the modern mind. The rigori作者: capillaries 時間: 2025-3-24 14:08 作者: FLAT 時間: 2025-3-24 18:33
1588: Pappus’ “Collection”cut statements on the aim and rules of geometrical problem solving, many examples of constructions, and suggestive information about analytical methods for finding the solutions of problems. At the same time Pappus’ practice of problem solving was often inconsistent with the rules and aims he profes作者: TAIN 時間: 2025-3-24 21:14
The early modern tradition of geometrical problem solving; survey and examplesness of construction during the period c. 1590 – c. 1650. The debates primarily concerned the solution of point construction problems, that is, problems that admitted one or a finite number of solutions only. Solving such problems was indeed seen as a major, if not the main, aim of geometry..作者: Neutropenia 時間: 2025-3-25 00:12
Early modern methods of analysissical mathematical texts. in which the constructions of problems were preceded by an argument referred to as “analysis;” in those cases the constructions were analysis called “synthesis.” Moreover, a few classical sources. spoke in general about this arrangement. The most important of these texts wa作者: Incorporate 時間: 2025-3-25 04:31 作者: 金盤是高原 時間: 2025-3-25 08:39 作者: 全等 時間: 2025-3-25 15:24
Claviusincipal dynamics in that field, and the questions of legitimation that were raised in relation to this process, I now turn to the actual debates on the interpretation of geometrical exactness with respect to constructions.作者: Obvious 時間: 2025-3-25 16:47
Vièteted to his ideas about construction. As we have seen, Viète considered problem solving by means of algebra as consisting of three parts, zetetics, poristics, and exegetics. Construction belonged to the exegetical part of geometrical problem solving. Two of Viète’s treatises were specially devoted to作者: 勤勉 時間: 2025-3-25 23:36
Kepleris of the concept of constructibility, as well as a precise and sharp criticism of the constructional practices of contemporary geometers and their use of algebra. For Kepler the issue was of central philosophical importance, and for that reason his analysis of constructional exactness in geometry w作者: Gingivitis 時間: 2025-3-26 03:55
Fermat general introduction (cf. Section 1.5), I consider this development as the principal dynamics within the early modern tradition of geometrical problem solving. Yet Fermat figures less prominently in my story than Viète, and much less so than Descartes. The reason is that, although Fermat was strong作者: Inkling 時間: 2025-3-26 05:07 作者: 使出神 時間: 2025-3-26 12:07
Introduction to Part II the structure of the story of construction (Section 1.3) as consisting of two periods and one central figure, Descartes. As in Part I, my primary subject is geometrical construction, and my main objective is to understand the processes involved in the interpretation of mathematical exactness. In th作者: antidote 時間: 2025-3-26 16:38
Construction and the interpretation of exactness in Descartes’ studies of c. 1619te to Beeckman in early 1619. In the second of these, dated 26 March 1619, Descartes formulated a program for his future investigations. The text is deservedly famous;. it shows how Descartes at an early age charted his scientific quest with remarkable clarity and determination. For my present purpo作者: 征稅 時間: 2025-3-26 19:55 作者: vibrant 時間: 2025-3-26 22:32
2196-8810 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 c作者: 魅力 時間: 2025-3-27 04:37
The legitimation of geometrical procedures before 1590e classical ideas on the legitimacy of constructions here; rather I can restrict myself to dealing with those few classical sources that actually influenced the early modern debates. Besides, and fortunately, I can refer to an excellent recent study on the classical tradition of geometrical problem solving, Wilbur Knorr’s ...作者: tinnitus 時間: 2025-3-27 06:19 作者: 手段 時間: 2025-3-27 12:29
Arithmetic, geometry, algebra, and analysissubject of Chapter 7. We find the first successful merging of the fields of algebra, arithmetic, and geometry in the work of Viète; Chapter 8 explains how Viète overcame the obstacles and the legitimation issues involved.作者: ablate 時間: 2025-3-27 16:42
Geometrical problem solving — the state of the art c. 1635therefore appropriate to conclude Part I by a sketch of the state of the art of geometrical problem solving around 1635, that is, just before Descartes published his innovations (and also before Fermat’s new techniques began to circulate among cognoscenti).作者: folliculitis 時間: 2025-3-27 20:37
Introduction to Part IIe early modern period Descartes was the key figure with respect to these issues. His . of 1637 was to be the dominating influence in mathematics for more than 50 years. It was, as I will show, largely motivated by the need, as perceived by its author, for a more precise and reasoned definition of exactness in geometry.作者: insurgent 時間: 2025-3-27 22:43
Construction and the interpretation of exactness in Descartes’ studies of c. 1619se the text has ad value because Descartes formulated his program entirely in terms of a classification of mathematical problems with respect to their solution by calculation or construction. Thus the letter to Beeckman provides a natural starting point of my inquiry into the development of Descartes’ ideas about construction.作者: 云狀 時間: 2025-3-28 02:27 作者: 表否定 時間: 2025-3-28 07:14 作者: 商店街 時間: 2025-3-28 13:10
https://doi.org/10.1007/978-1-4613-0087-8Canon; Discard; Mathematica; analytic geometry; arithmetic; construction; development; equation; field; form; 作者: Insensate 時間: 2025-3-28 16:42 作者: Aspiration 時間: 2025-3-28 21:07
MoltherIn the same year as Kepler’s . a book by a much lesser known mathematician was published in Frankfurt. It was entitled作者: CLAMP 時間: 2025-3-29 00:01
978-1-4612-6521-4Springer-Verlag New York, Inc. 2001作者: 泰然自若 時間: 2025-3-29 03:42 作者: 勛章 時間: 2025-3-29 08:54 作者: Inelasticity 時間: 2025-3-29 14:00 作者: Cpr951 時間: 2025-3-29 18:39 作者: 弄臟 時間: 2025-3-29 20:25
Henk J. M. Bosm mechanics since the literature is inundated with scattered articles in this field, and to pave the Reader’s way into this territory as rapidly as possible. The result: clear and understandable derivations with the necessary mathematical steps included so that the intelligent reader should be able 作者: Fretful 時間: 2025-3-30 01:59
Henk J. M. Bosm mechanics since the literature is inundated with scattered articles in this field, and to pave the Reader’s way into this territory as rapidly as possible. The result: clear and understandable derivations with the necessary mathematical steps included so that the intelligent reader should be able 作者: originality 時間: 2025-3-30 04:08 作者: 邊緣 時間: 2025-3-30 10:02 作者: exostosis 時間: 2025-3-30 14:13 作者: 歡樂中國 時間: 2025-3-30 20:17 作者: AVERT 時間: 2025-3-30 23:17
2196-8810 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 me978-1-4612-6521-4978-1-4613-0087-8Series ISSN 2196-8810 Series E-ISSN 2196-8829 作者: 懶惰人民 時間: 2025-3-31 02:10
Henk J. M. Bos understandable derivations with the necessary mathematical steps included so that the intelligent reader should be able 978-90-481-7447-8978-1-4020-5796-0Series ISSN 0168-1222 Series E-ISSN 2365-6425 作者: Working-Memory 時間: 2025-3-31 07:46 作者: FLIT 時間: 2025-3-31 11:46
2634-6575 n of the Federal Republic of Germany during the ‘long 1950s‘. In the public battle over the future direction of Germany, America stood as a symbol of social, political and economic corruption.978-1-349-31200-9978-0-230-25141-0Series ISSN 2634-6575 Series E-ISSN 2634-6583 作者: 討好美人 時間: 2025-3-31 16:16
