Prolegomena Mathematica: From Apollonius of Perga to the Late Neoplatonism. With an Appendix on Pappus and the History of Platonism

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This is the first study to deal with the history of Greek mathematics - starting with Appollonius and including astronomy - as part of the history of literary culture. It attempts to find out how mathematical works were presented by original authors (e.g. Ptolemy), and introduced and explained by commentators (e.g. Pappus who is at the centre of this enquiry, Eutocius, and prolegomena by late Anonymi). The manner in which mathematical treatises were presented and studied is entirely comparable to that practised in e.g. philosophy, medicine, biblical and literary studies (see the author's Prolegomena, (Brill, 1994)). Discussion of introductory issues is a standard feature, and in mathematics the development from the implicitly expressed to the explicitly expressed and from there to scholastic routine is the same as in these other fields.

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Editorial Reviews

From the Publisher
'Le style et la présentation matérielle sont très soignés…'
J. Mawhin, Revue des Questions Scientifiques, 2000.
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Product Details

  • ISBN-13: 9789004112674
  • Publisher: Brill Academic Publishers, Inc.
  • Publication date: 9/16/1998
  • Series: Philosophia Antiqua Series, #80
  • Pages: 182
  • Product dimensions: 6.36 (w) x 9.56 (h) x 0.69 (d)

Meet the Author

Jaap Mansfeld (1936), is Professor of Ancient and Medieval Philosophy, Utrecht University. He has published widely on ancient philosophy and its historiography, both in ancient and modern times.
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Table of Contents

Ch. I Preliminaries 1
Ch. II Pappus' Collectio 6
II 1 Introduction 6
II 2 Collectio Book VII 9
II 3 Collectio Book VI 14
II 4 Further Evidence from the Collectio 20
Ch. III Commentaries on Euclid, the Scholia on Euclid's Elements and Pappus' Commentary on Book X 23
III 1 Comments and Commentaries on the Elements and Data 23
III 2 The Scholia in Euclidem: Proclus, Pappus and Others 26
III 3 Pappus' Commentary on Elements Book X 31
Ch. IV Apollonius' Proems and Eutocius' Commentary 36
IV 1 The Proems of Apollonius' Conica 36
IV 2 Eutocius' Commentary on Apollonius' Conica I-IV 40
Ch. V Eutocius' Commentaries on Archimedes, and the Vita 44
V 1 Archimedes' Proems 44
V 2 Eutocius' Commentaries on Archimedes 45
V 3 The Vita of Archimedes 48
Ch. VI Heron of Alexandria 49
VI 1 Introduction 49
VI 2 The Belopoiica 49
VI 3 The Pneumatica 50
VI 4 The Automata 51
VI 5 The Catoptrica 52
VI 6 The Metrica 53
VI 7 The Dioptra 54
VI 8 A Theoretical Work: the So-called Definitiones, i.e. [actual symbol not reproducible] 55
Ch. VII Theon(?)'s Preface to Euclid's Optica 58
Ch. VIII Marinus on Euclid's Data 61
Ch. IX Ptolemy's Prefaces 66
IX 1 The Mathematike Suntaxis 66
IX 2 The Apotelesmatica 71
Ch. X Commentaries on Ptolemy 76
X 1 Pappus and Theon on the Mathematike Suntaxis and Handy Tables 76
X 2 The Anonymous Introduction to the Mathematike Suntaxis 79
X 3 Commentaries on the Apotelesmatica 81
Ch. XI Nicomachus of Gerasa and his Commentators 82
XI 1 The Introductio Arithmetica 82
XI 2 Iamblichus' Version and Asclepius' and Philoponus' Commentaries 87
XI 3 The Anonymous Prolegomena to the Introductio Arithmetica 89
Ch. XII Conclusion 92
App. 1 The Title of Ptolemy's Astrological Treatise 96
App. 2 Pappus and the History of Platonism 99
Complementary Notes 122
Bibliography 133
Index Locorum Potiorum 151
Index Rerum et Nominum Antiquorum 168
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