The commentary of al-Nayrizi on Books II-IV of Euclid's Elements of Geometry : with a translation...
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The Commentary of al-Nayrizi (circa 920) on Euclid's Elements of Geometry occupies an important place both in the history of mathematics and of philosophy, particularly Islamic philosophy. It is a compilation of original work by al-Nayrizi and of translations and commentaries made by others, such as Heron. It is the most influential Arabic mathematical manuscript in existence and a principle vehicle whereby mathematics was reborn in the Latin West. Furthermore, the Commentary on Euclid by the Platonic philosopher Simplicius, entirely reproduced by al-Nayrizi, and nowhere else extant, is essential to the study of the attempt to prove Euclid's Fifth Postulate from the preceding four. Al-Nayrizi was one of the two main sources from which Albertus Magnus (1193-1280), the Doctor Universalis, learned mathematics. This work presents an annotated English translation of Books II-IV and of a hitherto lost portion of Book I.
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1 online resource. :
Includes bibliographical references (p. [209]-212) and index. :
9789047444411 :
Available to subscribing member institutions only.
Socrates and the socratic dialogue /
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Socrates and the Socratic Dialogue assembles the most complete range of studies on Socrates and the Socratic dialogue. It focuses on portrayals of Socrates, whether as historical figure or protagonist of 'Socratic dialogues', in extant and fragmentary texts from Classical Athens through Late Antiquity. Special attention is paid to the evolving power and texture of the Socratic icon as it adopted old and new uses in philosophy, biography, oratory, and literature. Chapters in this volume focus on Old Comedy, Sophistry, the first-generation Socratics including Plato and Xenophon, Aristotle and Aristoxenus, Epicurus and Stoicism, Cicero and Persius, Plutarch, Apuleius and Maximus, Diogenes Laertius, Libanius, Themistius, Julian, and Proclus.
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1 online resource (viii, 931 pages) :
Includes bibliographical references and index. :
9789004341227 :
Available to subscribing member institutions only.
Prolegomena mathematica : from Apollonius of Perga to 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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1 online resource (vi, 178 pages) :
Includes bibliographical references (p. 133-149) and indexes. :
9789004321052 :
0079-1687 ; :
Available to subscribing member institutions only.
"Mathesis of the mind" : a study of Fichte's Wissenschaftslehre and geometry /
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This is the first major study in any language on J.G. Fichte's philosophy of mathematics and theory of geometry. It investigates both the external formal and internal cognitive parallels between the axioms, intuitions and constructions of geometry and the scientific methodology of the Fichtean system of philosophy. In contrast to "ordinary" Euclidean geometry, in his Erlanger Logik of 1805 Fichte posits a model of an "ursprüngliche" or original geometry - that is to say, a synthetic and constructivistic conception grounded in ideal archetypal elements that are grasped through geometrical or intelligible intuition. Accordingly, this study classifies Fichte's philosophy of mathematics as a whole as a species of mathematical Platonism or neo-Platonism, and concludes that the Wissenschaftslehre itself may be read as an attempt at a new philosophical mathesis, or "mathesis of the mind."
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Based on the author's thesis (Ph. D.)--Ludwig-Maximilians-Universität, Munich, 2009. :
1 online resource (iii, 304 pages) : illustrations. :
Includes bibliographical references. :
9789401207683 :
Available to subscribing member institutions only.
Later Platonists and their Heirs among Christians, Jews, and Muslims /
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Later Platonists and their Heirs among Christians, Jews and Muslims offers a thought-provoking exploration of the reception of Platonism among communities of faith from early Christianity to the sixteenth century, from the Byzantine East to the Latin West. Rare emphasis is placed on the importance of Platonic thought and its diffusion in late antique and medieval Syria, Armenia, and Georgia but also among Arab and Jewish intellectuals from the seventh century onwards. As such, the volume makes a statement against the separation of Neoplatonic philosophy from Christianity and the other Abrahamic faiths, since all four traditions promoted a life of virtue and goodness despite operating under different divine auspices. The volume seeks to establish paths of transmission and modes of adaptation across times and places.
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1 online resource :
Includes bibliographical references and index. :
9789004450264
9789004527850