"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.
Tarjuma-yi Kitāb al-Nijāra : Dar handasa-yi ʿamalī /
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Abu ʼl-Wafāʾ Būzjānī (d. 388/998) was a mathematician and astronomer and a native of Būzjān near Nishapur. He studied arithmetic with two of his uncles, probably in Būzjān. When he was nineteen years old he went to Baghdad. There he further developed himself to become one of the leading scientists of his age, working at the Buyid court. He was a contemporary and protector of the chronicler of intellectual and artistic life in Baghdad at the time, Abū Ḥayyān al-Tawḥīdī (d. ca. 414/1023). In the bibliographical literature more than twenty works are ascribed to him, many of which were lost. The present work was originally written in Arabic under the title Kitāb fī mā yaḥtāj ilayhi ʼl-ṣāniʿ fī aʿmāl al-handasa . It is a groundbreaking work in that Būzjānī was the first to write a monograph on practical geometry as justified by the rules of theoretical geometry. Medieval Persian and French translation, with introductions and notes.
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1 online resource. :
9789004405646
9789648700992
Ibrāhīm Ibn Sinān. Logique et Géométrie au Xe siècle /
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Ibrāhīm Ibn Sinān was one of the most famous scientists of the tenth century. His specialities were geometry, logic and philosophy of mathematics. In this volume, three new hypotheses are presented. The first one concerns the existence and the development of philosophy of mathematics in Arabic, independently of traditional metaphysics and philosophy. It is mainly concerned with the logic of discovery and the logic of proof. The second hypothesis concerns the development of a new chapter in mathematics devoted to geometrical transformations. The close connection between astronomy and mathematics, used to develop this last chapter, is discussed in the third hypothesis. The book presents a critical edition done for the first time and based on all available manuscripts, French translations, and long historical and mathematical commentaries.
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1 online resource. :
Includes bibliographical references and index. :
9789004453135
9789004118041
The commentary of al-Nayrizi on Books II-IV of Euclid's Elements of Geometry : with a translation of that portion of Book I missing from ms Leiden or. 399.1 but present in the new...
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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.