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The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry: 15 (Synthese Historical Library) - Tapa dura
Sinopsis
The present work has three principal objectives: (1) to fix the chronology of the development of the pre-Euclidean theory of incommensurable magnitudes beginning from the first discoveries by fifth-century Pythago reans, advancing through the achievements of Theodorus of Cyrene, Theaetetus, Archytas and Eudoxus, and culminating in the formal theory of Elements X; (2) to correlate the stages of this developing theory with the evolution of the Elements as a whole; and (3) to establish that the high standards of rigor characteristic of this evolution were intrinsic to the mathematicians' work. In this third point, we wish to counterbalance a prevalent thesis that the impulse toward mathematical rigor was purely a response to the dialecticians' critique of foundations; on the contrary, we shall see that not until Eudoxus does there appear work which may be described as purely foundational in its intent. Through the examination of these problems, the present work will either alter or set in a new light virtually every standard thesis about the fourth-century Greek geometry. I. THE PRE-EUCLIDEAN THEORY OF INCOMMENSURABLE MAGNITUDES The Euclidean theory of incommensurable magnitudes, as preserved in Book X of the Elements, is a synthetic masterwork. Yet there are detect able seams in its structure, seams revealed both through terminology and through the historical clues provided by the neo-Platonist commentator Proclus.
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The present work has three principal objectives: (1) to fix the chronology of the development of the pre-Euclidean theory of incommensurable magnitudes beginning from the first discoveries by fifth-century Pythago reans, advancing through the achievements of Theodorus of Cyrene, Theaetetus, Archytas and Eudoxus, and culminating in the formal theory of Elements X; (2) to correlate the stages of this developing theory with the evolution of the Elements as a whole; and (3) to establish that the high standards of rigor characteristic of this evolution were intrinsic to the mathematicians' work. In this third point, we wish to counterbalance a prevalent thesis that the impulse toward mathematical rigor was purely a response to the dialecticians' critique of foundations; on the contrary, we shall see that not until Eudoxus does there appear work which may be described as purely foundational in its intent. Through the examination of these problems, the present work will either alter or set in a new light virtually every standard thesis about the fourth-century Greek geometry. I. THE PRE-EUCLIDEAN THEORY OF INCOMMENSURABLE MAGNITUDES The Euclidean theory of incommensurable magnitudes, as preserved in Book X of the Elements, is a synthetic masterwork. Yet there are detect able seams in its structure, seams revealed both through terminology and through the historical clues provided by the neo-Platonist commentator Proclus.
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The Evolution of the Euclidean Elements. A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry.
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D. Reidel Publishing Company, Dordrecht / Boston, 1975
ISBN 10: 9027705097
ISBN 13: 9789027705099
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Librería: Emile Kerssemakers ILAB, Heerlen, Holanda
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23 x 16 cm, hardcover with dust jacket, xii, 374, (4) pages, text in English, first endpaper missing [probably removed name]. Paper slightly browned, otherwise in very good condition. See picture. From the series: Synthese Historical Library, Volume 15. Portions of this work originally included in the author's thesis, Harvard 1973. 740g. Nº de ref. del artículo: 80702
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The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry (Synthese Historical Library, 15)
Librería: International Book Project, Lexington, KY, Estados Unidos de America
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hardcover. Condición: Very Good. NOT ex-library. Pages are crisp with minor underlining. Dust jacket shows shelf wear, but boards and binding are in excellent condition. Minor foxing on top edge. 100% of proceeds go toward promoting literacy in under-served areas of the world. Nº de ref. del artículo: SKU0001307
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The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry (Synthese Historical Library)
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Springer-Verlag Publishing, 1974
ISBN 10: 9027705097
ISBN 13: 9789027705099
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Librería: Salish Sea Books, Bellingham, WA, Estados Unidos de America
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Condición: Very Good. Very Good in a Very Good dust jacket; Hardcover; Dust jacket is clean and intact with no tears, and has not been price-clipped (Now fitted with a new, Brodart jacket protector); Very light wear to the boards with "straight" edge-corners; The textblock edges are unblemished; The endpapers and all text pages are clean and unmarked; The binding is excellent with a straight spine; This book will be shipped in a sturdy cardboard box with foam padding; Medium Format (8.5" - 9.75" tall); 1.7 lbs; Dark brown and white jacket with title in black lettering; 1974, Springer-Verlag Publishing; 379 pages; "The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry (Synthese Historical Library)," by W. R. Knorr. Nº de ref. del artículo: SKU-1361AK03605275
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The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry (Synthese Historical Library)
Publicado por
Springer-Verlag Publishing, 1974
ISBN 10: 9027705097
ISBN 13: 9789027705099
Antiguo o usado
Tapa dura
Librería: Salish Sea Books, Bellingham, WA, Estados Unidos de America
Calificación del vendedor: 5 de 5 estrellas
Condición: Very Good. Very Good+ in a Very Good+ dust jacket; Hardcover; Dust jacket is clean and intact with no tears, and has not been price-clipped (Now fitted with a new, Brodart jacket protector); Unmarked boards with "straight" edge-corners; The textblock edges are unblemished; The endpapers and all text pages are bright and unmarked; The binding is tight with a straight spine; This book will be shipped in a sturdy cardboard box with foam padding; Medium Format (8.5" - 9.75" tall); Dark brown and white jacket with title in black lettering; 1974, Springer-Verlag Publishing; 379 pages; "The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry (Synthese Historical Library)," by W. R. Knorr. Nº de ref. del artículo: SKU-0514AI02503222
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The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry (Synthese Historical Library, 15)
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Evolution of the Euclidean Elements : A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry
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Evolution of the Euclidean Elements : A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry
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The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry (Synthese Historical Library, 15)
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The Evolution of the Euclidean Elements (Hardcover)
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Hardcover. Condición: new. Hardcover. The present work has three principal objectives: (1) to fix the chronology of the development of the pre-Euclidean theory of incommensurable magnitudes beginning from the first discoveries by fifth-century Pythago reans, advancing through the achievements of Theodorus of Cyrene, Theaetetus, Archytas and Eudoxus, and culminating in the formal theory of Elements X; (2) to correlate the stages of this developing theory with the evolution of the Elements as a whole; and (3) to establish that the high standards of rigor characteristic of this evolution were intrinsic to the mathematicians' work. In this third point, we wish to counterbalance a prevalent thesis that the impulse toward mathematical rigor was purely a response to the dialecticians' critique of foundations; on the contrary, we shall see that not until Eudoxus does there appear work which may be described as purely foundational in its intent. Through the examination of these problems, the present work will either alter or set in a new light virtually every standard thesis about the fourth-century Greek geometry. I. THE PRE-EUCLIDEAN THEORY OF INCOMMENSURABLE MAGNITUDES The Euclidean theory of incommensurable magnitudes, as preserved in Book X of the Elements, is a synthetic masterwork. Yet there are detect able seams in its structure, seams revealed both through terminology and through the historical clues provided by the neo-Platonist commentator Proclus. The present work has three principal objectives: (1) to fix the chronology of the development of the pre-Euclidean theory of incommensurable magnitudes beginning from the first discoveries by fifth-century PythagoA reans, advancing through the achievements of Theodorus of Cyrene, Theaetetus, Archytas and Eudoxus, and culminating in the formal theory of Elements X; (2) to correlate the stages of this developing theory with the evolution of the Elements as a whole; and (3) to establish that the high standards of rigor characteristic of this evolution were intrinsic to the mathematicians' work. In this third point, we wish to counterbalance a prevalent thesis that the impulse toward mathematical rigor was purely a response to the dialecticians' critique of foundations; on the contrary, we shall see that not until Eudoxus does there appear work which may be described as purely foundational in its intent. Through the examination of these problems, the present work will either alter or set in a new light virtually every standard thesis about the fourth-century Greek geometry. I. THE PRE-EUCLIDEAN THEORY OF INCOMMENSURABLE MAGNITUDES The Euclidean theory of incommensurable magnitudes, as preserved in Book X of the Elements, is a synthetic masterwork. Yet there are detectA able seams in its structure, seams revealed both through terminology and through the historical clues provided by the neo-Platonist commentator Proclu Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Nº de ref. del artículo: 9789027705099
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The Evolution of the Euclidean Elements
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