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Author: Robert Hahn Publisher: State University of New York Press ISBN: 1438464916 Category : Philosophy Languages : en Pages : 301
Book Description
Bringing together geometry and philosophy, this book undertakes a strikingly original study of the origins and significance of the Pythagorean theorem. Thales, whom Aristotle called the first philosopher and who was an older contemporary of Pythagoras, posited the principle of a unity from which all things come, and back into which they return upon dissolution. He held that all appearances are only alterations of this basic unity and there can be no change in the cosmos. Such an account requires some fundamental geometric figure out of which appearances are structured. Robert Hahn argues that Thales came to the conclusion that it was the right triangle: by recombination and repackaging, all alterations can be explained from that figure. This idea is central to what the discovery of the Pythagorean theorem could have meant to Thales and Pythagoras in the sixth century BCE. With more than two hundred illustrations and figures, Hahn provides a series of geometric proofs for this lost narrative, tracing it from Thales to Pythagoras and the Pythagoreans who followed, and then finally to Plato's Timaeus. Uncovering the philosophical motivation behind the discovery of the theorem, Hahn's book will enrich the study of ancient philosophy and mathematics alike.
Author: Robert Hahn Publisher: State University of New York Press ISBN: 1438464916 Category : Philosophy Languages : en Pages : 301
Book Description
Bringing together geometry and philosophy, this book undertakes a strikingly original study of the origins and significance of the Pythagorean theorem. Thales, whom Aristotle called the first philosopher and who was an older contemporary of Pythagoras, posited the principle of a unity from which all things come, and back into which they return upon dissolution. He held that all appearances are only alterations of this basic unity and there can be no change in the cosmos. Such an account requires some fundamental geometric figure out of which appearances are structured. Robert Hahn argues that Thales came to the conclusion that it was the right triangle: by recombination and repackaging, all alterations can be explained from that figure. This idea is central to what the discovery of the Pythagorean theorem could have meant to Thales and Pythagoras in the sixth century BCE. With more than two hundred illustrations and figures, Hahn provides a series of geometric proofs for this lost narrative, tracing it from Thales to Pythagoras and the Pythagoreans who followed, and then finally to Plato's Timaeus. Uncovering the philosophical motivation behind the discovery of the theorem, Hahn's book will enrich the study of ancient philosophy and mathematics alike.
Author: Robert Hahn Publisher: SUNY Press ISBN: 1438464894 Category : Philosophy Languages : en Pages : 301
Book Description
Explores Thaless speculative philosophy through a study of geometrical diagrams. Bringing together geometry and philosophy, this book undertakes a strikingly original study of the origins and significance of the Pythagorean theorem. Thales, whom Aristotle called the first philosopher and who was an older contemporary of Pythagoras, posited the principle of a unity from which all things come, and back into which they return upon dissolution. He held that all appearances are only alterations of this basic unity and there can be no change in the cosmos. Such an account requires some fundamental geometric figure out of which appearances are structured. Robert Hahn argues that Thales came to the conclusion that it was the right triangle: by recombination and repackaging, all alterations can be explained from that figure. This idea is central to what the discovery of the Pythagorean theorem could have meant to Thales and Pythagoras in the sixth century BCE. With more than two hundred illustrations and figures, Hahn provides a series of geometric proofs for this lost narrative, tracing it from Thales to Pythagoras and the Pythagoreans who followed, and then finally to Platos Timaeus. Uncovering the philosophical motivation behind the discovery of the theorem, Hahns book will enrich the study of ancient philosophy and mathematics alike.
Author: Irene Caiazzo Publisher: BRILL ISBN: 9004499466 Category : Philosophy Languages : en Pages : 512
Book Description
For the first time, the reader can have a synoptic view of the reception of Pythagoras and Pythagoreanism in the Middle Ages and the Renaissance, East and West, in a multicultural perspective. All the major themes of Pythagoreanism are addressed, from mathematics, number philosophy and metaphysics to ethics and religious thought.
Author: Carl Huffman Publisher: Cambridge University Press ISBN: 9781139444071 Category : Philosophy Languages : en Pages : 704
Book Description
Archytas of Tarentum is one of the three most important philosophers in the Pythagorean tradition, a prominent mathematician, who gave the first solution to the famous problem of doubling the cube, an important music theorist, and the leader of a powerful Greek city-state. He is famous for sending a trireme to rescue Plato from the clutches of the tyrant of Syracuse, Dionysius II, in 361 BC. This 2005 study was the first extensive enquiry into Archytas' work in any language. It contains original texts, English translations and a commentary for all the fragments of his writings and for all testimonia concerning his life and work. In addition there are introductory essays on Archytas' life and writings, his philosophy, and the question of authenticity. Carl A. Huffman presents an interpretation of Archytas' significance both for the Pythagorean tradition and also for fourth-century Greek thought, including the philosophies of Plato and Aristotle.
Author: Kitty Ferguson Publisher: Bloomsbury Publishing USA ISBN: 0802779638 Category : Biography & Autobiography Languages : en Pages : 384
Book Description
The enthralling story of Pythagoras and the Pythagoreans, whose insights transformed the ancient world and still inspire the realms of science, mathematics, philosophy, and the arts. "Pythagoras's influence on the ideas, and therefore on the destiny, of the human race was probably greater than that of any single man before or after him," wrote Arthur Koestler. Though most people know of him only for the famous Pythagorean Theorem (a2 +b2=c2), in fact the pillars of our scientific tradition-belief that the universe is rational, that there is unity to all things, and that numbers and mathematics are a powerful guide to truth about nature and the cosmos-hark back to the convictions of this legendary sixth-century B.C. scholar. Born around 570 B.C. on the cultured Aegean island of Samos, Pythagoras (according to ancient tales) studied with the sage Thales nearby at Miletus, and with priests and scribes in Egypt and Babylon. Eventually he founded his own school at Croton in southern Italy, where he and his followers began to unravel the surprising deep truths concealed behind such ordinary tasks as tuning a lyre. While considering why some string lengths produced beautiful sounds and others discordant ones, they uncovered the ratios of musical harmony, and recognized that hidden behind the confusion and complexity of nature are patterns and orderly relationships. They had surprised the Creator at his drafting board and had glimpsed the mind of God! Some of them later would also find something darker in numbers and nature: irrationality, a revelation so unsettling and subversive that it may have contributed to the destruction of their brotherhood.
Author: Robert Hahn Publisher: State University of New York Press ISBN: 9780791491546 Category : Science Languages : en Pages : 354
Book Description
Anaximander and the Architects opens a previously unexplored avenue into Presocratic philosophy—the technology of monumental architecture. The evidence, coming directly from sixth century B.C.E. building sites and bypassing Aristotle, shows how the architects and their projects supplied their Ionian communities with a sprouting vision of natural order governed by structural laws. Their technological innovations and design techniques formed the core of an experimental science and promoted a rational, not mythopoetical, discourse central to our understanding of the context in which early Greek philosophy emerged. Anaximander's prose book and his rationalizing mentality are illuminated in surprising ways by appeal to the ongoing, extraordinary projects of the archaic architects and their practical techniques.
Author: Phillip Sidney Horky Publisher: Oxford University Press ISBN: 0190465700 Category : History Languages : en Pages : 328
Book Description
Was Plato a Pythagorean? Plato's students and earliest critics thought so, but later scholars have been more skeptical. Plato and Pythagoreanism reconsiders this question by arguing that a specific type of Pythagorean philosophy, called "mathematical" Pythagoreanism, played a profound role in Plato's philosophy.
Author: Eli Maor Publisher: Princeton University Press ISBN: 0691196885 Category : Mathematics Languages : en Pages : 284
Book Description
Frontmatter --Contents --List of Color Plates --Preface --Prologue: Cambridge, England, 1993 --1. Mesopotamia, 1800 BCE --Sidebar 1: Did the Egyptians Know It? --2. Pythagoras --3. Euclid's Elements --Sidebar 2: The Pythagorean Theorem in Art, Poetry, and Prose --4. Archimedes --5. Translators and Commentators, 500-1500 CE --6. François Viète Makes History --7. From the Infinite to the Infinitesimal --Sidebar 3: A Remarkable Formula by Euler --8. 371 Proofs, and Then Some --Sidebar 4: The Folding Bag --Sidebar 5: Einstein Meets Pythagoras --Sidebar 6: A Most Unusual Proof --9. A Theme and Variations --Sidebar 7: A Pythagorean Curiosity --Sidebar 8: A Case of Overuse --10. Strange Coordinates --11. Notation, Notation, Notation --12. From Flat Space to Curved Spacetime --Sidebar 9: A Case of Misuse --13. Prelude to Relativity --14. From Bern to Berlin, 1905-1915 --Sidebar 10: Four Pythagorean Brainteasers --15. But Is It Universal? --16. Afterthoughts --Epilogue: Samos, 2005 --Appendixes --Chronology --Bibliography --Illustrations Credits --Index.
Author: Dirk L. Couprie Publisher: State University of New York Press ISBN: 0791487784 Category : Philosophy Languages : en Pages : 306
Book Description
Promoting a new, broadly interdisciplinary horizon for future studies in early Greek philosophy, Dirk L. Couprie, Robert Hahn, and Gerard Naddaf establish the cultural context in which Anaximander's thought developed and in which the origins of Greek philosophy unfolded in its earliest stages. In order to better understand Anaximander's achievement, the authors call our attention to the historical, social, political, technological, cosmological, astronomical, and observational contexts of his thought. Anaximander in Context brings to the forefront of modern debates the importance of cultural context, and the indispensability of images to clarify ancient ideologies.
Author: Carl A. Huffman Publisher: Cambridge University Press ISBN: 1139915983 Category : Philosophy Languages : en Pages : 659
Book Description
This is a comprehensive, authoritative and innovative account of Pythagoras and Pythagoreanism, one of the most enigmatic and influential philosophies in the West. In twenty-one chapters covering a timespan from the sixth century BC to the seventeenth century AD, leading scholars construct a number of different images of Pythagoras and his community, assessing current scholarship and offering new answers to central problems. Chapters are devoted to the early Pythagoreans, and the full breadth of Pythagorean thought is explored including politics, religion, music theory, science, mathematics and magic. Separate chapters consider Pythagoreanism in Plato, Aristotle, the Peripatetics and the later Academic tradition, while others describe Pythagoreanism in the historical tradition, in Rome and in the pseudo-Pythagorean writings. The three great lives of Pythagoras by Diogenes Laertius, Porphyry and Iamblichus are also discussed in detail, as is the significance of Pythagoras for the Middle Ages and Renaissance.
Author: Robert Hahn
Author: Robert Hahn
Author: Robert Hahn
Author: Irene Caiazzo
Author: Carl Huffman
Author: Kitty Ferguson
Author: Robert Hahn
Author: Phillip Sidney Horky
Author: Eli Maor
Author: Dirk L. Couprie
Author: Carl A. Huffman