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The Thirteen Books of Euclid's Elements, Vol. 3: Translated From the Text of Heiberg, With Introduction and Commentary; Books X-XIII and Appendix (Classic Reprint) - Softcover
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Excerpt from The Thirteen Books of Euclid's Elements, Vol. 3: Translated From the Text of Heiberg, With Introduction and Commentary; Books X-XIII and Appendix
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Excerpt from The Thirteen Books of Euclid's Elements, Vol. 3: Translated From the Text of Heiberg, With Introduction and Commentary; Books X-XIII and Appendix
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Excerpt from The Thirteen Books of Euclid's Elements, Vol. 3: Translated From the Text of Heiberg With Introduction and Commentary
The discovery of the doctrine of incommensurables is attributed to Pythagoras. Thus Proclus says (Comm, on Eucl. 1. p. 65, 19) that Pythagoras "discovered the theory of irrationals"; and, again, the scholium on the beginning of Book x., also attributed to Proclus, states that the Pythagoreans were the first to address themselves to the investigation of commensurability, having discovered it by means of their observation of numbers. They discovered, the scholium continues, that not all magnitudes have a common measure. "They called all magnitudes measurable by the same measure commensurable, but those which are not subject to the same measure incommensurable, and again such of these as are measured by some other common measure commensurable with one another, and such as are not, incommensurable with the others. And thus by assuming their measures they referred everything to different commensurabilities, but, though they were different, even so (they proved that) not all magnitudes are commensurable with any." The scholium quotes further the legend according to which "the first of the Pythagoreans who made public the investigation of these matters perished in a shipwreck," conjecturing that the authors of this story "perhaps spoke allegorically, hinting that everything irrational and formless is properly concealed, and, if any soul should rashly invade this region of life and lay it open, it would be carried away into the sea of becoming and be overwhelmed by its unresting currents." There would be a reason also for keeping the discovery of irrationals secret for the time in the fact that it rendered unstable so much of the groundwork of geometry as the Pythagoreans had based upon the imperfect theory of proportions which applied only to numbers. We have already, after Tannery, referred to the probability that the discovery of incommensurability must have necessitated a great recasting of the whole fabric of elementary geometry, pending the discovery of the general theory of proportion applicable to incommensurable as well as to commensurable magnitudes.
It seems certain that it was with reference to the length of the diagonal of a square or the hypotenuse of an isosceles right-angled triangle that Pythagoras made his discovery.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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The Thirteen Books of Euclid's Elements, Vol. 3
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The Thirteen Books of Euclid's Elements, Vol. 3 (Classic Reprint)
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Paperback. Zustand: New. Print on Demand. This book delves into the world of mathematics, specifically focusing on the groundbreaking work of Euclid and his exploration of irrational numbers. It offers a historical perspective on this significant discovery, attributing it to the Pythagorean school and highlighting the contributions of mathematicians like Theodorus and Theaetetus. The author meticulously examines the evolution of the concept of incommensurability, tracing its development from the Pythagorean theorem to the more general theory of proportions. The book delves into the intricacies of Euclid's classifications of irrational numbers, including binomials, apotomes, and medials, and their connection to quadratic equations. By exploring the historical context and mathematical intricacies of Euclid's work, this book sheds light on a pivotal moment in the history of mathematics. It underscores the profound impact of the discovery of irrational numbers, not only in geometry but also in the broader realm of algebra and number theory. Ultimately, the book reveals how Euclid's insights into incommensurability laid the foundation for a more comprehensive understanding of the nature of numbers and their relationships. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781330231593_0
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