Excerpt from Science, Vol. 7: A Weekly Journal Devoted to the Advancement of Science; January-June, 1898
Now consider the analogous case in space. Two pyramids upon congruent bases may be proved equal by bringing them into congruence with each other. But suppose that they differ only in that one is the obverse of the other, so that they could be brought into congruence only by looking at one of them in a mirror and then placing the other into congruence with the image of the first as seen in the mirror. Would we detract from the rigor of the demonstration by assuming the possibility of such an obversion without changing the volume of the pyramid? With a fourth dimension we should have no. Detraction from rigor. We would simply obvert the pyramid as we would turn over the triangle.
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Paperback. Zustand: New. Print on Demand. This book explores the concepts of non-Euclidean geometry, considering the possibility of a fourth spatial dimension and the implications of curved space. The author uses clear and concise language to delve into complex ideas, providing examples and analogies to aid understanding. The text covers the history of non-Euclidean geometry, from its origins in the work of Gauss, Bolyai and Lobachevsky, through to its development in the 20th century and its applications in fields such as cosmology and astrophysics. By examining the nature of space and the limits of our perception, the book encourages critical thinking about the fundamental principles of geometry and its relationship to our understanding of the universe. 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 9780243110674_0
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