Euclids Heritage Is Space Three Dimensional

We live in a space, we get about in it. We also quantify it, we think of it as having dimensions. Ever since Euclid's ancient geometry, we have thought of bodies occupying parts of this space (including our own bodies), the space of our practical orientations (our 'moving abouts'), as having three dimensions. Bodies have volume specified by measures of length, breadth and height. But how do we know that the space we live in has just these three dimensions? It is theoreti cally possible that some spaces might exist that are not correctly described by Euclidean geometry. After all, there are the non Euclidian geometries, descriptions of spaces not conforming to the axioms and theorems of Euclid's geometry. As one might expect, there is a history of philosophers' attempts to 'prove' that space is three-dimensional. The present volume surveys these attempts from Aristotle, through Leibniz and Kant, to more recent philosophy. As you will learn, the historical theories are rife with terminology, with language, already tainted by the as sumed, but by no means obvious, clarity of terms like 'dimension', 'line', 'point' and others. Prior to that language there are actions, ways of getting around in the world, building things, being interested in things, in the more specific case of dimensionality, cutting things. It is to these actions that we must eventually appeal if we are to understand how science is grounded.

This book presents to the reader a modern axiomatic construction of three-dimensional Euclidean geometry in a rigorous and accessible form. It is helpful for high school teachers who are interested in the modernization of the teaching of geometry.

Excerpt from Geometry in Space: Containing Parts of Euclid's Eleventh and Twelfth Books; And Some Properties of Polyhedra and Solids of Revolution, With Exercises This little volume would have had its natural place as Part III of Euclid Revised, had not that Book extended to a quite sufficient size in its present form. But, mindful of the maxim - 'Great book, great evil' - the Editor thought that it would be better to make a separate volume of those parts of Euclid's Eleventh and Twelfth Books, which are, by common consent, desirable for a student; with such analogous additional matter as it might seem advisable to treat from a purely geometrical standpoint. There is too the additional reason for taking this course, that the number of those who extend the study of Geometry from two to three dimensions is few compared with the number who content themselves with what can be done in one plane. No doubt the conception of solid figures, beyond the very simplest, is difficult; and the graphic exhibition of them is perhaps more difficult still. Yet there can be no doubt also that the study of Pure Geometry in Space is of immense value, whether considered as a mental discipline, or with regard to its utility for other purposes. Respecting the range and amount of matter that should be included in a treatise designed to give an introduction to the purely geometrical treatment of figures in space, the Editor has had difficulty in coming to a decision ; and he would put forward what is here given as, to a considerable extent, tentative. Thus, for example, it was originally intended that there should be a separate chapter on Surface Spherics; but, on reflection, it appeared dubious whether such a chapter would not be a 'game not worth the candle'-adding to the expense of the book, and not really wanted. 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.

"A biography of ancient Greek mathematician Euclid, known as the father of geometry and author of the mathematics textbook Elements"--Provided by publisher.

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This ambitious book explores the relationship between the Western "scientific revolution" that began with Galileo in the early seventeenth century and the Renaissance "artistic revolution" inaugurated by Giotto three hundred years earlier. The fruit of many years of thought and research, it demonstrates the crucial role that Italian Renaissance painting, sculpture, and architecture played in what we call "modern science". Samuel Y. Edgerton, Jr., shows that rather than being symptomatic in nature, the arts served as a catalyst for the transformation in perception which occurred in the West in the fourteenth century. According to Edgerton, the new way in which "reality" was represented, through the use of the unique Renaissance tools of perspective and chiaroscuro, set the stage for modern scientific practice.