2009, ISBN: 0217218091, Lieferbar binnen 4-6 Wochen

Internationaler Buchtitel. In englischer Sprache. Verlag: Cambridge Scholars Publishing, 246 Seiten, L=152mm, B=229mm, H=14mm, Gew.=363gr, Kartoniert/Broschiert, Klappentext: Purchase of … Mehr…

Internationaler Buchtitel. In englischer Sprache. Verlag: Cambridge Scholars Publishing, 246 Seiten, L=152mm, B=229mm, H=14mm, Gew.=363gr, Kartoniert/Broschiert, Klappentext: Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: GEOMETRICAL INSTRUMENTS AND MODELS. Next to the science of number, the science of space is that which is at once the most abstract, and admits of the most universal application to the study of natural phenomena. Everything that takes place takes place in space; and thus Geometry, or the science of space, necessarily intervenes in all exact observation of events. When we begin to think about space at all, the properties of it which first impress the mind are its continuity, and its apparently indefinite extent, our imaginations being perhaps unable to conceive the absence of either of these two properties. Probably we next notice the existence of three dimensions of space (as seen in the length, breadth, and height of any object), and we cannot conceive it to possess more or fewer. We further observe, (1) that at any two different points space is exactly similar to itself, and (2) that in all the directions which exist at any one point it has identical properties. These general assertions, if not really of themselves evident, are at least readily admitted as being in accordance with universal experience. They are all assumed in, and may be said to form the basis of, that analytical representation of space which we owe to Descartes, and which justly entitles him to be regarded as the founder of modern geometry. In accordance with this representation we regard space as a complex (if we may use this word as a translation of the German mannigfaltigkeH) of three indeterminate quantities corresponding to its three dimensions; the surfaces, lines, and points which exist in space, being, in technical phraseology, the " loci" obtained by imposing one, two, or three restrictive conditions upon these indeterminates. As often happens in similar cases, the mode of representation thus ...<