It is often argued that the history of nineteenth-century mathematics is that of the replacement of geometry by algebra and analysis. Synthetic or coordinatefree geometric reasoning which had produced some of the greatest achievements of mankind — Euclid’s Elements and Newton’s Philosophiæ Naturalis Principia Mathematica (the Principia) to name but two — was finally shifted from its long-standing central position in mathematics to a marginal one.
KeywordsNonstandard Analysis Geometry Theory Ofscientific History Nonstandard Approach Nonstandard Treatment
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