Blackwell Reference Online

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At the hands of the early Greeks, especially Euclid ( c . 300 bc ), geometry achieved a degree of perfection unmatched by any other science prior to the modern period. Ancient and medieval astronomy, although extensively pursued, was little more than applied geometry, for it lacked an adequate dynamical explanation of the phenomena it studied. Indeed, not until Newton's Principia (1687) did any scientific body of knowledge equal Euclid's Elements in fertility, scope, rigour, or systematic development. For almost exactly two millennia, Euclidean geometry constituted the paradigm of systematic scientific knowledge. The import of this fact for the history of philosophy would be hard to overrate. Geometry did not originate with Euclid; as every school-child knows, the ancient Egyptians used geometry as a practical art in building pyramids and surveying land. At some time – perhaps about 600 bc – the Greeks began to transform this art into a rigorous deductive science. Certainly by P lato 'S time ( c .429–347 bc ) it had reached a high level of sophistication, and Plato was duly impressed. According to legend, a sign at the entrance to his academy read, ‘Let no one enter here who does not know geometry.’ Plato realized that, strictly speaking, geometry is not about physical things; its subject matter consists of such abstract entities as perfect straight lines, perfect ... log in or subscribe to read full text