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Already in antiquity Archimedes (about 287–212 BC) succeeded in computing tangents to given curves and areas under curves. However, in his day he was unable to recognise the two operations – computing tangents and areas – are in fact inverse operations: this can be seen from the fundamental theorem of calculus which was first discovered by Newton and Leibniz. Leibniz transformed it from the geometry of Isaac Barrow (1630–1677) into the new language of symbolic algebra, in which form it could display its full power.
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