The Emergence of the Calculus
Overview
The calculus describes a set of powerful analytical techniques, including differentiation and integration, that utilize the concept of a limit in the mathematical description of the properties of functions, especially curves. The formal development of the calculus in the later half of the seventeenth century, primarily through the independent work of English physicist and mathematician Sir Isaac Newton (1642-1727) and German mathematician Gottfried Wilhelm Leibniz (1646-1716), was the crowning mathematical achievement of the Scientific Revolution. The subsequent advancement of the calculus profoundly influenced the course and scope of mathematical and scientific inquiry.
Background
Important mathematical developments that laid the foundation for the calculus of Newton and Leibniz can be traced back to mathematical techniques first advanced in ancient Greece and Rome. In addition to existing methods to determine the tangent to a circle, the Greek mathematician and inventor Archimedes (c. 290-c. 211 B.C.) developed a technique to determine the tangent to a spiral, an important component of his water screw.
The majority of other ancient fundamental advances ultimately related to the calculus were concerned with techniques that allowed the determination of areas under curves (principally the area and volume of curved shapes).
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