The Concept of Construction and the Representation of Curves in Seventeenth-Century Mathematics
نویسنده
چکیده
Example 1. An exponential curve. My topic is best introduced by an example. I take it from the correspondence between Leibniz and Huygens in 1690-1691. Leibniz wrote about his new differential and integral calculus. Huygens was very skeptical and proposed problems for Leibniz to solve. In the course of this exchange Leibniz came to use an exponential equation to represent a curve. This was entirely new; the only curve equations used until then were algebraic ones. Huygens was even more skeptical about this novelty: he thought that Leibniz boasted, using fancy but empty symbolism. So Leibniz explained further. He took as an example the curve representing the relation between the time t and the velocity v of a body falling in a medium with resistance proportional to v. That curve, he said, was given by the following exponential equation:
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