History
The first definition of a tangent was "a right line which touches a curve, but which when produced, does not cut it". This old definition prevents inflection points from having any tangent. It has been dismissed and the modern definitions are equivalent to those of Leibniz.
Pierre de Fermat developed a general technique for determining the tangents of a curve using his method of adequality in the 1630s.
Leibniz defined the tangent line as the line through a pair of infinitely close points on the curve.
Read more about this topic: Tangent
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