Between 1620 and 1670, the most eminent mathematicians, including René Descartes, Pierre de Fermat and John Wallis, sought a method for determining the equation of the tangent to a curve. Isaac Newton and Gottfried Wilhelm Leibniz's introduction of differential calculus in the late 17th century solved the problem brilliantly. The inverse problem arose immediately: given a family of lines, can we find a curve to which they are all tangent?
From geometry to analysis
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Let us take a simple geometric example. Consider perpendicular coordinate axes (Ox) and (Oy)
and slide a line segment [AB] of length a, with A on the (Ox) axis and B on the (Oy) axis:
