<P> In 1659, Wallis credited William Neile's discovery of the first rectification of a nontrivial algebraic curve, the semicubical parabola . The accompanying figures appear on page 145 . On page 91, William Neile is mentioned as Gulielmus Nelius . </P> <P> Before the full formal development of calculus, the basis for the modern integral form for arc length was independently discovered by Hendrik van Heuraet and Pierre de Fermat . </P> <P> In 1659 van Heuraet published a construction showing that the problem of determining arc length could be transformed into the problem of determining the area under a curve (i.e., an integral). As an example of his method, he determined the arc length of a semicubical parabola, which required finding the area under a parabola . In 1660, Fermat published a more general theory containing the same result in his De linearum curvarum cum lineis rectis comparatione dissertatio geometrica (Geometric dissertation on curved lines in comparison with straight lines). </P> <P> Building on his previous work with tangents, Fermat used the curve </P>

When does a finite line appear as an infinite line