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[[Nicole Oresme]] at the [[University of Paris]] and the Italian [[Giovanni di Casali]] independently provided graphical demonstrations of this relationship, asserting that the area under the line depicting the constant acceleration, represented the total distance traveled.<ref>Clagett, Marshall (1961) ''The Science of Mechanics in the Middle Ages,'' (Madison: University of Wisconsin Press), pp. 332–45, 382–91.</ref> In a later mathematical commentary on Euclid's ''Elements'', Oresme made a more detailed general analysis in which he demonstrated that a body will acquire in each successive increment of time an increment of any quality that increases as the odd numbers. Since Euclid had demonstrated the sum of the odd numbers are the square numbers, the total quality acquired by the body increases as the square of the time.<ref>Nicole Oresme, "Questions on the ''Geometry'' of Euclid" Q. 14, pp. 560–65, in Marshall Clagett, ed., ''Nicole Oresme and the Medieval Geometry of Qualities and Motions,'' (Madison: University of Wisconsin Press, 1968).</ref>
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