<p>In the first part of this study, we compare the different approaches Francesco Maurolico (1557) and Adriaan van Roomen took to develop a universal mathematics. Maurolico sought to ground practical numerical calculation of lines, surfaces, volumes, weights, times, etc., in Euclidean theory while van Roomen sought to establish a general theory of ratio and proportion that precedes arithmetic and geometry. One key difference is that Maurolico’s numbers measure the various species of quantity via a posited unit while van Roomen’s numbers measure their ratios. In the second part, we compare two unfinished drafts by van Roomen (ca. 1598–99) and Descartes (the <i>Regulae</i>, ca. 1628–31) which propose a universal algebra that can model all quantities, including numbers and geometric magnitudes. In fact, there can be no such algebra, since the arithmetical unit as a multiplicative identity is incompatible with the heterogeneous dimensions of Euclidean geometry. Thus, van Roomen abandoned his draft. Descartes, whose interest lay with numerical problem-solving, initially avoided the problem by positing a unit for each species of quantity. But once he became acquainted with theoretical, unitless geometry through the Pappus problem he, too, abandoned his draft and worked with two algebras in <i>La géométrie</i> (1637).</p>