 Although the philosophy of measurement formed as a distinct area of inquiry only during the second half of the nineteenth century, fundamental concepts of measurement such as magnitude and quantity have been discussed since antiquity. According to Euclid’s Elements, a magnitude—such as a line, a surface or a solid—measures another when the latter is a whole multiple of the former (Book V, def. 1 &amp; 2). Two magnitudes have a common measure when they are both whole multiples of some magnitude, and are incommensurable otherwise (Book X, def. 1). The discovery of incommensurable magnitudes allowed Euclid and his contemporaries to develop the notion of a ratio of magnitudes. Ratios can be either rational or irrational, and therefore the concept of ratio is more general than that of measure (Michell 2003, 2004a; Grattan-Guinness 1996).