 Prior to the end of the sixteenth century, mathematicians had already used algebra in the analysis of geometrical problems, but the program Viète details marks a significant step forward. On the one hand, in his Isagoge [Introduction to the analytic art] of 1591, which was presented as part of a larger project to restore ancient analysis (entitled Book of the restored mathematical analysis or the new algebra), Viète introduces a notation that allowed him to treat magnitudes in a general way. The literal symbols he uses (consonants and vowels depending on whether the variable in the equation was unknown or indeterminate, respectively) represent magnitudes generally and do not specify whether they are arithmetical magnitudes (numbers) or geometrical magnitudes (such as line segments or angles). He can thus represent arithmetic operations as applied to magnitudes in general. For instance, \(A + B\) represents the addition of two magnitudes and does not specify whether \(A\) and \(B\) are numbers (in which case the addition represents a process of counting) or geometrical objects (in which case the addition represents the combination of two line segments) (see Viète 1591, 11–27; for the significance of Viète’s “new algebra” for early modern mathematics see Bos 2001, Chp. 8; Mahoney 1973, Chp. 2; and Pycior 1997, Chp. 1).