Yeah, the "should" is editorializing. The avoidance of negatives is pretty easy to explain as a simple mistake. From the article:
> Luca Pacioli, often referred to as "The Father of Accounting," wrote, printed and distributed the first complete description of double-entry accounting in 1494.
> In 1545, Cardano in his Ars Magna did not allow negative numbers in his consideration of cubic equations, so he had to treat, for example, x^3 + ax = b separately from x^3 = ax + b (with a,b > 0 in both cases). In all, Cardano was driven to the study of thirteen different types of cubic equations, each expressed purely in terms of positive numbers.
> In A.D. 1759, Francis Maseres, an English mathematician, wrote that negative numbers "darken the very whole doctrines of the equations and make dark of the things which are in their nature excessively obvious and simple".
> Luca Pacioli, often referred to as "The Father of Accounting," wrote, printed and distributed the first complete description of double-entry accounting in 1494.
From http://en.wikipedia.org/wiki/Negative_number#History :
> In 1545, Cardano in his Ars Magna did not allow negative numbers in his consideration of cubic equations, so he had to treat, for example, x^3 + ax = b separately from x^3 = ax + b (with a,b > 0 in both cases). In all, Cardano was driven to the study of thirteen different types of cubic equations, each expressed purely in terms of positive numbers.
> In A.D. 1759, Francis Maseres, an English mathematician, wrote that negative numbers "darken the very whole doctrines of the equations and make dark of the things which are in their nature excessively obvious and simple".