From yesterday's ancients we skip forward quickly (due to my ignorance and subjectivity, as well as the demands of my broader points) to the early modern era in Europe, specifically to a publication by a fellow named Rafael Bombelli, (pictured above) of the city-state of Bologna, in AD 1572. Negative numbers were still new in Europe then, but the more advanced thinkers, including Bombelli, had a handle on that. By way of review: multiplying two negative numbers yields a positive. Multiplying a negative and a positive yields a negative, multiplying two positives yields a positive. One consequence of these rules is that there are no square roots of negative numbers. No rational square roots and no irrational square roots either. No square roots of any level of rationality for negative numbers. Why? Because if you had a square root for a negative number then, by definition, you would have a situation in which the multiplication of that number by itself would yield that negati...