."We do not perceive any quantity such as that its square is negative!" (Bhāskara II, "Bijaganita", 12th century)
"A second type of the false position makes use of roots of negative numbers. I will give an example: If someone says to you, divide 10 into two parts, one of which multiplied into the other shall produce 30 or 40, it is evident that this case or question is impossible. [.. .] Nevertheless, we shall solve it in this fashion. This, however, is closest to the quantity which is truly imaginary since operations may not be performed with it as with a pure negative number, nor as in other numbers. [...] This subtlety results from arithmetic of which this final point is, as I have said, as subtle as it is useless." (Girolamo Cardano, "Ars Magna", 1545)
"Someone could also ask what these impossible solutions are. I would answer that they are good for three things: for the certainty of the general rule, for being sure that there are no other solutions, and for its utility." (Albert Girard, "L'Invention nouvelle de l'Algébre", 1629)
"Thus we can give three names to the other solutions, seeing that there are some which are greater than nothing, other less than nothing, and other enveloped, as those which have like √- or √-3 or other similar numbers." (Albert Girard, "L'Invention nouvelle de l'Algébre", 1629)
“[…] neither the true roots nor the false are always real; sometimes they are, however, imaginary; namely, whereas we can always imagine as many roots for each equation as I have predicted, there is still not always a quantity which corresponds to each root so imagined. Thus, while we may think of the equation x^3 - 6xx + 13x - 10 = 0 as having three roots, yet there is just one real root, which is 2, and the other two [2+i and 2-i]], however, increased, diminished, or multiplied them as we just laid down, remain always imaginary.” (René Descartes, “Gemetry”, 1637)
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