Date: Dec 11, 2012 11:11 AM
Author: Joe Niederberger
Subject: Re: In "square root of -1", should we say "minus 1" or "negative<br> 1"?
R. Hansen says:
>That is interesting. I haven't dug deep, but that would be like replacing "i" with "-". But then what would happen to something like 3+2i? That would become 3 + (-2), but is that added like we do, or did he have a new rule of adding as well or was the unary sign symbol not related to subtraction at all?
Addition remains the same, but you have to be careful not to interpret the minus sign as an implicit "multiply by negative 1" because "multiplication" is in fact refined (obviously, because he "mult." we know uses the usual sign rule!) In fact this new "mult." ends up being only right-distributive and non-commutative.)
As I said, it seems that Cardano was motivated by the desire to find a system that had negative numbers, but not imaginary numbers (which he must have considered as even more insidious than merely negative numbers!)
Beware though -- "Card games, dice and chess were the methods he used to make a living."