Subject: Re: [MATHEDCC] square root of -1 history
From: Phil Mahler (mahlerp@middlesex.cc.ma.us)
Date: Fri Jan 21 2000 - 19:29:55 EST
haehl@kcmetro.cc.mo.us writes:
>Hi all,
>
>I have 2 questions.
>
>1. Does anyone know what mathematicians first studied the square root of
>-1
>and when it was first called an imaginary number?
>
...
>
>
>Martha
Florian Cajori "A History of Mathematical Notations" discusses "Symbolism
for Imaginaries and Vector Analysis". (An great book to own. Thankfully
this 1920s book is now back in print.)
"The earliest mathematician seriously to consider imaginaries and to
introduce them in the expression for the roots of equations was H.
Cardan." He used these in the Ars magna in 1545, but not with the radix
symbol. 5 + sqrt(-15) was 5p:Rm:15, for example.
In 1629 Albert Girard uses the radix for sqrt(-2). ... Before Euler the
sign sqrt(-1) (with the radix, and using 1) as distinct from sqrt(-a)
seldom, if ever, occurs.
It was Euler who first used the letter i for sqrt(-1) in a memoir in 1777.
Phil Mahler
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