Definition:Complex Natural Logarithm/Historical Note

Historical Note on Complex Natural Logarithm
In $1702$, encountered solutions of the primitive $\ds \int \dfrac {\d x} {a x^2 + b x + c}$ which seemed to require logarithms of complex numbers, which at that time had not been considered.

and both investigated, and by $1712$ they had developed opposing viewpoints on how to handle the logarithm of a negative number.

used the argument:
 * $\dfrac {\map \d {-x} } {-x} = \dfrac {\map \d x} x$, so by integration $\map \ln {-x} = \map \ln x$

while insisted that the integration was only valid for positive $x$.

noticed that the integration in question required an arbitrary constant, and so:
 * $\map \ln {-x} = \map \ln x + c$

where $c$ was necessarily imaginary.

This resolved the matter.