> Somewhere it was said that the first instance of a problem leading > to an imaginary number is in Stereometrica, by Heron of Alexandria. > Does anyone have access to that book and is able to give me some > more information about the problem in question?
Quoting Ed Sandifer's review of the book: _An Imaginary Tale: The Story Of Sqrt(-1)_ by Paul J. Nahim.
<quote> The book follows a roughly historical trail, opening with a story of how ancient mathematicians Heron and Diophantus missed a chance to discover imaginary numbers. Both knew a formula for the volume of a truncated square pyramid in terms of the sides of the upper and lower square surfaces and the length of the edge connecting those sides. In one of his examples, Heron picked a length, 15, for the edge that wasn't long enough to reach the corners of the squares, of sides 28 and 4. Perhaps he was teaching too many classes that semester, for when Heron reached a point where he was to take the square root of a negative value, he just took the root of a positive instead, and thus missed a chance to discover imaginary numbers. It took over a thousand years until del Ferro and Cardano actually made the discovery in their pursuit of roots of cubic equations. Nahin tells this familiar story with delightful enthusiasm. </quote>