Part One: History of the Cubic Scipione del Ferro (1465-1526) held the Chair of Arithmetic and Geometry at the University of Bologna. dal Ferro is credited with solving cubic equations algebraically but the picture is somewhat more complicated. We believe that dal Ferro could only solve cubic equation of the form
x3 + mx = n.
In fact this is all that is required. For, given the general cubic
y3 - by2 + cy - d = 0
substitute
y = x + b/3
to get
x3 + mx = n
where
m = c - b2/3, n = d - bc/3 + 2b3/27. |       | However, without the Hindu's knowledge of negative numbers, dal Ferro would not have been able to use his solution of the one case to solve all cubic equations. Remarkably, dal Ferro solved this cubic equation around 1515 but kept his work a complete secret until just before his death, in 1526, when he revealed his method to his student Antonio Fior. Fior was a mediocre mathematician and far less good at keeping secrets than dal Ferro. Soon rumours started to circulate in Bologna that the cubic equation had been solved. Nicolo of Brescia, known as Tartaglia meaning 'the stammerer', prompted by the rumours managed to solve equations of the form x3 + mx2 = n and made no secret of his discovery. |
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