A quotation by Niccolo Fontana,


[The poem in which he revealed the secret of solving the cubic to Cardan]
When the cube and the things together
Are equal to some discrete number, 1
Find two other numbers differing in this one.
Then you will keep this as a habit
That their product shall always be equal
Exactly to the cube of a third of the things. 2
The remainder then as a general rule
Of their cube roots subtracted
Will be equal to your principal thing. 3
1 [Solve x3 + cx = d]
2 [Find u, v such that u - v = d and uv = (c/3)3 ]
3 [Then x = 3u - 3v ]


JOC/EFR February 2006

The URL of this page is:
http://www-history.mcs.st-andrews.ac.uk/Quotations/Tartaglia.html