A quotation by Tartaglia

[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 December 2013

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