PROBLEM VIII.

Solution of Cubic Equations.

Let aaa + ba = c be proposed. A Cubic equation of the first Formula.
In numbers aaa + 24 a = 587914

Theor. x = c — ggg — bg

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3 gg + b

With the equation marked by dots (as we have shown)

aaa + 0̇2̇4 a = 5̇8̇7̇9̇1̇4̇

that is, aaa + 0a = 587, whence g = 8, and so on for the rest.

c — ggg — bg = + 75

3 gg + b = 192) + 750 (+ 3 = x

+ 3

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g = 83

c — ggg — bg = + 14135.

3 gg + b = 20691) + 14135.0 (+ ,68 = x

83.

+ .68

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g = 83.68

+ c — ggg — bg = — 50.332032

3 gg + b = 210131.) — 50.332032 (— ,002393 = x

83.68

— .002393

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a = 83.677607