Harriot, Thomas - Harriot papers, vol. I: Algebra, geometry, calendar, conic sections [HMC 241 I]

197

For this problem in Viete's De numerosa see (Viete 1600b, Prob . ]

prob. 11.

a a a - d d a = x x z

a a a - d d a = x z

3.
Vietæ
[Translation: Viète's example ]
ubi
artificium parabolæ

[Translation: with the method of the epanorthic ]

a a - 6400, a = 153000

Species

[Translation: Canonical ]

Tot debent esse puncta cubica
quot quadratica in coefficiente

[Translation: The cubic points must be as many as the squares in the coefficient of the linear ]

\sqrt{64}

. est 8
cuius cubus 512
+ 153
665. cuius latus cubicum
proxime maius. 9.
pro prima figura.
si cætera
[Translation: The square root of 64 is 8, whose cube is 512, plus 153 makes 665, whose nearest cube root above is 9, for the first figure if the rest ]

In æquationis affirmatis.

a a a + d d a = x x z

a a a + d d a = x x z

4.
Vietæ
[Translation: Viète's example ]

[Translation: ]

a a + 64, a = 1024

\sqrt{64}

. est. 8.
cuius cubus 512
1024
Differentia 512. cuius
latus cubicum. 8.
pro prima
[Translation: The square root of 64 is 8, whose cube is 512, from 1024 leaves difference 512, whose cube root is 8, for the first ]