Harriot, Thomas - Mss. 6782

634317

[Commentary:

An examination of the equation

a a a - 9 a a + 24 a = 20

, which has roots 2, 2, 5. This is one of several equations with multiple roots treated by Viète in De numerosa potestatum resolutione (Viète . Harriot solved it in full on Add MS 6783 f. . ]

Triens coeff: long:

b + c

[Translation: A third of the longitudinal ]
Triplum quadrat:

3 b b + 6 b c + 3 c c

[Translation: Three times the ]
maius est coefficientibus planis
per

3 c c

[Translation: greater than the plane coefficient by

3 c c

Duplus cubus e triente.

b + c

[Translation: Twice the cube of the ]

[Translation: greater ]

b + c

in
coefficientibus
[Translation:

b + c

times the plane coefficient

Excessus maximi laterus supra

b + c

sit

e

[Translation: Let the excess of the greatest side over

b + c

e

reliqua duo sunt minora

b + d

[Translation: the remaining two are less than

b + d

maxium latus

[Translation: the greatest side will ]

[Translation: ]

e

in

[Translation:

e

601 (300v)	602 (301)
603 (301v)	604 (302)
605 (302v)	606 (303)
607 (303v)	608 (304)
609 (304v)	610 (305)

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