Harriot, Thomas, Mss. 6782

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741
741 (370v)
742
742 (371)
743
743 (371v)
744
744 (372)
745
745 (372v)
746
746 (373)
747
747 (373v)
748
748 (374)
749
749 (374v)
750
750 (375)
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636318
[Commentary:
An examination of the equation aaa-18aa+95a=126, which has roots 2, 7, 9. This is one of several equations with multiple roots treated by Viète in De potestatum numerosa resolutione (Viète . Harriot solved it in full on Add MS 6783 f. . ]
Triens coefficientis longituidnis. b-d
[Translation: A third of the longitudinal ]

Triplum quadratum. 3bb-6bd+3dd
[Translation: Three times the ]

maius est coefficientibus planis
per 3dd+9cc-9cd
[Translation: greater than the plane coefficient ]
Duplus cubus e triente. b-d
[Translation: Twice the cube of the ]


[Translation: less ]

b-d
in coefficientibus
[Translation: b-d times the plane coefficient


[Translation: ]
medium et maximum latus
excedunt. b-d
[Translation: medium and maximum sides ]

sit unus vel alter excessu, e
[Translation: let one or other excess be e
erit e=d, excessus medij 1. adde b-d erit: b medium.
erit e=3c-2d, excessus maximi 3. adde b-d erit: b+3c-2d
[Translation: if e=d, the excess of the medium, add b-d, then b will be the medium;
if e=3c-2d, the excess of the maximum, add b-d, then b+3c-3d will be the maximum;

[Translation: ]

3c in 2d
in coeff
[Translation: 3c times 2d times the plane coefficient

cubus 3c-2d
[Translation: The cube of 3c-2d


[Translation: ]
Operationes sunt
in dorso
[Translation: The working is on the back of ]
[Commentary: The back of sheet D.1 is Add MS f. .

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