Harriot, Thomas, Mss. 6782

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741
741 (370v)
742
742 (371)
743
743 (371v)
744
744 (372)
745
745 (372v)
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746 (373)
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747 (373v)
748
748 (374)
749
749 (374v)
750
750 (375)
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646323
[Commentary:
A continuation from Add MS f. of work on the equation arising from the multiplication (a-b)(a-c)(a+d).
Harriot states without proof the special form the equation will take when d=b+c, when the term in aa vanishes. For a full derivation see Add MS 6783 f. (d.3). Harriot calls this form of the cubic equation an 'elliptic' or 'Bombellian' equation. The special case where b=c he calls 'parabolic'. For Harriot's definitions of the hyperbolic, elliptic, and parabolic forms of a cubic equation without a square term, see Add MS 6783 f. (e.8).
On this page Harriot also gives the form the equation will take when bc=bd+cd, when the term in a vanishes. For a full derivation see Add MS 6783 f. (d.3).
]
In charta
[Translation: In sheet ac
[Commentary: Sheet ac is Add MS f. .

Eliptica.
seu Bombellica si

[Translation: Elliptic, or the Bombellian kind if the signs are ]

Vide
[Translation: See ]
[Commentary: Sheet D. is Add MS f. .

æquatio
[Translation: parabolic ]

[Translation: ]

[Translation: ]

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